;;;
;;;Proposition #47--Euclid's proof of Pythagorean Theorem
;;;
;;;	by Takaya Iwamoto   Nov 18,2001
;;;
;;;
;;;	euclid_47_1	Euclid's Proof in the "Elements" (c 300 B.C.)
;;;	euclid_47_2a
;;;	euclid_47_2b	dissection_1
;;;	euclid_47_2c	dissection_2
;;;	euclid_47_2d	dissection_3
;;;	euclid_47_3	Quadrilateral version of Proof #1
;;;	euclid_47_4	Generalization by Pappus of Alexandria
;;;	euclid_47_5	Leonardo da Vinci (1452 - 1519)	
;;;	euclid_47_6	Thabit ibn Qurra (826 - 901)
;;;	euclid_47_7	Pythagoras
;;;	euclid_47_8
;;;	euclid_47_9	Yanney's proof
;;;	
;;;	dissection	General dissection scheme
;;;	dissect_1		Liu Hui's              proof
;;;	dissect_2		J.E.Boettcher's   proof
;;;	refresh_all	delete all objects(incl. block) for restart
;;;	Abe_origami_1	Hisashi Abe's origami solution(original)
;;;	Abe_origami_2	Hisashi Abe's origami solution(variation)
;;;
;;;*****************EUCLID_47_1*******************************************************
;;;	Proof by Euclid
;;;
;;;	Euclid_main
(defun c:Euclid_main()
	
	(setq dcl_id (load_dialog "euclid_47.dcl"))
	(if (not (new_dialog "euclid_47" dcl_id))
		(exit)
	)
	(setq proof_list '("47_1" "47_d1" "47_d2" "47_d3" "47_3"
			   "47_4" "47_5"  "47_6"  "47_7"  "47_8"
		           "47_9" "47_grid" "47_LH" "47_BO" "")
	)
	(foreach sld_name proof_list
	  (start_image sld_name)
	  (slide_image 0 0 
		(- (dimx_tile sld_name) 1)  (- (dimy_tile sld_name) 1)
		(strcat "euclid_47" "(" sld_name ")")
	  )
	  (end_image)
	);;;end of foreach loop
	(setq pr_mode "47_1")
	(mode_tile pr_mode 4)
	(foreach pd0 proof_list
	   (action_tile pd0
		"(mode_tile pr_mode 4) (setq pr_mode $key)(mode_tile pr_mode 4)"
	   )
	)
	(action_tile "help" "(help \"\" \"ddptype\")")
	(start_dialog)
	;;;execute the selected program
	(cond
		((= pr_mode "47_1")	 (c:euclid_47_1)	 )
		((= pr_mode "47_d1")	 (c:euclid_47_2b)	 )
		((= pr_mode "47_d2")	 (c:euclid_47_2c)	 )
		((= pr_mode "47_d3")	 (c:euclid_47_2d)	 )
		((= pr_mode "47_3")	 (c:euclid_47_3)	 )
		((= pr_mode "47_4")	 (c:euclid_47_4)	 )
		((= pr_mode "47_5")	 (c:euclid_47_5)	 )
		((= pr_mode "47_6")	 (c:euclid_47_6)	 )
		((= pr_mode "47_7")	 (c:euclid_47_7)	 )
		((= pr_mode "47_8")	 (c:euclid_47_8)	 ) 
		((= pr_mode "47_9")	 (c:euclid_47_9)	 )
		((= pr_mode "47_grid")	 (c:dissection)		 )
		((= pr_mode "47_LH")	 (c:dissect_1)		 )
		((= pr_mode "47_BO")	 (c:dissect_2)		 )
		(t nil)
	);;;end of cond 
	
);;;EUCLID_MAIN
;;;
(defun c:Euclid_47_1()
	(setup_47_1)
	(make_jpg)
	(make_jpg)
		(step_11_text)
	(alert "      Step 1: \nTriangle ACK ---> Triangle BCK\n\n(common base CK, height is AC)")
		(setq ACK (shaded_triangle "layer3" pnt_a pnt_c pnt_k ))
	(make_jpg)
		(command "_.delay" 2000)
		(setq pnt_cr1 '(7.6 5.7) pnt_cr2 '(-2.6 -5.5))
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_1" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_1" '(8.5 3.5) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
		(entdel ACK)
		
		(command "_.layer" "set" "layer3" "")
		(tri_along_line "layer3" pnt_a pnt_b n_sec n_speed pnt_c pnt_k 1)
		(setq trig_BCK last_hatch)
	(make_jpg)
		(entdel last_pline)
		(make_line_1 "layer8" 8 pnt_a pnt_l)
		(step_21_text)
	(make_jpg)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_2" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_2" '(12.75 3.5) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
	(alert "      Step 2: \nRotate Triangle BCK about C\n ---> Triangle ECA")
		(rotate_ent trig_BCK pnt_c pnt_k 90. 25 25 1)
	(make_jpg)
		(step_31_text)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_3" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_3" '(17.0 3.5) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
	(make_jpg)
		(entdel trig_BCK)
	(alert "      Step 3: \nTriangle ACE \n---> Triangle LEC")
		(command "_.layer" "set" "layer3" "")
		(tri_along_line "layer3" pnt_a pnt_l n_sec n_speed pnt_c pnt_e 1)
		(setq trig_LEC last_hatch)
	(make_jpg)
		(entdel last_pline)
		(setq trig_ACK (shaded_triangle "layer3" pnt_a pnt_c pnt_k))
	(make_jpg)
		(step_41_text)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_4" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_4" '(21.25 3.5) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
	(alert "      It is proved that\narea of ACK == area of CLE")
		(blink_layer "layer3" 100 3)
	
	(alert "      Step 4: \nTriangle AFB ---> Triangle CFB")
		(setq AFB (shaded_triangle "layer2" pnt_a pnt_f pnt_b ))
	(make_jpg)
		(command "_.delay" 2000)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_5" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_5" '(9.0 -6.5) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
	(make_jpg)
		(entdel AFB)
	
		(command "_.layer" "set" "layer2" "")
		(tri_along_line "layer2" pnt_a pnt_c n_sec n_speed pnt_b pnt_f 2)
	(make_jpg)
		(setq trig_CBF last_hatch)
		(entdel last_pline)

		(step_51_text)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_6" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_6" '(13.25 -6.5) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
	(alert "      Step 5: \nRotate Triangle CBF around point B\n ---> Triangle DBA")
		(rotate_ent trig_CBF pnt_b pnt_c -90. 25 25 1)

		(step_61_text)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_7" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_7" '(17.5 -6.5) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
	(make_jpg)
		(entdel trig_CBF)
	
	(alert "      Step 6: \nTriangle ABD ---> Triangle LBD")
		
		(command "_.layer" "set" "layer2" "")
		(tri_along_line "layer2" pnt_a pnt_l n_sec n_speed pnt_b pnt_d 2)
		(make_jpg)
		(command "_.layer" "set" "0" "")
		(make_point "layer8" 0  pnt_m  "M" 1 chr_size)

		(step_71_text)

		(setq AFB (shaded_triangle "layer2" pnt_a pnt_f pnt_b ))
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_8" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_8" '(21.75 -6.5) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
	(alert "      It is proved that\narea of AFB == area of LBD")
			(blink_layer "layer2" 100 3)
	(alert "We proved the following\n\nAFB = LBD--->AGFB = MBDL\n\nACK = LEC --->ACKH = LECM")
	
		(shaded_quad "layer2" pnt_b pnt_a pnt_g pnt_f )
		(shaded_quad "layer2" pnt_b pnt_d pnt_l pnt_m )
			(blink_layer "layer2" 100 3)

		(shaded_quad "layer3" pnt_a pnt_c pnt_k pnt_h )
		(shaded_quad "layer3" pnt_l pnt_e pnt_c pnt_m )
			(blink_layer "layer3" 100 3)
	 (make_jpg)
	(make_jpg)
	(command "_.layer" "set" "0" "")
	(alert "We proved the following\n\nAGFB = MBDL\n\nACKH = LECM\n\nTherefore\n  AGFB + ACKH = DECB")
	(make_jpg)
	(make_jpg)
	(reset_sysvar)
);;;EUCLID_47_1 - - - main
;;;
;;;
(defun setup_47_1()
	(setup_sysvar)
	(setvar "OSMODE" 0)
	(command "_.ucsicon" "off")
	(setq len_a 3. len_b 4. len_c 5.
		pnt_a '(1.8 2.4)	pnt_b '(0 0)	pnt_c '(5 0)
		pnt_d '(0 -5)	pnt_e '(5 -5)
		pnt_f (point_off_line pnt_b pnt_a 0. (dtr 90.)  len_a )
		pnt_g (pld pnt_c pnt_a (+ len_a len_b))	pnt_h (pld pnt_b pnt_a (+ len_a len_b))
		pnt_k (point_off_line pnt_c pnt_a 0. (dtr -90)  len_b)
		pnt_l '(1.8 -5)	pnt_m '(1.8 0)
	)
	(command "_.pline" pnt_c pnt_a pnt_h pnt_k "_c")
	(command "_.pline" pnt_a pnt_b pnt_f pnt_g "_c")
	(command "_.pline" pnt_b pnt_c pnt_e pnt_d "_c")
	(command "_.pline" pnt_a pnt_b pnt_c "c")
 ;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.5)
	(regapp "my_point")
	(make_point "layer8" 0  pnt_a  "A" 2 chr_size)
	(make_point "layer8" 0  pnt_b  "B" 3 chr_size)
	(make_point "layer8" 0  pnt_c  "C" 1 chr_size)
	(make_point "layer8" 0  pnt_d  "D" 4 chr_size)
	(make_point "layer8" 0  pnt_e  "E" 4 chr_size)
	(make_point "layer8" 0  pnt_f  "F" 3 chr_size)
	(make_point "layer8" 0  pnt_g  "G" 2 chr_size)
	(make_point "layer8" 0  pnt_h  "H" 1 chr_size)
	(make_point "layer8" 0  pnt_k  "K" 1 chr_size)
	(make_point "layer8" 0  pnt_l  "L" 4 chr_size)
	(command "_.point" '(24.5 8.0))
	(command "_.point" '(24.5 -7.0))
  ;;;zoom to the extent
	(command "_.zoom" "_EXTENT")
	(setq n_speed 75 n_sec 10)
	(setq t_pnt '(14.4 2.3) t_height 0.5 t_angle 0.)
	(command "_.rectangle" '(14.25 -1.8) '(25 3))

);setup_47_1
;;;
;;;Texts in the text box
;;;
(defun step_11_text()
	(command "_.text" t_pnt t_height t_angle "Step:1")
		(setq text_ent_1 (entlast))
	(command "_.text" ""  "move the triangle ACK to BCK")
		(setq text_ent_2 (entlast))
)
;;;
(defun step_21_text()
	(command "_.layer" "_set" "0" "")
	(entdel text_ent_1)
	(entdel text_ent_2)
	(command "_.text" t_pnt t_height t_angle "Step:2")
		(setq text_ent_1 (entlast))
	(command "_.text" ""  "Rotate triangle BCK about point C")
		(setq text_ent_2 (entlast))
	(command "_.text" "" "until it matches Triangle ECA")
		(setq text_ent_3 (entlast))
)
;;;
(defun step_31_text()
	(command "_.layer" "_set" "0" "")
	(entdel text_ent_1)
	(entdel text_ent_2)
	(entdel text_ent_3)
	(command "_.text" t_pnt t_height t_angle "Step:3")
		(setq text_ent_1 (entlast))
	(command "_.text" ""  "move the triangle ACE to LEC")
		(setq text_ent_2 (entlast))
)
;;;
(defun step_41_text()
	(command "_.layer" "_set" "0" "")
	(entdel text_ent_1)
	(entdel text_ent_2)
	(command "_.text" t_pnt t_height t_angle "Step:4")
		(setq text_ent_1 (entlast))
	(command "_.text" ""  "move the triangle AFB to CFB")
		(setq text_ent_2 (entlast))
)
;;;
(defun step_51_text()
	(command "_.layer" "_set" "0" "")
	(entdel text_ent_1)
	(entdel text_ent_2)
	(command "_.text" t_pnt t_height t_angle "Step:5")
		(setq text_ent_1 (entlast))
	(command "_.text" ""  "Rotate triangle CBF about point B")
		(setq text_ent_2 (entlast))
	(command "_.text" "" "until it matches Triangle DBA")
		(setq text_ent_3 (entlast))
)
;;;
(defun step_61_text()
	(command "_.layer" "_set" "0" "")
	(entdel text_ent_1)
	(entdel text_ent_2)
	(entdel text_ent_3)
	(command "_.text" t_pnt t_height t_angle "Step:6")
		(setq text_ent_1 (entlast))
	(command "_.text" ""  "move the triangle DBA to DBL")
		(setq text_ent_2 (entlast))
)
;;;
(defun step_71_text()
	(command "_.layer" "_set" "0" "")
	(entdel text_ent_1)
	(entdel text_ent_2)
	(command "_.text" t_pnt t_height t_angle "We have proved that")
	(command "_.text" ""  "ABFG = BDLM")	
	(command "_.text" ""  "ACKH = MLEC")
	(command "_.text" "" "Therefore, ")
	(command "_.text" "" "  BDEC = ABFG + ACKH")
	(command "_.text" "" "   Q. E. D. ")
)
;;;
;;;*****************EUCLID_47_2*******************************************************
;;;
(defun C:Euclid_47_2a()
	(setup_47_2)
	(alert "Step 1: Define point H on Line AC such that\nAH = BC = b\nThen HC = AD = a")
	(c:step1_2)
	(alert "Step 2: Compare Triangles DAH and HCG")
	(c:step2_2)
		(setq pnt_ad (mid_point pnt_a pnt_d)
			pnt_dh (mid_point pnt_d pnt_h)
			pnt_ah (mid_point pnt_a pnt_h)
			pnt_cg (mid_point pnt_c pnt_g)
		)
		(mark_id pnt_ad "a"  3 chr_size)
		(mark_id pnt_ah "b"  4 chr_size)
		(mark_id pnt_dh "c"  1 chr_size)
		(mark_id pnt_cg "b"  1 chr_size)
	(alert "Step 3: Since AH = BC  and  HC = AD\n Triangle DAH = Triangle HCG")
	(c:step3_2)
	(alert "Step 4: Rotate Triangle DAH 90 degrees CCW\nuntil A matches E")
	(c:step4_2a)
	(alert "Step 5: Rotate Triangle HCG 270 degrees CCW\nuntil C matches F")
	(c:step5_2a)
	(c:step6_2)
	(alert "Final: It is proved \nHGDJ = ABDE + BCFG\n\n or c*c = a*a + b*b\n\n\tQ.E.D.")
	(reset_sysvar)
);;;EUCLID_47_2a - - - main-2a
;;;
;;;
(defun C:Euclid_47_2b()
	(setup_47_2)
	(make_jpg)
	(alert "Step 1: Define point H on Line AC \n\nsuch that  AH = BC = b.\n\nThen HC = AD = a")
	(make_jpg)
		(c:step1_2)
	(make_jpg)
		(setq pnt_ad (mid_point pnt_a pnt_d)
			pnt_dh (mid_point pnt_d pnt_h)
			pnt_ah (mid_point pnt_a pnt_h)
			pnt_cg (mid_point pnt_c pnt_g)
		)
		(mark_id pnt_ad "a"  3 chr_size)
		(mark_id pnt_ah "b"  4 chr_size)
		(mark_id pnt_dh "c"  1 chr_size)
		(mark_id pnt_cg "b"  1 chr_size)
	(make_jpg)
	(alert "Step 2:\n Compare Triangles DAH and HCG\n\nSince AH = BC = b\nand   HC = AD = a\n\n DAH =  HCG.")
	(make_jpg)	
	;;;shade polygon DHGFE by 45 deg by 0.2 inch cross hatch
		(command "_.pline" pnt_d pnt_h pnt_g pnt_f pnt_e "_cl")
		(setq pl_DHGFE (entlast))
		(command "_.hatch" "_U" 45. 0.2 "_N" pl_DHGFE "")
	(make_jpg)
	;(alert "Step 3: Since AH = BC  and  HC = AD\n Triangle DAH = Triangle HCG")
	(make_jpg)
		(c:step3_2)
	(make_jpg)
		(setq pnt_cr1 '(9.0 9.0) pnt_cr2 '(-0.5 -0.5))
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "ACGJD_1" pnt_a whole)
		(command "_.oops")
		(my_block_insert "ACGJD_1" '(15.0 5.) 0.75)
		(command "_.zoom" "_EXTENT")
	(make_jpg)
	(alert "Step 4: Move Triangle DAH along line HG\nuntil H matches G")
	(make_jpg)
		(c:step4_2b)
	(make_jpg)
	(alert "Step 5: Move Triangle HCG along line HD\nuntil H matches D")
		(c:step5_2b)
	(make_jpg)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "ACGJD_2" pnt_a whole)
		(command "_.oops")
		(my_block_insert "ACGJD_2" '(15.0 -3) 0.75)
		(command "_.zoom" "_EXTENT")
		(command "_.delay" 1000)
	(make_jpg)
		(c:step6_2)
	(make_jpg)
	(alert "Final:\n\n It is proved \n\nHGDJ = ABED + BCGF\n\n or   c*c = a*a + b*b\n\n\tQ.E.D.")
		(textdisplay "c  = a  +  b" '(8.6 5.4) 0.81 0.)
		(textdisplay "2          2            2" '(9.2 6.1) 0.45 0.)
	(make_jpg)
		(reset_sysvar)
);;;EUCLID_47_2b - - - main-2b
;;;
;;;
(defun C:Euclid_47_2c()
	(setup_47_2c)
	(make_jpg)
	(alert "Step 1:\n\n   Shade 5 parts of the square DHGJ.")
		(setq trig_DHL (shaded_triangle "layer2" pnt_d pnt_h pnt_l)
			trig_HGK (shaded_triangle "layer3" pnt_h pnt_g pnt_k)
			trig_GJF (shaded_triangle "layer4" pnt_g pnt_j pnt_f)
			trig_JDE (shaded_triangle "layer5" pnt_j pnt_d pnt_e)
			quad_KFEL (shaded_quad "layer6" pnt_k pnt_f pnt_e pnt_l)
		)
	(make_jpg)
		(setq pnt_cr1 '(9.0 9.0) pnt_cr2 '(-0.5 -0.5))
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "ACGJD_1" pnt_a whole)
		(command "_.oops")
		(my_block_insert "ACGJD_1" '(15.0 5.) 0.75)
		(command "_.zoom" "E")
	(make_jpg)
	(alert "Step 2:\n\nMove Triangle GJF until GJ aligns with HD.")
		(command "_.layer" "_set" "layer8" "")
		(move_ent trig_GJF pnt_g pnt_h 100 6 1 "0")
		(command "_.layer" "_set" "0" "")
		(make_point "layer8" 0  pnt_a  "A" 4 chr_size)
	(make_jpg)
	(alert "Step 3:\n\nMove Triangle JDE until JD aligns with GH.")
		(command "_.layer" "_set" "layer8" "")
		(move_ent trig_JDE pnt_j pnt_g 100 6 1 "0")
		(command "_.layer" "_set" "0" "")
		(make_point "layer8" 0  pnt_c  "C" 4 chr_size)
		(make_line_1 "0" 0 pnt_b pnt_f)
		(make_point "layer8" 0  pnt_b  "B" 1 chr_size)
	(make_jpg)
	(alert "Step 4:\n\n   AB = a")
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "ACGJD_2" pnt_a whole)
		(command "_.oops")
		(my_block_insert "ACGJD_2" '(15.0 -3) 0.75)
		(command "_.zoom" "_EXTENT")
		(command "_.delay" 1000)
	(make_jpg)
	(alert "Final:\n\n It is proved \n\nHGJD = ABED + BCGF\n\n or   c*c = a*a + b*b\n\n\tQ.E.D.")

		(textdisplay "c  = a  +  b" '(8.6 5.4) 0.81 0.)
		(textdisplay "2          2            2" '(9.2 6.1) 0.45 0.)
	(make_jpg)
	(make_jpg)
		(reset_sysvar)
);;;EUCLID_47_2c - - - main-2c
;;;
;;;
(defun C:Euclid_47_2d()
	(setup_47_2d)
	(make_jpg)
	(alert "Step 1: Shade the square ABED \n\n(area= a*a)")
		(setq quad_DLHO (shaded_quad "layer3" pnt_d pnt_l pnt_h pnt_o)
			quad_AMHL (shaded_quad "layer4" pnt_a pnt_m pnt_h pnt_l)
			quad_BNHM (shaded_quad "layer5" pnt_b pnt_n pnt_h pnt_m)
			quad_EOHN (shaded_quad "layer6" pnt_e pnt_o pnt_h pnt_n)
		)
	(make_jpg)
	(alert "Step 2:\n Shade the square BCFG \n\n(area = b*b)" )
		;;;shade polygon DHGFE by 45 deg by 0.2 inch cross hatch
		(command "_.pline" pnt_b pnt_c pnt_g pnt_f  "cl")
		(setq quad_BCGF (entlast))
		(command "_.hatch" "_U" 45. 0.2 "_N" quad_BCGF "")
	(make_jpg)
	;(alert "Step 3: Since AH = BC  and  HC = AD\n Triangle DAH = Triangle HCG")
		(setq pnt_cr1 '(9.0 9.0) pnt_cr2 '(-0.5 -0.5))
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "ACGJD_1" pnt_a whole)
		(command "_.oops")
		(my_block_insert "ACGJD_1" '(15.0 5.) 0.75)
		(command "_.zoom" "_EXTENT")
	(make_jpg)
	(alert "Step 3: Move Quad DLHO until Point H reaches point J")
		(move_ent quad_DLHO pnt_h pnt_j 100 6 1 "0")
	(make_jpg)
	(alert "Step 4: Move Quad AMHL until Point H reaches point J")
		(move_ent quad_AMHL pnt_h pnt_k 100 6 1 "0")
	(make_jpg)
	(alert "Step 5: Move Quad EOHN until Point H reaches point J")
		(move_ent quad_EOHN pnt_h pnt_i 100 6 1 "0")
	(make_jpg)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "ACGJD_2" pnt_a whole)
		(command "_.oops")
		(my_block_insert "ACGJD_2" '(15.0 -3) 0.75)
		(command "_.zoom" "_EXTENT")
		(command "_.delay" 1000)
	(make_jpg)
	(alert "Final:\n\n It is proved \n\nHIJK = ABED + BCGF\n\n or   c*c = a*a + b*b\n\n\tQ.E.D.")

		(textdisplay "c  = a  +  b" '(8.6 5.4) 0.81 0.)
		(textdisplay "2          2            2" '(9.2 6.1) 0.45 0.)
	(make_jpg)
	(make_jpg)
		(reset_sysvar)
);;;EUCLID_47_2d - - - main-2d
;;;
;;;
(defun setup_47_2()
	(setup_sysvar)
	(setq len_a 5. ;(getreal "\nLength A= ")
		len_b 3. ;(getreal "\nLength B= ")
		len_ab (+ len_a len_b)  len_ab2 (* 3. len_ab)
		len_min (* 0.5 (min len_a len_b))
	)
	(setvar "OSMODE" 0)
	(command "_.ucsicon" "_off")
	(setq 	pnt_a '(0 0)  pnt_b (list len_a 0)   pnt_c (list len_ab 0)
		pnt_d (list 0 len_a)   pnt_e (list len_a len_a)
		pnt_f (list len_a len_b)   pnt_g (list len_ab len_b)
		pnt_r1 (list len_ab2 (+ len_ab 1.25))
		pnt_r2 (list len_ab2 (- (- len_min ) 2.0) )
	)
	(command "_.layer" "_set" "layer8" "")
	(command "_.pline" pnt_a pnt_b pnt_e pnt_d "_c")
	(command "_.pline" pnt_b pnt_c pnt_g pnt_f "_c")
	(command "_.layer" "_set" "0" "")
 ;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.5)
	(regapp "my_point")
	(make_point "layer8" 0  pnt_a  "A" 4 chr_size)
	(make_point "layer8" 0  pnt_b  "B" 4 chr_size)
	(make_point "layer8" 0  pnt_c  "C" 4 chr_size)
	(make_point "0" 0  pnt_d  "D" 3 chr_size)
	(make_point "layer8" 0  pnt_e  "E" 2 chr_size)
	(make_point "layer8" 0  pnt_f  "F" 3 chr_size)
	(make_point "0" 0  pnt_g  "G" 1 chr_size)
	;;;zoom to the extent
	(command "_.point" pnt_r1)
	(command "_.point" pnt_r2)
	(command "_.zoom" "_EXTENT")
	;(command "_.zoom" "scale" 0.65)
	(setq n_speed 100 n_sec 8)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -2)
);setup_47_2
;;;
;;;setup for case c
(defun setup_47_2c()
	(setup_sysvar)
	(setq len_a 5. ;(getreal "\nLength A= ")
		len_b 3. ;(getreal "\nLength B= ")
		len_ab (+ len_a len_b)	len_ab2 (* 3. len_ab)
		len_min (* 0.5 (min len_a len_b))
	)
	(setvar "OSMODE" 0)
	(command "_.ucsicon" "_off")
	(setq 	pnt_a '(0 0)  pnt_b (list len_a 0)  pnt_c (list len_ab 0)
		pnt_d (list 0 len_a)  pnt_e (list len_a len_a)
		pnt_f (list len_a len_b)  pnt_g (list len_ab len_b)
		pnt_h (list len_b 0)  pnt_l (list len_b len_a)
		pnt_k (list len_b len_b)  pnt_r1 (list len_ab2 (+ len_ab 3.5))
		pnt_r2 (list len_ab2 (- (- len_min ) 2.0) )
	)
	(setq pnt_j (list len_a (+ len_a len_b)) )
	
	(command "_.layer" "_set" "layer8" "")
	(command "_.pline" pnt_d pnt_h pnt_g pnt_j "_c")
	(command "_.pline" pnt_d pnt_a pnt_c pnt_g "")
	(make_line_1 "layer8" 0 pnt_d pnt_e)
	(make_line_1 "layer8" 0 pnt_h pnt_l)
	(make_line_1 "layer8" 0 pnt_g pnt_k)
	(make_line_1 "layer8" 0 pnt_j pnt_f)
	(command "_.layer" "_set" "0" "")
 ;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.5)
	(regapp "my_point")
	
	(make_point "0" 0  pnt_d  "D" 3 chr_size)
	(make_point "layer8" 0  pnt_e  "E" 2 chr_size)
	(make_point "layer8" 0  pnt_f  "F" 3 chr_size)
	(make_point "0" 0  pnt_g  "G" 1 chr_size)
	(make_point "layer8" 0  pnt_h  "H" 4 chr_size)
	(make_point "layer8" 0  pnt_j  "J" 2 chr_size)
	(make_point "layer8" 0  pnt_k  "K" 2 chr_size)
	(make_point "layer8" 0  pnt_l  "L" 2 chr_size)
	;;;zoom to the extent
	(command "_.point" pnt_r1)
	(command "_.point" pnt_r2)
	;;;identify the side length a,b,c
		(mark_id (mid_point pnt_a pnt_d) "a"  3 chr_size)
		(mark_id (mid_point pnt_a pnt_h) "b"  4 chr_size)
		(mark_id (mid_point pnt_d pnt_h) "c"  3 chr_size)
		(mark_id (mid_point pnt_c pnt_g) "b"  1 chr_size)
		(mark_id (mid_point pnt_f pnt_g) "b"  2 chr_size)
		(mark_id (mid_point pnt_g pnt_j) "c"  1 chr_size)
		(mark_id (mid_point pnt_c pnt_h) "a"  4 chr_size)
		(mark_id (mid_point pnt_d pnt_j) "c"  3 chr_size)
		(mark_id (mid_point pnt_g pnt_h) "c"  4 chr_size)
	(command "_.zoom" "_EXTENT")
	;(command "_.zoom" "_scale" 0.65)
	(setq n_speed 100 n_sec 8)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -2)
);setup_47_2c
;;;
;;;
(defun setup_47_2d()
	(setup_sysvar)
	(setq len_a 5. ;(getreal "\nLength A= ")
		len_b 3. ;(getreal "\nLength B= ")
		len_ab (+ len_a len_b) len_ab2 (* 3. len_ab)
		len_min (* 0.5 (min len_a len_b))
		half_a (* 0.5 len_a)  half_3a (* 1.5 len_a)
	)
	(setvar "OSMODE" 0)
	;(set_layer)
	(command "_.ucsicon" "_off")
	(setq 	pnt_a '(0 0)  pnt_b (list len_a 0)  pnt_c (list len_ab 0)
		pnt_d (list 0 len_a) pnt_e (list len_a len_a)
		pnt_f (list len_a len_b) pnt_g (list len_ab len_b)
		pnt_h (list half_a half_a) pnt_i (list (+ len_b half_a) (- half_a))
		pnt_j (list (+ len_b half_3a) (- len_b half_a))
		pnt_k (list half_3a (+ len_b half_a))	pnt_l (inters pnt_a pnt_d pnt_h pnt_k nil)
		pnt_m (inters pnt_a pnt_b pnt_h pnt_i nil)	pnt_n (inters pnt_b pnt_e pnt_h pnt_k nil)
		pnt_o (inters pnt_d pnt_e pnt_h pnt_i nil)	pnt_p (inters pnt_f pnt_g pnt_k pnt_j nil)
		pnt_q (inters pnt_c pnt_g pnt_i pnt_j nil)	pnt_r1 (list len_ab2 (+ len_ab 1.25))
		pnt_r2 (list len_ab2 (- (- len_min ) 2.0) )
	)
	(command "_.layer" "_set" "layer8" "")
	(command "_.pline" pnt_a pnt_b pnt_e pnt_d "_c")
	(command "_.pline" pnt_b pnt_c pnt_g pnt_f "_c")
	(command "_.layer" "_set" "0" "")
	(command "_.layer" "_set" "layer2" "")
	(command "_.pline" pnt_l pnt_k pnt_j pnt_i pnt_o "")
	(command "_.layer" "_set" "0" "")
	(make_line_1 "0" 8 pnt_g pnt_p)
	(make_line_1 "0" 8 pnt_c pnt_q)
 ;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.5)
	(regapp "my_point")
	(make_point "layer8" 0  pnt_a  "A" 4 chr_size)
	(make_point "layer8" 0  pnt_b  "B" 4 chr_size)
	(make_point "layer8" 0  pnt_c  "C" 1 chr_size)
	(make_point "0" 0  pnt_d  "D" 3 chr_size)
	(make_point "layer8" 0  pnt_e  "E" 2 chr_size)
	(make_point "layer8" 0  pnt_f  "F" 3 chr_size)
	(make_point "0" 0  pnt_g  "G" 2 chr_size)
	(make_point "layer8" 0  pnt_h  "H" 2 chr_size)
	(make_point "layer8" 0  pnt_i  "I" 4 chr_size)
	(make_point "layer8" 0  pnt_j  "J" 1 chr_size)
	(make_point "layer8" 0  pnt_k  "K" 1 chr_size)
	(make_point "layer8" 0  pnt_l  "L" 3 chr_size)
	(make_point "layer8" 0  pnt_m  "M" 4 chr_size)
	(make_point "layer8" 0  pnt_n  "N" 1 chr_size)
	(make_point "layer8" 0  pnt_o  "O" 2 chr_size)
	(make_point "layer8" 0  pnt_p  "P" 1 chr_size)
	(make_point "layer8" 0  pnt_q  "Q" 4 chr_size)
	
	;;;zoom to the extent
	(command "_.point" pnt_r1)
	(command "_.point" pnt_r2)
	(command "_.zoom" "_EXTENT")
	;(command "_.zoom" "_scale" 0.65)
	(setq n_speed 100 n_sec 8)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -2)
);setup_47_2d
;;;
;;;
(defun C:step1_2()
	(setq pnt_h (list len_b 0))
	(make_point "layer8" 0  pnt_h  "H" 4 chr_size)
	(slow_line n_speed "0" 8 pnt_d pnt_h)
	(slow_line n_speed "0" 8 pnt_h pnt_g)
);;;step1_2
;;;
;;;
(defun C:step3_2()
	(command "_.layer" "_set" "layer3" "")
	(command "_.pline" pnt_a pnt_h pnt_d "c")
	(setq pln_tr1 (entlast))
	(command "_.hatch" "_solid" pln_tr1 "")
	(make_jpg)
	(setq hat_tr1 (entlast))
	(command "_.layer" "_set" "0" "")
	(command "_.layer" "_set" "layer4" "")
	(command "_.pline" pnt_h pnt_c pnt_g "_c")
	(setq pln_tr2 (entlast))
	(command "_.hatch" "_solid" pln_tr2 "")
	(make_jpg)
	(setq hat_tr2 (entlast))
	(command "_.layer" "_set" "0" "")
);;;
;;;
(defun C:step4_2a()
	(command "_.layer" "_set" "layer8" "")
	(setq pnt_at pnt_a n_repeat 6 rot_speed 75 total_rot_angle 90.
		rot_step (/ total_rot_angle n_repeat)
		cur_angle 270.
	)
	(repeat n_repeat
		(slow_arc rot_speed "0" 1 pnt_d pnt_at rot_step 0)
		(command "_.rotate" hat_tr1  "" pnt_d rot_step)
		(setq pnt_at (polar pnt_d (dtr (setq cur_angle (+ cur_angle rot_step))) len_a))	
	)	
	(command "_.layer" "_set" "0" "")
);;;
;;;
(defun C:step4_2b()
	(command "_.layer" "_set" "layer8" "")
	(move_ent hat_tr1 pnt_h pnt_g 100 6 1 "0")
	(command "_.layer" "_set" "0" "")
);;;
;;;
(defun C:step5_2a()
	(command "_.layer" "_set" "layer8" "")
	(setq pnt_ct pnt_c n_repeat 6 rot_speed 75 total_rot_angle 270.
		rot_step (/ total_rot_angle n_repeat)
		cur_angle -90.
	)
	(repeat n_repeat
		(slow_arc rot_speed "0" 1 pnt_g pnt_ct rot_step 0)
		(command "_.rotate" hat_tr2 "" pnt_g rot_step)
		(setq pnt_ct (polar pnt_g (dtr (setq cur_angle (+ cur_angle rot_step))) len_b))	
	)	
	(command "_.layer" "_set" "0" "")
	(setq pnt_j (list len_a (+ len_a len_b)) )
	(make_point "layer8" 0  pnt_j  "J" 2 chr_size)
);;;
;;;
(defun C:step5_2b()
	(command "_.layer" "_set" "layer8" "")
	(move_ent hat_tr2 pnt_h pnt_d 100 6 1 "0")
	(command "_.layer" "_set" "0" "")
	(setq pnt_j (list len_a (+ len_a len_b)) )
	(make_point "layer8" 0  pnt_j  "J" 2 chr_size)
);;;
;;;
(defun C:step6_2()
	(command "_.layer" "_set" "layer4" "")
	(command "_.hatch" "_solid" pln_tr2 "")
	(command "_.layer" "_set" "0" "")
	(make_jpg)
	(command "_.layer" "_set" "layer3" "")
	(command "_.hatch" "_solid" pln_tr1 "")
	(command "_.layer" "_set" "0" "")
	(make_jpg)
);;;
;;;
;;;*****************EUCLID_47_3*******************************************************
;;;
(defun C:Euclid_47_3()
	(setup_47_3)
	(make_jpg)

	(alert "STEP 0: \nExtend FG and KH and the intersection point is N")
		(setq pnt_n (inters pnt_f pnt_g pnt_k pnt_h nil))
		(make_point "layer8" 0  pnt_n  "N" 2 chr_size)
		(make_line_1 "layer8" 8 pnt_g pnt_n)
		(make_line_1 "layer8" 8 pnt_h pnt_n)
		(make_line_1 "layer8" 8 pnt_a pnt_n)
		(make_line_1 "layer8" 8 pnt_a pnt_l)
		(command "_.zoom" "e")
	(make_jpg)
	(make_jpg)
	(alert "STEP 0: \nGet intersection of EC and NK--point P")
		(setq pnt_p (inters pnt_e pnt_c pnt_k pnt_n nil))
		(make_line_1 "layer8" 8 pnt_c pnt_p)
		(make_point "layer8" 0  pnt_p  "P" 2 chr_size)
	(make_jpg)
	(alert "STEP 0: \nGet intersection of DB and FN--point Q")
		(setq pnt_q (inters pnt_b pnt_d pnt_f pnt_n nil))
		(make_line_1 "layer8" 8 pnt_b pnt_q)
		(make_point "layer8" 0  pnt_q  "Q" 3 chr_size)
	(make_jpg)
 ;;;copy ACKH & BAGF to the right
	(setq ACKH  (shaded_quad  "layer3" pnt_a pnt_c pnt_k pnt_h)
		BAGF  (shaded_quad  "layer2" pnt_b pnt_a pnt_g pnt_f)
	)
	(make_jpg)
	(setq pnt_cr1 (list (+ (car pnt_k) chr_size)  (+ (cadr pnt_n) chr_size))
		 pnt_cr2 (list (- (car pnt_f) chr_size)  (- (cadr pnt_d) chr_size)))
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_1" pnt_d whole)
		(command "_.oops")
		(my_block_insert "WHOLE_1" '(12.0 1.5) 0.4)
		(command "_.zoom" "_EXTENT")
	(make_jpg)
	(make_jpg)
		(entdel ACKH)
		(entdel BAGF)
	(make_jpg)
	(alert "Step 1: \nQuadrilateral ACKH ---> Quadrilateral ACPN")
		(command "_.layer" "_set" "layer3" "")
		(quad_along_line "layer3" pnt_h pnt_n n_sec n_speed pnt_c pnt_a 1 len_b)
		(command "_.layer" "_set" "0" "")
		(setq right_hatch last_hatch)
	(make_jpg)
	(alert "Step 2: \nQuadrilateral BAGF ---> Quadrilateral BANQ")
		(command "_.layer" "set" "layer2" "")
		(quad_along_line "layer3" pnt_g pnt_n n_sec n_speed pnt_b pnt_a 1 len_a)
		(command "_.layer" "set" "0" "")
		(setq left_hatch last_hatch)
	(make_jpg)
  ;;;copy ACPN & BANQ to the right
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_2" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_2" '(17.0 1.5) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
	(alert "Step 3: \nSlide down Quadrilateral ACPN")
		(move_ent right_hatch pnt_n pnt_a 100 6 1 "0")
	(make_jpg)
	(alert "Step 4: \nSlide down Quadrilateral BANQ")
		(move_ent left_hatch pnt_n pnt_a 100 6 1 "0")
	(make_jpg)

  ;;;copy WHOLE_3 to the right
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_3" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_3" '(22.0 1.5) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
	(alert "Step 5: \nSlide down the right quadrilateral ")
			(entdel right_hatch)
		(command "_.layer" "set" "layer3" "")
		(quad_along_line "layer3" pnt_a pnt_m n_sec n_speed pnt_e pnt_c 1 (- len_c))
		(command "_.layer" "set" "0" "")
		(setq right_hatch last_hatch)
	(make_jpg)
	(alert "Step 6: \nSlide down the left quadrilateral")
			(entdel left_hatch)
		(command "_.layer" "set" "layer2" "")
		(quad_along_line "layer3" pnt_a pnt_m n_sec n_speed pnt_d pnt_b 1 (- len_c))
		(command "_.layer" "set" "0" "")
		(setq left_hatch last_hatch)
	(make_jpg)
  ;;;copy WHOLE_4 to the right
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_4" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_4" '(12.0 -6.0) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
	(alert "We proved the following\n\nAFB = LBD--->AGFB = MBDL")
		(setq quad_ABFG (shaded_quad "layer2" pnt_a pnt_b pnt_f pnt_g))
		(blink_layer "layer2" 100 3)
	(make_jpg)
	(alert "We proved the following\n\nACK = LEC --->ACKH = LECM")
		(setq quad_ACHK (shaded_quad "layer3" pnt_a pnt_c pnt_k pnt_h))
		(blink_layer "layer3" 100 3)
		;(c:step7_3)
	(make_jpg)
   ;;;copy WHOLE_5 to the right
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_5" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_5" '(17.0 -6.0) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
	(alert "We proved the following\n\nAGFB = MBDL\n\nACKH = LECM\n\nTherefore\n  AGFB + ACKH = DECB")
	(make_jpg)
	(make_jpg)
	(reset_sysvar)
);;;EUCLID_47_3 - - - main
;;;
;;;
(defun setup_47_3()
	(setup_sysvar)
	(setvar "OSMODE" 0)
	(command "_.ucsicon" "off")
	(setq len_a 3. len_b 4. len_c 5. pnt_a '(1.8 2.4) pnt_b '(0 0) pnt_c '(5 0) 
		pnt_d '(0 -5)	pnt_e '(5 -5)
		pnt_f (point_off_line pnt_b pnt_a 0. (dtr 90.)  len_a )
		pnt_g (pld pnt_c pnt_a (+ len_a len_b))
		pnt_h (pld pnt_b pnt_a (+ len_a len_b))
		pnt_k (point_off_line pnt_c pnt_a 0. (dtr -90)  len_b)
		pnt_l '(1.8 -5)	pnt_m '(1.8 0)
	)
	(command "_.pline" pnt_c pnt_a pnt_h pnt_k "c")
	(command "_.pline" pnt_a pnt_b pnt_f pnt_g "c")
	(command "_.pline" pnt_b pnt_c pnt_e pnt_d "c")
	(command "_.pline" pnt_a pnt_b pnt_c "c")
 ;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.5)
	(regapp "my_point")
	(make_point "layer8" 0  pnt_a  "A" 2 chr_size)
	(make_point "layer8" 0  pnt_b  "B" 3 chr_size)
	(make_point "layer8" 0  pnt_c  "C" 1 chr_size)
	(make_point "layer8" 0  pnt_d  "D" 4 chr_size)
	(make_point "layer8" 0  pnt_e  "E" 4 chr_size)
	(make_point "layer8" 0  pnt_f  "F" 3 chr_size)
	(make_point "layer8" 0  pnt_g  "G" 2 chr_size)
	(make_point "layer8" 0  pnt_h  "H" 1 chr_size)
	(make_point "layer8" 0  pnt_k  "K" 1 chr_size)
	(make_point "layer8" 0  pnt_l  "L" 4 chr_size)
	(make_point "layer8" 0  pnt_m  "M" 1 chr_size)
	(command "_.point" '(23 6))
	(command "_.point" '(23 -5.8))
  ;;;zoom to the extent
	(command "_.zoom" "E")
	(setq n_speed 75 n_sec 10)

);setup_47_3
;;;
;;;
;;;*****************EUCLID_47_4*******Pappus of Alexandria*********************************
;;;
(defun C:Euclid_47_4()
	(setup_47_4)
	(make_jpg)
   ;;;copy ACKH & BAGF to the right
	(setq pnt_cr1 (list (car pnt_h) (cadr pnt_n))
		 pnt_cr2 (list (car pnt_f) (cadr pnt_d)))
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_1" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_1" '(12.0 1.5) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
		(entdel ACHK)
		(entdel BAGF)
	(alert "Step 1: \nQuadrilateral ACKH ---> Quadrilateral ACPN")
		(command "_.layer" "set" "layer3" "")
		(quad_along_line "layer3" pnt_k pnt_n n_sec n_speed pnt_c pnt_a 1 len_b)
		(command "_.layer" "set" "0" "")
		(setq right_hatch last_hatch pl_achk last_pline)
	(make_jpg)
	(alert "Step 2: \nQuadrilateral BAGF ---> Quadrilateral BANQ")
		(command "_.layer" "set" "layer2" "")
		(quad_along_line "layer3" pnt_g pnt_n n_sec n_speed pnt_b pnt_a 1 len_a)
		(command "_.layer" "set" "0" "")
		(setq left_hatch last_hatch pl_bagf last_pline)
	(make_jpg)
   ;;;copy ACPN & BANQ to the right
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_2" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_2" '(17.0 1.5) 0.4)
		(command "_.zoom" "E")
	(make_jpg)	
	(alert "Step 3: \nSlide down Quadrilateral ACPN")
		(move_ent right_hatch pnt_n pnt_a 100 6 1 "0")
	(make_jpg)
	(alert "Step 4: \nSlide down Quadrilateral BANQ")
		(move_ent left_hatch pnt_n pnt_a 100 6 1 "0")
	(make_jpg)
   ;;;copy WHOLE_3 to the right
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_3" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_3" '(22.0 1.5) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
	(alert "Step 5: \nSlide down the right quadrilateral ")
			(entdel right_hatch)
		(command "_.layer" "set" "layer3" "")
		(quad_along_line "layer3" pnt_a pnt_l n_sec n_speed pnt_e pnt_c 1 (- len_na))
		(command "_.layer" "set" "0" "")
		(setq right_hatch last_hatch pl_mecl last_pline)
    	(make_jpg)

	(alert "Step 6: \nSlide down the left quadrilateral")
			(entdel left_hatch)
		(command "_.layer" "set" "layer2" "")
		(quad_along_line "layer3" pnt_a pnt_l n_sec n_speed pnt_d pnt_b 1 (- len_na))
		(command "_.layer" "set" "0" "")
		(setq left_hatch last_hatch pl_dmlb last_pline)
	(make_jpg)
   ;;;copy WHOLE_4 to the right
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_4" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_4" '(12.0 -6.0) 0.4)
		(command "_.zoom" "E")
	(make_jpg)
	(alert "We proved the following\n\nAFB = LBD--->AGFB = MBDL")
		(setq quad_ABFG (shaded_quad "layer2" pnt_a pnt_b pnt_f pnt_g))
	(make_jpg)
		(blink_layer "layer2" 100 3)
	(alert "We proved the following\n\nACK = LEC --->ACKH = LECM")
		(setq quad_ACHK (shaded_quad "layer3" pnt_a pnt_c pnt_h pnt_k))
	(make_jpg)
		(blink_layer "layer3" 100 3)
   ;;;copy WHOLE_5 to the right
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_5" pnt_d whole)
		(command "oops")
		(my_block_insert "WHOLE_5" '(17.0 -6.0) 0.4)
		(command "_.zoom" "E")
	(make_jpg)	
	(alert "We proved the following\n\nAGFB = MBDL\n\nACKH = LECM\n\nTherefore\n  AGFB + ACKH = DECB")
	(make_jpg)
	(reset_sysvar)
	
);;;EUCLID_47_4 - - - main
;;;
;;;
(defun setup_47_4()
	(setup_sysvar)
	(setvar "OSMODE" 0)
	(command "_.ucsicon" "off")
	(setq 	pnt_a '(1.8 2.4)  pnt_b '(0 0)   pnt_c '(7 0)
		len_a (distance pnt_a pnt_b)  len_b (distance pnt_a pnt_c)
		len_c (distance pnt_b pnt_c)
	)
	(make_line_1 "0" 0 pnt_c pnt_a)
		(setq line_ac (entlast))
	(make_line_1 "0" 0 pnt_b pnt_a)
		(setq line_ab (entlast))
	(make_line_1 "0" 0 pnt_b pnt_c)
		(setq line_bc (entlast))
	
 ;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.5)
	(regapp "my_point")
	(make_point "layer8" 0  pnt_a  "A" 2 chr_size)
	(make_point "layer8" 0  pnt_b  "B" 3 chr_size)
	(make_point "layer8" 0  pnt_c  "C" 1 chr_size)
	
	(command "_.point" '(23 6))
	(command "_.point" '(23 -5.8))
	(command "_.point" '(-3 0))
	(command "_.text" '(-1.5 -5.5) chr_size 0. "Generalized Pythagorean Theorem")
	(command "_.text" "" "Proof by :  Pappus of Alexandria")
	
  ;;;zoom to the extent
	(command "_.zoom" "E")
	(setq n_speed 75 n_sec 10)
	
	(alert "\nmake a parallelogram with AC as a base")
		(make_parallelogram line_ac pnt_c pnt_a   3)
		(setq pnt_h new_pnt1 pnt_k new_pnt2)
		(make_point "layer8" 0  pnt_h  "H" 2 chr_size)
		(make_point "layer8" 0  pnt_k  "K"2 chr_size)
	(make_jpg)
	(alert "\nmake a parallelogram with AB as a base")
		(make_parallelogram line_ab pnt_b pnt_a   2)
		(setq pnt_f new_pnt1 pnt_g new_pnt2)
		(make_point "layer8" 0  pnt_f  "F" 3 chr_size)
		(make_point "layer8" 0  pnt_g  "G" 2 chr_size)
	(make_jpg)
	(alert "\nextend FG and HK . Intersection is point N")
		(setq pnt_n (inters pnt_f pnt_g pnt_h pnt_k nil))
		(make_point "layer8" 0  pnt_n  "N" 2 chr_size)
		(make_line_1 "0" 8 pnt_n pnt_a)
		(setq line_na (entlast))
		(make_line_1 "0" 8 pnt_g pnt_n)
		(make_line_1 "0" 8 pnt_n pnt_k)
	(make_jpg)
	(alert "\nExtend NA to line SC. Intersection is L")
		(setq pnt_l (inters pnt_n pnt_a pnt_b pnt_c nil))
		(make_point "layer8" 0  pnt_l  "L" 1 chr_size)
		(make_line_1 "0" 8 pnt_a pnt_l)
	(make_jpg)
	(alert "\nextend line NL so that NM = NA")
		(command "_.copy" line_na "" pnt_n pnt_l)
		(setq line_lm (entlast))
		(setq pnt_m (cdr (assoc 11 (entget line_lm))))
		(make_point "layer8" 0  pnt_m "M" 4 chr_size)
	(make_jpg)
	(alert "\nDraw a line from B parallel to LM")
		(command "_.copy" line_lm "" pnt_l pnt_b)
		(setq pnt_d (cdr (assoc 11 (entget (setq line_bd (entlast))))))
	(make_jpg)
	(alert "\nDraw a line from C parallel to LM")
		(command "_.copy" line_lm "" pnt_l pnt_c)
		(setq pnt_e (cdr (assoc 11 (entget (setq line_ce (entlast))))))
		(command "_.pline" pnt_b pnt_c pnt_e pnt_d "c")
		(entdel line_bd)
		(entdel line_ce)
		(make_point "layer8" 0  pnt_d  "D" 4 chr_size)
		(make_point "layer8" 0  pnt_e  "E" 4 chr_size)
		(setq len_na (distance pnt_n pnt_a))
	(make_jpg)
	(setq ACHK (shaded_quad "layer3" pnt_a pnt_c pnt_h pnt_k)
	      BAGF (shaded_quad "layer2" pnt_b pnt_a pnt_g pnt_f)
	)
	(make_jpg)
	(make_jpg)

);setup_47_4
;;;
;;;
(defun make_parallelogram(ref_line ref_pnt1 ref_pnt2  ncolor)
	(command "_.copy" ref_line "" ref_pnt1 pause)
	(setq new_line (entlast))
	(setq new_pnt1 (cdr (assoc 10 (entget new_line)))
		new_pnt2 (cdr (assoc 11 (entget new_line))) 
	)
	(command "_.pline" ref_pnt1 ref_pnt2 new_pnt2 new_pnt1 "c")
)
;;;
;;;
(defun c:check_result()
	(command "area" "O" pl_achk)
	(command "area" "O" pl_mecl)
	(command "area" "O" pl_bagf)
	(command "area" "O" pl_dmlb)
);check_area
;;;***********************************************************************************
;;;		Proof by Leonardo Da Vinci
;;;*****************EUCLID_47_5*******************************************************
;;;
(defun C:Euclid_47_5()
	(setup_47_5)
	(make_jpg)
	(make_jpg)
	(alert "Step 1:\n\nWe will show \n\nthat the area of FBCK is equal to FGHK")
	(shaded_triangle "layer4" pnt_f pnt_g pnt_a)
	(make_jpg)
		(command "_.delay" 500)	
	(shaded_triangle "layer5" pnt_g pnt_a pnt_h)
	(make_jpg)
		(command "_.delay" 500)
	(shaded_triangle "layer6" pnt_a pnt_h pnt_k)
	(make_jpg)
		(command "_.delay" 1500)

	(shaded_triangle "layer4" pnt_f pnt_b pnt_a)
	(make_jpg)
		(command "_.delay" 500)	
	(shaded_triangle "layer5" pnt_b pnt_a pnt_c)
	(make_jpg)
		(command "_.delay" 500)
	
	(shaded_triangle "layer6" pnt_a pnt_c pnt_k)
	(make_jpg)
		(make_line_1 "0" 0 pnt_f pnt_k)
	(make_jpg)

	(shaded_triangle "layer5" pnt_d pnt_l pnt_e)
	(make_jpg)
		(command "_.delay" 2500)
		
	(alert "Step 2:Therefore\n\narea of FBCKHG is \n\ntwice that of FBCK")
		(setq pnt_ll '(-2.93 0.15) pnt_ur '(8.0 6.1))
		(setq whole (ssget "C" pnt_ur pnt_ll))
		(my_block_def "FBCKHG" pnt_b whole)
		(command "oops")
		(my_block_insert "FBCKHG" '(18.0 0.) 1.0)
		(command "_.zoom" "E")
	(make_jpg)

	(alert "Step 4: \n\nWe will show \n\nthat quadrilateral FBCK is equal to ABDL")
	(setq quad_FBCK1 (shaded_quad "layer2" pnt_f pnt_b pnt_c pnt_k)	)
	(make_jpg)
	(command "_.delay" 1500)
	(rotate_ent quad_FBCK1 pnt_b pnt_c -90. 25 25 1)
	(make_jpg)
	(make_jpg)
	(alert "Step 5: \n\nquadrilateral FBCK is equal to LECA")
	(setq quad_FBCK2 (shaded_quad "layer3" pnt_f pnt_b pnt_c pnt_k)	)
	(make_jpg)
	(make_jpg)
	(command "_.delay" 1500)
	(rotate_ent quad_FBCK2 pnt_c pnt_b 90. 25 25 1)
	(make_jpg)
	(make_jpg)
	(alert "Step 6:Thewrefore\n\narea of ABDLEC is \n\ntwice that of FBCK.")

	(setq pnt_ll '(-1.1 -8.2) pnt_ur '(6.14 3.2))
		(setq whole (ssget "W" pnt_ll pnt_ur))
		(my_block_def "ABDLEC" pnt_b whole)
		(command "oops")
		(my_block_insert "ABDLEC" '(11.0 0.) 1.0)
	
	(command "_.zoom" "E")
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(alert "Step 7:\n\nTherefore\n\n\n FBCKHG = ABDLEC")
	(alert "Step 8:\n\nFBCKHG = FBAG + ACKH \n\n+ 2 Triangles(Blue)")
	(alert "Step 9:\n\nABDLEC = BDEC \n\n+ 2 Triangles(Blue)")
	(alert "Step 10: Therefore\n\n\nBDEC = FBAG + ACKH\n\n\n\t Q. E. D.")
	(reset_sysvar)
);;;EUCLID_47_5 - - - main
;;;
;;;
(defun setup_47_5()
	(setup_sysvar)
	(setvar "OSMODE" 0)
	(command "_.ucsicon" "off")
	(setq len_a 3. len_b 4. len_c 5.
		pnt_a '(1.8 2.4)  pnt_b '(0 0)  pnt_c '(5 0)
		pnt_d '(0 -5)  pnt_e '(5 -5)
		pnt_f (point_off_line pnt_b pnt_a 0. (dtr 90.)  len_a )
		pnt_g (pld pnt_c pnt_a (+ len_a len_b))
		pnt_h (pld pnt_b pnt_a (+ len_a len_b))
		pnt_k (point_off_line pnt_c pnt_a 0. (dtr -90)  len_b)
		pnt_l '(3.2 -7.4)  pnt_m '(1.8 0)  pnt_o '(2.5 -2.5)
	)
	(command "_.pline" pnt_c pnt_a pnt_h pnt_k "c")
	(command "_.pline" pnt_a pnt_b pnt_f pnt_g "c")
	(command "_.pline" pnt_b pnt_c pnt_e pnt_d "c")
	(command "_.pline" pnt_a pnt_b pnt_c "c")
	(command "_.line"  pnt_d pnt_l pnt_e "")
			
	(command "_.pline" pnt_f pnt_g pnt_h pnt_k "c")
	(command "_.line" pnt_b pnt_o pnt_c "")
 ;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.5)
	(regapp "my_point")
	(make_point "layer8" 0  pnt_a  "A" 2 chr_size)
	(make_point "layer8" 0  pnt_b  "B" 3 chr_size)
	(make_point "layer8" 0  pnt_c  "C" 1 chr_size)
	(make_point "layer8" 0  pnt_d  "D" 3 chr_size)
	(make_point "layer8" 0  pnt_e  "E" 4 chr_size)
	(make_point "layer8" 0  pnt_f  "F" 3 chr_size)
	(make_point "layer8" 0  pnt_g  "G" 2 chr_size)
	(make_point "layer8" 0  pnt_h  "H" 1 chr_size)
	(make_point "layer8" 0  pnt_k  "K" 1 chr_size)
	(make_point "layer8" 0  pnt_l  "L" 4 chr_size)
	(make_point "layer8" 0  pnt_o  "O" 1 chr_size)

	(command "_.point" '(23 6))
	(command "_.point" '(23 -5.8))
	(setq text_loc1 '(8 6) text_loc2 '(8 5.4))
  ;;;zoom to the extent
	(textdisplay "Proof By :" text_loc1 chr_size 0.)
	(textdisplay "Leonardo Da Vinci" text_loc2 chr_size 0.)
	(command "_.zoom" "E")
	(setq n_speed 75 n_sec 10)
	(setq t_pnt '(11.4 2.3) t_height 0.5 t_angle 0.)
);setup_47_5
;;;
;;;*****************EUCLID_47_6*******************************************************
;;;
(defun C:Euclid_47_6()
	(setup_47_6)
	(make_jpg)
	(make_jpg)
	(alert "Step 1: \nThe areas of these triangles \n are the same")
		(setq trig_ABC (shaded_triangle "layer5" pnt_a pnt_b pnt_c)
			trig_KEC (shaded_triangle "layer5" pnt_k pnt_e pnt_c)
			trig_IDE (shaded_triangle "layer5" pnt_i pnt_d pnt_e)
			trig_FBD (shaded_triangle "layer5" pnt_f pnt_b pnt_d)
		)
	(make_jpg)
	(make_jpg)	
	(alert "Step 2: \nThe areas of these triangles \n are the same")
		(entdel trig_IDE)
		(entdel trig_FBD)
		(setq trig_GAI (shaded_triangle "layer5" pnt_g pnt_a pnt_i)
			trig_HIA (shaded_triangle "layer5" pnt_h pnt_i pnt_a)
		)
		(make_line_1 "layer8" 0 pnt_i pnt_a)
		(command "_.delay" 1000)
	(make_jpg)
	(make_jpg)	
	(alert "Step 3: \nPentagon  FBCKI is \n\nTwo squares (ABFG & AHKC)\n\n+3 Triangles")
		;(entdel trig_ABC)
		(entdel trig_KEC)
		(setq quad_ABFG (shaded_quad "layer3" pnt_a pnt_b pnt_f pnt_g)
			quad_AHKC (shaded_quad "layer4" pnt_a pnt_h pnt_k pnt_c)
			pnt_cr1 '(8.5 8.5) pnt_cr2 '(-3.4 -0.7)
		)
	(make_jpg)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "PENTA_1" pnt_b whole)
		(command "oops")
		(my_block_insert "PENTA_1" '(18.0 3.) 1.0)
		(command "_.zoom" "E")
	(make_jpg)	
	(alert "Step 4: \nPentagon  FBCKI is \n\nOne square ( BCED )\n\n+3 Triangles")
		(entdel trig_ABC)
		(entdel trig_GAI)
		(entdel trig_HIA)
		(entdel quad_ABFG)
		(entdel quad_AHKC)
	(make_jpg)
		(command "_.delay" 500)
		(setq quad_BDEC (shaded_quad "layer2" pnt_b pnt_d pnt_e pnt_c)
			trig_KEC (shaded_triangle "layer5" pnt_k pnt_e pnt_c)
			trig_IDE (shaded_triangle "layer5" pnt_i pnt_d pnt_e)
			trig_FBD (shaded_triangle "layer5" pnt_f pnt_b pnt_d)
		)
	(make_jpg)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "PENTA_2" pnt_b whole)
		(command "oops")
		(my_block_insert "PENTA_2" '(18.0 -6.) 1.0)
		(command "_.zoom" "E")
	(make_jpg)
	(make_jpg)
	(make_jpg)
		(command "_.delay" 500)
		(entdel quad_BDEC)
		(entdel trig_KEC)
		(entdel trig_IDE)
		(entdel trig_FBD)
	(make_jpg)			
	(alert "Step 5: \nThree triangles are common for two Penatgons.")
		
	(alert "Step 6: Therefore \n\narea of BDEC = sum of the areas of\n\nABFG and AHKC\n\tQ.E.D.")
	(reset_sysvar)
);;;EUCLID_47_6 - - - main
;;;
;;;
(defun setup_47_6()
	(setup_sysvar)
	(setvar "OSMODE" 0)
	(command "_.ucsicon" "off")
	(setq len_a 3. len_b 4. len_c 5.
		pnt_a '(1.8 2.4)  pnt_b '(0 0)  pnt_c '(5 0)
		pnt_f (point_off_line pnt_b pnt_a 0. (dtr 90.)  len_a )
		pnt_g (pld pnt_c pnt_a (+ len_a len_b))
		pnt_h (pld pnt_b pnt_a (+ len_a len_b))
		pnt_k (point_off_line pnt_c pnt_a 0. (dtr -90)  len_b)
		pnt_d (pld pnt_f pnt_g len_b)  pnt_e (pld pnt_k pnt_h len_a)
		pnt_i (inters pnt_f pnt_g pnt_k pnt_h nil)
	)
	(command "_.pline" pnt_c pnt_a pnt_h pnt_k "c")
	(command "_.pline" pnt_a pnt_b pnt_f pnt_g "c")
	(command "_.pline" pnt_b pnt_c pnt_e pnt_d "c")
	(command "_.pline" pnt_a pnt_b pnt_c "c")
	(make_line_1 "layer8" 8 pnt_g pnt_i)
	(make_line_1 "layer8" 8 pnt_a pnt_i)
	(make_line_1 "layer8" 8 pnt_h pnt_i)
 ;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.5)
	(regapp "my_point")
	(make_point "layer8" 0  pnt_a  "A" 1 chr_size)
	(make_point "layer8" 0  pnt_b  "B" 4 chr_size)
	(make_point "layer8" 0  pnt_c  "C" 4 chr_size)
	(make_point "layer8" 0  pnt_d  "D" 3 chr_size)
	(make_point "layer8" 0  pnt_e  "E" 1 chr_size)
	(make_point "layer8" 0  pnt_f  "F" 3 chr_size)
	(make_point "layer8" 0  pnt_g  "G" 3 chr_size)
	(make_point "layer8" 0  pnt_h  "H" 1 chr_size)
	(make_point "layer8" 0  pnt_i  "I" 2 chr_size)
	(make_point "layer8" 0  pnt_k  "K" 1 chr_size)
	
	(command "_.point" '(23 10))
	(command "_.point" '(23 -8))
	(textdisplay "Proof  by :  Thabit ibn Quarra" '(-2 -3.5) chr_size 0.)
  ;;;zoom to the extent
	(command "_.zoom" "E")
	(setq n_speed 75 n_sec 10)
	(setq t_pnt '(11.4 2.3) t_height 0.5 t_angle 0.)
	;(command "_.rectangle" '(11.25 -3) '(22 3))

);setup_47_6
;;;
copy

;;;*****************EUCLID_47_7*******************************************************
;;;
;;;
(defun C:Euclid_47_7()
	(setup_47_7)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(alert "Step 1: Move Triangle FBO to Corner A")
		(move_ent trig_1 pnt_f pnt_a n_speed ndiv 1 "0")
	(make_jpg)
		(make_point "layer8" 0  pnt_i "I" 4 chr_size)
	(make_jpg)
	(alert "Step 2: Move Triangle GOB to Corner C")
		(move_ent trig_2 pnt_g pnt_c n_speed ndiv 1 "0")
	(make_jpg)
		(make_point "layer8" 0  pnt_j "J" 1 chr_size)
	(make_jpg)
	(alert "Step 3: Move Triangle EOH to Corner B")
		(move_ent trig_3 pnt_h pnt_j n_speed ndiv 1 "0")
	(make_jpg)
	(alert "Final: It is proved \nHGDJ = ABDE + BCFG")
	(make_jpg)
		
	(alert "Copy the result to the right and reverse the process")
		(setq whole (ssget "C" pnt_cc pnt_aa))
		(command "_.copy" whole "" pnt_a pnt_a_new)
		(command "_.zoom" "E")
	(make_jpg)
	(make_jpg)
	(command "_.delay" 500)
	(alert "Step 3-: Move Triangle IBJ to EOH ")
		(move_ent trig_3 pnt_j pnt_h n_speed ndiv 1 "0")
	(make_jpg)
	(alert "Step 2-: Move Triangle CHJ to GOB ")
		(move_ent trig_2 pnt_c pnt_g n_speed ndiv 1 "0")
	(make_jpg)
	(alert "Step 1-: Move Triangle AIE to FBO")
		(move_ent trig_1 pnt_a pnt_f n_speed ndiv 1 "0")
	(make_jpg)
		(command "_.delay" 500)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(alert "Step 6: Therefore \n\narea of EHJI = sum of the areas of\n\nEOFA and HCGO\n\tQ.E.D.")
	(reset_sysvar)
		
);;;EUCLID_47_7 
;;;
;;;
(defun setup_47_7()
	(setup_sysvar)
	;;fix len_a & len_b for now.
	(setq len_a 5.0 len_b 3.0  len_ab (+ len_a len_b)  len_ab3 (* 3. len_ab)
		len_ab2 (* 2. len_ab)  len_min (* 0.5 (min len_a len_b))
	)
	(setvar "OSMODE" 0)
	(command "_.ucsicon" "off")
	(setq 	pnt_a '(0 0)  pnt_b (list len_ab 0)  pnt_c (list len_ab len_ab)
		pnt_d (list 0 len_ab)  pnt_e (list 0 len_a)  pnt_f (list len_a 0)
		pnt_g (list len_ab len_a)  pnt_h (list len_a len_ab)
		pnt_i (list len_b 0)  pnt_j (list len_ab len_b)
		pnt_o (list len_a len_a)  pnt_r1 (list len_ab3 len_ab)
		pnt_r2 (list len_ab3 (- len_min))  pnt_aa (list -0.5 -0.5)
		pnt_cc (list 8.5 8.5)  	pnt_a_new (list len_ab2 0)
	)
	(command "_.layer" "set" "layer8" "")
	(command "_.pline" pnt_a pnt_b pnt_c pnt_d "c")
	(command "_.layer" "set" "0" "")
 ;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.5
		n_speed 100
		ndiv 6
	)
	(regapp "my_point")
	(make_point "layer8" 0  pnt_a  "A" 4 chr_size)
	(make_point "layer8" 0  pnt_b  "B" 4 chr_size)
	(make_point "layer8" 0  pnt_c  "C" 1 chr_size)
	(make_point "0" 0  pnt_d  "D" 3 chr_size)
	(make_point "layer8" 0  pnt_e  "E" 3 chr_size)
	(make_point "layer8" 0  pnt_f  "F" 4 chr_size)
	(make_point "0" 0  pnt_g  "G" 1 chr_size)
	(make_point "layer8" 0  pnt_h  "H" 2 chr_size)
	(make_point "layer8" 0  pnt_o  "O" 1 chr_size)
  ;;;draw 4 triangles
	(setq trig_1 (shaded_triangle "layer2" pnt_f pnt_b pnt_o)
	 	trig_2 (shaded_triangle "layer3" pnt_g pnt_o pnt_b)
	 	trig_3 (shaded_triangle "layer4" pnt_e pnt_o pnt_h)
		trig_4 (shaded_triangle "layer5" pnt_d pnt_e pnt_h)
	)
	;;;zoom to the extent
	(command "_.point" pnt_r1)
	(command "_.point" pnt_r2)
	(textdisplay "Proof  by :  Pythagoras" '(0 -2.5) chr_size 0.)
	(command "_.zoom" "E")
	;(command "_.zoom" "scale" 0.65)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -2)
	
);setup_47_7
;;;
;;;*****************EUCLID_47_8*******************************************************
;;;	special dissection
;;;		command	euclid_47_8
;;;		ref-dwg		euclid_47_8.dwg
;;;
(defun C:Euclid_47_8()
	(setup_47_8)
	(make_jpg)	
	(alert "       Step 1:\n Rotate Triangle ABC \n around point A")
		(rotate_ent trig_1 pnt_a pnt_b 90. 25 25 1)
	(make_jpg)
	(command "_.delay" 500)	
		(setq whole (ssget "C" pnt_dd pnt_aa))
		(my_block_def "step_1" pnt_a whole)
		(command "oops")
		(my_block_insert "step_1" '(4.75 2.5) 0.5)
	(make_jpg)	 
	(alert "       Step 2:\n Move Triangle IGB \n to point E")
		(move_ent trig_2 pnt_b pnt_e n_speed 5 1 "0")
	(make_jpg)
	(command "_.delay" 500)
		(setq pnt_k (pld pnt_a pnt_e (+ 2.0 (distance pnt_b pnt_g))))

		(setq whole (ssget "C" pnt_dd pnt_aa))
		(my_block_def "step_2" pnt_a whole)
	(make_jpg)
	(command "_.delay" 500)
		(command "oops")
		(my_block_insert "step_2" '(6.75 2.5) 0.5)
	(make_jpg)
	(command "_.delay" 500)
	(alert "       Step 3:\n Rotate Triangle LEK \n around point E")
		(rotate_ent trig_2 pnt_e pnt_k -90. 25 25 1)
	(make_jpg)
	(command "_.delay" 500)
		(setq whole (ssget "C" pnt_dd pnt_aa))
		(my_block_def "step_3" pnt_a whole)
		(command "oops")
		(my_block_insert "step_3" '(4.75 0.5) 0.5)
	(make_jpg)
	(command "_.delay" 500)	
	(alert "       Step 4:\n Move Triangle FHD\n aound point D")
		(rotate_ent trig_3 pnt_d pnt_f -270. 25 25 1)
	(make_jpg)
	(command "_.delay" 500)	
		(setq whole (ssget "C" pnt_dd pnt_aa))
		(my_block_def "step_4" pnt_a whole)
		(command "oops")
		(my_block_insert "step_4" '(6.75 0.5) 0.5)
	(make_jpg)
	(command "_.delay" 500)	
	(alert "       Step 5:\n Move Square IHDM \n along BF to Point B")
		(setq ss (ssadd)
			ss (ssadd trig_3 ss)
			ss (ssadd quad_4 ss)
		)
		(move_ent ss pnt_i pnt_b n_speed 5 1 "0")
	(make_jpg)
	(command "_.delay" 500)
		(setq whole (ssget "C" pnt_dd pnt_aa))
		(my_block_def "step_5" pnt_a whole)
		(command "oops")
		(my_block_insert "step_5" '(4.75 -1.5) 0.5)
	(make_jpg)
	(command "_.delay" 500)
	(make_jpg)
	(command "_.delay" 500)
	(make_jpg)
	(command "_.delay" 500)
	(make_jpg)
	(command "_.delay" 500)
	(alert "Reverse the process")

		(move_ent ss pnt_b pnt_i n_speed 5 1 "0")
	(make_jpg)
	(command "_.delay" 500)
	(alert "       Step R-1:\n Move Triangle FHD\n aound point D")
		(rotate_ent trig_3 pnt_d pnt_g 270. 25 25 1)
	(make_jpg)
	(command "_.delay" 500)
	(make_jpg)
	(command "_.delay" 500)
	(alert "       Step R-2:\nMove Triangle EFK\n to point G")
		(rotate_ent trig_2 pnt_e pnt_f 90. 25 25 1)
	(make_jpg)
	(command "_.delay" 500)

		(move_ent trig_2 pnt_e pnt_b n_speed 5 1 "0")
	(make_jpg)
	(command "_.delay" 500)	
	(alert "       Step R-4:\n Rotate Triangle ABC\n around point A")
		(rotate_ent trig_1 pnt_a pnt_e -90. 25 25 1)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(reset_sysvar)	
);;;EUCLID_47_8 
;;;
;;;
(defun setup_47_8()
	(setup_sysvar)
	(setvar "OSMODE" 512)		;; snap mode  "nearest"
	(command "_.ucsicon" "off")
	;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.25   n_speed 100	ndiv 6	)
	(setq pnt_a '(-1 0) pnt_b '(1 0) pnt_o '(0 0)
		pnt_d '(1 2) pnt_e '(-1 2)
		low_left '(-2.2 -1.8) up_right '(8.5 4.0)
	)
	(regapp "my_point")
	(make_point "layer8" 0  pnt_a  "A" 4 chr_size)
	(make_point "layer8" 0  pnt_b  "B" 4 chr_size)
	;(make_point "layer8" 0  pnt_c  "C" 1 chr_size)
	(make_point "layer8" 0  pnt_d  "D" 1 chr_size)
	(make_point "layer8" 0  pnt_e  "E" 3 chr_size)

	(make_line_1 "0" 0 pnt_a pnt_b)
	(command "_.arc" "CE" pnt_o pnt_b "A" 180.)

	(command "_.zoom" "E")
	(command "_.regen")
	(make_jpg)
	(command "_.delay" 500)
	(alert "Select point C\non the semi-circle")
	(setq pnt_c (getpoint "\nSelect point C on the semi-circle"))
	(setq len_a (distance pnt_a pnt_c)
		len_b (distance pnt_b pnt_c)
		pnt_f (inters pnt_d pnt_e pnt_b pnt_c nil)
		dist_df (distance pnt_d pnt_f)
		pnt_g (pld pnt_d pnt_b dist_df)
		dist_fh (* 0.5 len_b dist_df)
		pnt_h (pld pnt_f pnt_b dist_fh)
		pnt_i (pld pnt_h pnt_b len_b)
	)
	(setvar "OSMODE" 0)
	(setq 
		len_ab (+ len_a len_b)	len_ab3 (* 3. len_ab)
		len_ab2 (* 2. len_ab)	len_min (* 0.5 (min len_a len_b))
	)
	(setq 	pnt_r1 (list len_ab3 len_ab)	pnt_r2 (list len_ab3 (- len_min))
		pnt_a_new (list len_ab2 0)
		del    (* 2.5 chr_size)
		del_dd (list del del)		del_aa (list (- del) (- del))
		pnt_aa (shift_pnt pnt_a del_aa)   pnt_dd (shift_pnt pnt_d del_dd)
	)
  ;;;draw shaded triangles & quadrilaterals
	(setq trig_1 (shaded_triangle "layer2" pnt_a pnt_b pnt_c)
	 	trig_2 (shaded_triangle "layer3" pnt_b pnt_i pnt_g)
	 	trig_3 (shaded_triangle "layer4" pnt_d pnt_f pnt_h)
		quad_4 (shaded_quad "layer5" pnt_g pnt_d pnt_h pnt_i)
		quad_5 (shaded_quad "layer6" pnt_e pnt_a pnt_c pnt_f)
	)
	;;;zoom to the extent
	(command "_.point" pnt_r1)
	(command "_.point" pnt_r2)
	(command "_.zoom" "_Win" low_left up_right)
	;(command "_.zoom" "scale" 1.55)
	(make_point "layer8" 1  pnt_c  "C" 2 chr_size)
	(make_point "layer8" 0  pnt_f  "F" 1 chr_size)
	(make_point "layer8" 0  pnt_g  "G" 1 chr_size)
	(make_point "layer8" 0  pnt_h  "H" 2 chr_size)
	(make_point "layer8" 1  pnt_i  "I" 1 chr_size)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -2)
);setup_47_8
;;;
;;;*****************EUCLID_47_9*******************************************************
;;;	Yanneys's Proof
;;;		command	euclid_47_9
;;;
(defun C:Euclid_47_9()
	(setup_47_9)
	(make_jpg)
	(make_jpg)
	(alert "Step 1: extend CK and find an intersect M on HL")
		(setq pnt_m (inters pnt_c pnt_k pnt_h pnt_l nil))
		(setq pnt_n (inters pnt_f pnt_e pnt_a pnt_l nil))
		(make_line_2 "0" 2 "HIDDEN2" pnt_c pnt_m)
		(make_point "layer8" 0  pnt_m  "M" 1 chr_size)
		(make_point "0" 0  pnt_o  "O" 4 chr_size)
	(make_jpg)
	(command "_.delay" 500)
	(alert "Step 2: extend FE and find an intersect N on AL")
		(setq pnt_n (inters pnt_f pnt_e pnt_a pnt_l nil))
		(make_line_2 "0" 2 "HIDDEN2" pnt_f pnt_n)
		(make_point "layer8" 0  pnt_n  "N" 3 chr_size)
	(make_jpg)
	(command "_.delay" 500)
	(alert "Step 3: \nquad ALMO")
		(setq ALMO (shaded_quad "layer2" pnt_a pnt_l pnt_m pnt_o))
	(make_jpg)
	(command "_.delay" 500)
		(setq ALMO (entlast))
		(setq pnt_cr1 '(9.0 9.0) pnt_cr2 '(-0.5 -0.5))
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "ACFHL_1" pnt_c whole)
		(command "oops")
	(make_jpg)
	(command "_.delay" 500)
		(my_block_insert "ACFHL_1" '(10.0 5.) 0.5)
		(command "_.zoom" "_EXTENT")
		(entdel ALMO)
	(make_jpg)
	(command "_.delay" 500)
	(alert "Step 4: \nquad ALMO ---> quad ALKC")
		(command "_.layer" "_set" "layer2" "")
		(setq len_c (distance pnt_a pnt_l))
		(quad_along_line "layer3" pnt_o pnt_c n_sec n_speed pnt_l pnt_a 1 len_c)
	(make_jpg)
	(command "_.delay" 500)
		(command "_.layer" "_set" "0" "")
		(setq ALKC last_hatch)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "ACFHL_2" pnt_c whole)
		(command "_.oops")
		(my_block_insert "ACFHL_2" '(15.0 5.) 0.5)
		(command "_.zoom" "_EXTENT")
	(make_jpg)
	(command "_.delay" 500)
	(alert "Step 5:\n quad ALKC ---> quad AEDC")
		(entdel ALKC)
		(command "_.layer" "_set" "layer2" "")
		(setq len_c (distance pnt_a pnt_l))
		(quad_along_line "layer3" pnt_k pnt_d n_sec n_speed pnt_a pnt_c 1 len_a)
	(make_jpg)
	(command "_.delay" 500)
		(command "_.layer" "_set" "0" "")
		(setq AEDC last_hatch)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "ACFHL_3" pnt_c whole)
		(command "_.oops")
		(my_block_insert "ACFHL_3" '(20.0 5.) 0.5)
		(command "_.zoom" "_EXTENT")
	(make_jpg)
	(command "_.delay" 500)	
	(alert "Step 6: \nquad BHMO")
		(entdel AEDC)
		(setq BHMO (shaded_quad "layer3" pnt_b pnt_h pnt_m pnt_o))
	(make_jpg)
	(command "_.delay" 500)
		(setq BHMO (entlast))
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "ACFHL_4" pnt_c whole)
		(command "_.oops")
		(my_block_insert "ACFHL_4" '(10.0 -3.5) 0.5)
		(command "_.zoom" "_EXTENT")
		(entdel BHMO)
	(make_jpg)
	(command "_.delay" 500)
	(alert "Step 7: \nquad BHMO ---> quad BHKC")
		(command "_.layer" "_set" "layer3" "")
		(quad_along_line "layer3" pnt_o pnt_c n_sec n_speed pnt_h pnt_b 1 len_c)
	(make_jpg)
	(command "_.delay" 500)
		(command "_.layer" "_set" "0" "")
		(setq BHKC last_hatch)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "ACFHL_5" pnt_c whole)
		(command "oops")
		(my_block_insert "ACFHL_5" '(15.0 -3.5) 0.5)
		(command "_.zoom" "E")
	(make_jpg)
	(command "_.delay" 500)
	(alert "Step 8:\n quad KHBC ---> quad KHFD")
		(entdel BHKC)
		(command "_.layer" "_set" "layer3" "")
		(quad_along_line "layer3" pnt_b pnt_f n_sec n_speed pnt_k pnt_h 1 len_b)
	(make_jpg)
	(command "_.delay" 500)
		(command "_.layer" "_set" "0" "")
		(setq KHBC last_hatch)
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "ACFHL_6" pnt_c whole)
		(command "_.oops")
		(my_block_insert "ACFHL_6" '(20.0 -3.5) 0.5)
		(command "_.zoom" "_EXTENT")
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(command "_.delay" 500)
		(reset_sysvar)
);;;EUCLID_47_9 
;;;
;;;
(defun setup_47_9()
	(setup_sysvar)
	(setq len_a 3. ;(getreal "\nLength A= ")
		len_b 5. ;(getreal "\nLength B= ")
		len_ab (+ len_a len_b)  len_ab2 (* 3. len_ab)
		len_min (* 0.5 (min len_a len_b))
	)
	(setvar "OSMODE" 0)
	(command "_.ucsicon" "_off")
	(setq 	pnt_a (list 0 len_a)        pnt_b (list len_b 0)     pnt_c (list 0 0)
		pnt_d (list len_a 0)        pnt_e (list len_a len_a) pnt_f (list len_ab 0)
		pnt_h (list len_ab len_b)   pnt_k (list len_a len_b)
		pnt_l (list len_a len_ab)   pnt_o (inters pnt_a pnt_b pnt_c pnt_k )
		pnt_r1 (list len_ab2 (+ len_ab 1.25))
		pnt_r2 (list len_ab2 (- (- len_min ) 2.0) )
	)
	(command "_.layer" "_set" "layer8" "")
	(command "_.pline" pnt_a pnt_c pnt_d pnt_e "_c")
	(command "_.pline" pnt_a pnt_b pnt_h pnt_l "_c")
	(command "_.pline" pnt_l pnt_d pnt_f pnt_h pnt_k "")
	(command "_.layer" "_set" "0" "")
 ;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.5 n_speed 100 n_sec 8)
	(regapp "my_point")
	(make_point "layer8" 0  pnt_a  "A" 3 chr_size)
	(make_point "layer8" 0  pnt_b  "B" 4 chr_size)
	(make_point "layer8" 0  pnt_c  "C" 4 chr_size)
	(make_point "0" 0  pnt_d  "D" 4 chr_size)
	(make_point "layer8" 0  pnt_e  "E" 3 chr_size)
	(make_point "layer8" 0  pnt_f  "F" 4 chr_size)
	(make_point "0" 0  pnt_h  "H" 1 chr_size)
	(make_point "0" 0  pnt_k  "K" 3 chr_size)
	(make_point "0" 0  pnt_l  "L" 2 chr_size)
	;;;zoom to the extent
	(command "_.point" pnt_r1)
	(command "_.point" pnt_r2)
	(command "_.zoom" "_EXTENT")
	;(command "_.zoom" "_scale" 0.65)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -2)
);setup_47_9
;;;
;;;************************dissection*********************************
;;;
(defun C:dissection()
	(setup_dissection)
	(loc_xdir)
	(setq ss_lines (ssadd))	;;;selection set initialized
	(array_row_1)
	(array_all_rows)
	(square_net)
	(alert "Move the grid net\n\nclick mouth to select location") 
		(my_block_def "ref_grid" pnt_a ss_lines)
		(c:move_grid)
	(reset_sysvar)
);dissection
;;;
(defun c:move_grid()
	(setvar "OSMODE" 41)
	(if (/= grid_block nil) (entdel grid_block))
		(command "_.insert" "ref_grid" PAUSE 1. 1. 0.)
		(setq grid_block (entlast))
);;;move ref_grid block
;;;
(defun setup_dissection()
	(setup_sysvar)
	(setq len_a 5. ;(getreal "\nLength A= ")
		len_b 3. ;(getreal "\nLength B= ")
		len_ab (+ len_a len_b)
		len_ab2 (* 2. len_ab)
		len_min (* 0.5 (min len_a len_b))
	)

	(setvar "OSMODE" 0)
	(command "_.ucsicon" "off")
	(setq 	pnt_a '(0 0 )  pnt_b (list len_a 0)  pnt_c (list len_ab 0)
		pnt_d (list 0 len_a)  pnt_e (list len_a len_a)  pnt_f (list len_a len_b )
		pnt_g (list len_ab len_b)  pnt_h (list len_b 0)
		pnt_i (list (* 0.5 len_a) (* 0.5 len_a))
		pnt_j (list (+ len_a (* 0.5 len_b)) (* 0.5 len_b))
		len_c (distance pnt_a pnt_f)  pnt_k (list len_c 0)
	)
	(command "_.layer" "set" "layer1" "")
	(command "_.pline" pnt_a pnt_b pnt_e pnt_d "c")
	(command "_.pline" pnt_b pnt_c pnt_g pnt_f "c")
	
	(command "_.layer" "set" "0" "")
	(setq	quad_BCGF (shaded_quad "layer161" pnt_b pnt_c pnt_g pnt_f))
	 
 ;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.5 n_speed 100 n_sec 8 ref_dist (distance pnt_a pnt_f))
	;(regapp "my_point")
	(make_pt "layer8" 0  pnt_i  )
	(make_pt "layer8" 0  pnt_j  )
	;;;zoom to the extent
	(command "_.zoom" "E")
	;(command "_.zoom" "scale" 0.25)
	
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -2)
);setup_dissection
;;;
;;;
(defun loc_xdir()
	(setq rot_angle (rtd (angle pnt_a pnt_f)))
	(command "_.rotate" "all" "" pnt_a (- rot_angle))
	;(command "align" "all" "" pnt_a  pnt_a  pnt_f  pnt_k  ""  "")
);loc_xdir
;;;
;;;
(defun array_row_1()
	(command "_array" "all" "" "R" 1 5 ref_dist)
);array_row_1
;;;
;;;
(defun array_all_rows()
	(command "_array" "all" "" "R" 5 1 ref_dist)
);array_row_1
;;;
;;;
(defun square_net()
	(setq minus_ref (- ref_dist)
		pnt_org (list minus_ref minus_ref)
		pnt_right (list (* 2. ref_dist) minus_ref)
		pnt_up	  (list minus_ref (* 2. ref_dist))
	)
	(multi_ln_dy pnt_org pnt_right ref_dist 4 2)
	(multi_ln_dx pnt_org pnt_up    ref_dist 4 2)
	(command "_.zoom" "e")
	
);square_net
;;;
;;;
(defun multi_ln_dx(pnt_1 pnt_2 delta_x n_lines ncolor
			/
			pnt_from pnt_to x1 x2 y1 y2 nstep )
	(setq pnt_from pnt_1
		pnt_to pnt_2
		x1 (car pnt_1) x2 (car pnt_2)
		y1 (cadr pnt_1) y2 (cadr pnt_2)
		nstep 0
	)
	(repeat n_lines	
		(make_line_1 "0" ncolor pnt_from pnt_to )
		(setq ss_lines (ssadd (entlast) ss_lines))	;;;add entity to the selection set ss
		(setq nstep (1+ nstep)
			pnt_from (list (+ x1 (* nstep delta_x)) y1)
			pnt_to   (list (+ x2 (* nstep delta_x)) y2)
		)
	)
);multi_ln_dx
;;;
;;;
(defun multi_ln_dy(pnt_1 pnt_2 delta_y n_lines ncolor
			/
			pnt_from pnt_to x1 x2 y1 y2 nstep )
	(setq pnt_from pnt_1
		pnt_to pnt_2
		x1 (car pnt_1) x2 (car pnt_2)
		y1 (cadr pnt_1) y2 (cadr pnt_2)
		nstep 0
	)
	(repeat n_lines	
		(make_line_1 "0" ncolor pnt_from pnt_to )
		(setq ss_lines (ssadd (entlast) ss_lines))	;;;add entity to the selection set ss
		(setq nstep (1+ nstep)
			pnt_from (list x1 (+ y1 (* nstep delta_y)) )
			pnt_to   (list x2 (+ y2 (* nstep delta_y)) )
		)
	)
);multi_ln_dy
;;;
;;;
(defun multi_ln_dxdy(pnt_1 pnt_2 delta_x delta_y n_lines ncolor
			/
			pnt_from pnt_to x1 x2 y1 y2 nstep )
	(setq pnt_from pnt_1
		pnt_to pnt_2
		x1 (car pnt_1) x2 (car pnt_2)
		y1 (cadr pnt_1) y2 (cadr pnt_2)
		nstep 0
	)
	(repeat n_lines	
		(make_line_1 "0" ncolor pnt_from pnt_to )
		(setq ss_lines (ssadd (entlast) ss_lines))	;;;add entity to the selection set ss
		(setq nstep (1+ nstep)
			pnt_from (list (+ x1 (* nstep delta_x)) (+ y1 (* nstep delta_y)) )
			pnt_to   (list (+ x2 (* nstep delta_x)) (+ y2 (* nstep delta_y)) )
		)
	)
);multi_ln_dxdy
;;;
;;;*******************************************************************************
;;;		Liu Hui's proof by dissection
;;;**********************************************************************
(defun C:DISSECT_1()
	(setup_dissect_1)
	(make_jpg)
	(command "_.delay" 500)
	(alert "Step 1: Shade the squareCBHI \n\n(area=c*c)")
		(setq quad_LMJK    (shaded_quad "layer210" pnt_l pnt_m pnt_j pnt_k)
			trig_CMN (shaded_triangle "layer50" pnt_c pnt_m  pnt_n)
			trig_HKO (shaded_triangle "layer52" pnt_h pnt_k  pnt_o)
			trig_CJI    (shaded_triangle "layer80" pnt_c pnt_j  pnt_i)
			trig_BLH  (shaded_triangle "layer81" pnt_b pnt_l  pnt_h)
			trig_BNC (shaded_triangle "layer130" pnt_b pnt_n  pnt_c)
			trig_IOH  (shaded_triangle "layer132" pnt_i pnt_o  pnt_h)
		)
	(make_jpg)
	(command "_.delay" 500)
	(make_jpg)
	(command "_.delay" 500)
		(setq pnt_cr1 '(9.0 9.0) pnt_cr2 '(-5.5 -3.8) whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_1" pnt_a whole)
		(command "oops")
		(my_block_insert "WHOLE_1" '(17.0  5.0) 0.75)
		(command "_.zoom" "E")
	(make_jpg)
	(command "_.delay" 500)
	(alert "Step 2:\n Move CMN & HKO to  square ABED \n\n(area = b*b)" )
		(blink_layer "layer50" 100  2)
		(command "_.delay" 2000)
		(setq trig_ABE (shaded_triangle "layer50" pnt_a pnt_b  pnt_e))
		(blink_layer "layer50" 100  2)
		(entdel trig_CMN)
		(command "_.delay" 2000)
	(make_jpg)
	(command "_.delay" 500)
		(blink_layer "layer52" 100  2)
		(command "_.delay" 2000)
		(setq trig_EDA (shaded_triangle "layer52" pnt_e pnt_d  pnt_a))
		(blink_layer "layer52" 100  2)
		(entdel trig_HKO)
		(command "_.delay" 2000)
	(make_jpg)
	(command "_.delay" 500)	
	(alert "Step 3:\n Move CJI &BLH to  square ACFG \n\n(area = a*a)" )
		(blink_layer "layer80" 100  2)
		(command "_.delay" 2000)
		(setq trig_CFQ (shaded_triangle "layer80" pnt_c pnt_f  pnt_q))
		(blink_layer "layer80" 100  2)
		(entdel trig_CJI)
		(command "_.delay" 2000)
	(make_jpg)
	(command "_.delay" 500)
		(blink_layer "layer81" 100  2)
		(command "_.delay" 2000)
		(setq trig_RAC (shaded_triangle "layer81" pnt_r pnt_a  pnt_c))
		(blink_layer "layer81" 100  2)
		(entdel trig_BLH)
		(command "_.delay" 2000)
	(make_jpg)
	(command "_.delay" 500)	
	(alert "Step 4:\n Move BNC & IOH to  square ACFG \n\n(area = a*a)" )
		(blink_layer "layer130" 100  2)
		(command "_.delay" 2000)
		(setq trig_QPC (shaded_triangle "layer130" pnt_q pnt_p  pnt_c))
		(blink_layer "layer130" 100  2)
		(entdel trig_BNC)
		(command "_.delay" 2000)
	(make_jpg)
	(command "_.delay" 500)
		(blink_layer "layer140" 100  2)
		(command "_.delay" 2000)
		(setq trig_RPC (shaded_triangle "layer140" pnt_r pnt_p  pnt_c))
		(blink_layer "layer140" 100  2)
		(entdel trig_IOH)
		(command "_.delay"2000)
	(make_jpg)
	(command "_.delay" 500)	
	(alert "Step 5:\n Move LMJK to  square ACFG \n\n(area = a*a)" )
		(blink_layer "layer210" 100  2)
		(command "_.delay" 2000)
		(setq quad_GQPR (shaded_quad "layer210" pnt_g pnt_q pnt_p  pnt_r))
		(blink_layer "layer210" 100  2)
		(entdel quad_LMJK)
		(command "_.delay" 2000)
	(make_jpg)
	(command "_.delay" 500)
	 	(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_2" pnt_a whole)
		(command "oops")
		(my_block_insert "WHOLE_2" '(17.0 -4.5) 0.75)
		(command "_.zoom" "E")
	(make_jpg)
	(command "_.delay" 500)
		(command "_.delay" 1000)
	   	 (shaded_quad "layer210" pnt_l pnt_m pnt_j pnt_k)
		 (shaded_triangle "layer50" pnt_c pnt_m  pnt_n)
		 (shaded_triangle "layer52" pnt_h pnt_k  pnt_o)
		 (shaded_triangle "layer80" pnt_c pnt_j  pnt_i)
		 (shaded_triangle "layer81" pnt_b pnt_l  pnt_h)
		 (shaded_triangle "layer130" pnt_b pnt_n  pnt_c)
		 (shaded_triangle "layer132" pnt_i pnt_o  pnt_h)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(alert "It is proved \n\nCBHI = ABED + ACFG\n\n or   c*c = a*a + b*b\n\n\tQ.E.D.")
		(reset_sysvar)
);;;DISSECT_1 - - - main
;;;
;;;
(defun setup_dissect_1()
	(setup_sysvar)
	(setq len_a 5. ;(getreal "\nLength A= ")
		len_b 3. ;(getreal "\nLength B= ")
		len_ab (+ len_a len_b)  len_ab2 (* 3. len_ab)
		len_min (* 0.5 (min len_a len_b))
	)
	(setvar "OSMODE" 0)
	(command "_.ucsicon" "off")
	(setq 	pnt_a '(0 0)  pnt_b (list len_b 0)   pnt_c (list 0 len_a)
		pnt_d (list 0 (- len_b))   pnt_e (list len_b (- len_b))
		pnt_f (list (- len_a) len_a)   pnt_g (list (- len_a) 0)
		pnt_h (list len_ab len_b) pnt_i (list len_a len_ab)
		pnt_j (list len_a len_a) pnt_k (list len_a len_b)
		pnt_l (list len_b len_b) pnt_m (list len_b len_a)
		pnt_n (list len_b (- len_a len_b)) pnt_o (list len_a (* 2. len_b))
		pnt_p (list (- len_b) (- len_a len_b)) pnt_q (list (- len_a) (- len_a len_b))
		pnt_r (list (- len_b) 0)
		pnt_r1 (list len_ab2 (+ len_ab 3.0))
		pnt_r2 (list len_ab2 (- (- len_min ) 5.5) )
	)
	(command "_.layer" "set" "layer8" "")
	(command "_.pline" pnt_a pnt_e pnt_b pnt_c "c")
	(command "_.pline" pnt_a pnt_b pnt_e pnt_d "c")
	(command "_.pline" pnt_a pnt_c pnt_f pnt_g "c")
	(command "_.pline" pnt_c pnt_b pnt_h pnt_i "c")
	(command "_.pline" pnt_b pnt_m pnt_c pnt_n "")
	(command "_.pline" pnt_c pnt_r pnt_p pnt_c pnt_q pnt_p "")
	(command "_.pline" pnt_l pnt_h pnt_o pnt_i pnt_k pnt_l pnt_m pnt_j "")
	(command "_.layer" "set" "0" "")
 ;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.50)
	(regapp "my_point")
	
	(make_point "layer8" 0 pnt_a "A"  1 chr_size)
	(make_point "layer8" 0 pnt_b "B"  4 chr_size)
	(make_point "layer8" 0 pnt_c "C"  2 chr_size)
	(make_point "layer8" 0 pnt_d "D"  4 chr_size)
	(make_point "layer8" 0 pnt_e "E"  4 chr_size)
	(make_point "layer8" 0 pnt_f "F"  3 chr_size)
	(make_point "layer8" 0 pnt_g "G"  3 chr_size)
	(make_point "layer8" 0 pnt_h "H"  4 chr_size)
	(make_point "layer8" 0 pnt_i "I"  1 chr_size)
	(make_point "layer8" 0 pnt_j "J"  4 chr_size)
	(make_point "layer8" 0 pnt_k "K"  4 chr_size)
	(make_point "layer8" 0 pnt_l "L"  4 chr_size)
	(make_point "layer8" 0 pnt_m "M"  4 chr_size)
	(make_point "layer8" 0 pnt_n "N"  4 chr_size)
	(make_point "layer8" 0 pnt_o "O"  1 chr_size)
	(make_point "layer8" 0 pnt_p "P"  4 chr_size)
	(make_point "layer8" 0 pnt_q "Q"  3 chr_size)
	(make_point "layer8" 0 pnt_r "R"  4 chr_size)
	;;;zoom to the extent
	(command "_.point" pnt_r1)
	(command "_.point" pnt_r2)
	(command "_.text" '(-1.5 -5.5) chr_size 0. "Dissection  #1")
	(command "_.text" "" "Proof by :  Liu Hui")

	(command "_.zoom" "E")
	(setq n_speed 100 n_sec 8)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -2)
);dissect_1
;;;
;;;*******************************************************************************
;;;	J.E.Boettcher's proof  by  dissection
;;;***************dissect_2*******************************************************
(defun C:DISSECT_2()
	(setup_dissect_2)
	(make_jpg)
	(command "_.delay" 500)
	(alert "Step 1: Shade the squareCBHI \n\n(area=c*c)")
		(setq 	trig_CML (shaded_triangle "layer2" pnt_c pnt_m  pnt_l)
			trig_HKJ (shaded_triangle "layer2" pnt_h pnt_k  pnt_j)
			trig_CRM (shaded_triangle "layer3" pnt_c pnt_r  pnt_m)
			trig_HSK (shaded_triangle "layer96" pnt_h pnt_s  pnt_k)
			trig_BMR (shaded_triangle "layer4" pnt_b pnt_m  pnt_r)
			trig_IKS (shaded_triangle "layer4" pnt_i pnt_k  pnt_s)
			trig_BJM (shaded_triangle "layer170" pnt_b pnt_j  pnt_m)
			trig_ILK (shaded_triangle "layer151" pnt_i pnt_l  pnt_k)
		)
	(make_jpg)
	(command "_.delay" 500)
	(make_jpg)
	(command "_.delay" 500)
		(setq pnt_cr1 '(9.0 9.0) pnt_cr2 '(-5.5 -3.8))
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_1" pnt_a whole)
		(command "oops")
		(my_block_insert "WHOLE_1" '(17.0  5.0) 0.75)
		(command "_.zoom" "E")
	(make_jpg)
	(command "_.delay" 500)
	(alert "Step 2:\n Move CML,HKJ,ARM & HSK \nto  square ABED \n\n(area = b*b)" )
		(move_ent trig_CML pnt_l pnt_o n_speed n_div 0 "0")
	(make_jpg)
		(command "_.delay" 2000)
		(move_ent trig_HKJ pnt_j pnt_n n_speed n_div 0 "0")
	(make_jpg)
		;(blink_layer "layer52" 100  2)
		(command "_.delay" 2000)

		(move_ent trig_CRM pnt_c pnt_d n_speed n_div 0 "0")
	(make_jpg)
		(command "_.delay" 500)
		(rotate_ent trig_CRM pnt_d pnt_e 90. 25 25 1)
	(make_jpg)
		(command "_.delay" 2000)
		(move_ent trig_HSK pnt_h pnt_b n_speed n_div 0 "0")
	(make_jpg)
		(command "_.delay" 500)
		(rotate_ent trig_HSK pnt_b pnt_a 90. 25 25 1)
	(make_jpg)
		;(blink_layer "layer52" 100  2)
		(command "_.delay" 2000)
				
	(alert "Step 3:\n Move BMR,IKS ,BJM & ILK to  square ACFG \n\n(area = a*a)" )
	
		(move_ent trig_BJM pnt_j pnt_q n_speed n_div 0 "0")
	(make_jpg)
		(command "_.delay" 2000)
		(move_ent trig_ILK pnt_l pnt_p n_speed n_div 0 "0")
	(make_jpg)
		(command "_.delay" 2000)

		(move_ent trig_BMR pnt_m pnt_f n_speed n_div 0 "0")
	(make_jpg)
		(command "_.delay" 500)
		(rotate_ent trig_BMR pnt_f pnt_g 90. 25 25 1)
	(make_jpg)
		(command "_.delay" 2000)
		(move_ent trig_IKS pnt_k pnt_a n_speed n_div 0 "0")
	(make_jpg)
		(command "_.delay" 500)
		(rotate_ent trig_IKS pnt_a pnt_c 90. 25 25 1)
	(make_jpg)
		(command "_.delay" 2000)
		
		(setq whole (ssget "C" pnt_cr1 pnt_cr2))
		(my_block_def "WHOLE_2" pnt_a whole)
		(command "oops")
		(my_block_insert "WHOLE_2" '(17.0 -4.5) 0.75)
		(command "_.zoom" "_EXTENT")
	(make_jpg)
	(command "_.delay")	
		 (shaded_triangle "layer2" pnt_c pnt_m  pnt_l)
		 (shaded_triangle "layer2" pnt_h pnt_k  pnt_j)
		 (shaded_triangle "layer3" pnt_c pnt_r  pnt_m)
		 (shaded_triangle "layer96" pnt_h pnt_s  pnt_k)
		 (shaded_triangle "layer4" pnt_b pnt_m  pnt_r)
		 (shaded_triangle "layer4" pnt_i pnt_k  pnt_s)
		 (shaded_triangle "layer170" pnt_b pnt_j  pnt_m)
		 (shaded_triangle "layer151" pnt_i pnt_l  pnt_k)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(make_jpg)	
	(alert "It is proved \n\nCBHI = ABED + ACFG\n\n or   c*c = a*a + b*b\n\n\tQ.E.D.")
		(reset_sysvar)
);;;DISSECT_2 - - - main
;;;
;;;
(defun setup_dissect_2()
	(setup_sysvar)
	(setq len_a 5. ;(getreal "\nLength A= ")
		len_b 3. ;(getreal "\nLength B= ")
		len_ab (+ len_a len_b)  len_ab2 (* 3. len_ab)
		len_min (* 0.5 (min len_a len_b))
	)
	(setvar "OSMODE" 0)
	(command "_.ucsicon" "off")
	(setq 	pnt_a '(0 0)  pnt_b (list len_b 0)   pnt_c (list 0 len_a)
		pnt_d (list 0 (- len_b))   pnt_e (list len_b (- len_b))
		pnt_f (list (- len_a) len_a)   pnt_g (list (- len_a) 0)
		pnt_h (list len_ab len_b) pnt_i (list len_a len_ab)
		pnt_k (list len_a len_b)  pnt_m (list len_b len_a)
		pnt_j (inters pnt_b pnt_h pnt_m pnt_k nil)  
		pnt_l (inters pnt_c pnt_i pnt_m pnt_k nil)  
		pnt_n (inters pnt_b pnt_h pnt_a pnt_e nil)
		pnt_o (pld pnt_e pnt_a (distance pnt_a pnt_n))
		pnt_p (inters pnt_c pnt_i pnt_a pnt_f nil)
		pnt_q (pld pnt_a pnt_f (distance pnt_f pnt_p))
		pnt_r (pld pnt_c pnt_b (distance pnt_b pnt_n))
		pnt_s (pld pnt_h pnt_i (distance pnt_b pnt_n))
		pnt_r1 (list len_ab2 (+ len_ab 3.0))
		pnt_r2 (list len_ab2 (- (- len_min ) 5.5) )
	)
	(command "_.layer" "set" "layer8" "")
	(command "_.pline" pnt_a pnt_b pnt_c "c")
	(command "_.pline" pnt_a pnt_b pnt_e pnt_d "c")
	(command "_.pline" pnt_a pnt_c pnt_f pnt_g "c")
	(command "_.pline" pnt_c pnt_b pnt_h pnt_i "c")

	(command "_.pline" pnt_a pnt_b pnt_n "c")
	(command "_.pline" pnt_d pnt_e pnt_o "c")
	(command "_.pline" pnt_a pnt_d pnt_o "c")
	(command "_.pline" pnt_e pnt_b pnt_n "c")

	(command "_.pline" pnt_f pnt_f pnt_p "c")
	(command "_.pline" pnt_a pnt_g pnt_q "c")
	(command "_.pline" pnt_a pnt_c pnt_p "c")
	(command "_.pline" pnt_f pnt_g pnt_q "c")

	(command "_.pline" pnt_c pnt_m pnt_l "c")
	(command "_.pline" pnt_h pnt_k pnt_j "c")
	(command "_.pline" pnt_k pnt_l pnt_i "c")
	(command "_.pline" pnt_b pnt_m pnt_j "c")

	(command "_.pline" pnt_c pnt_m pnt_r "c")
	(command "_.pline" pnt_b pnt_m pnt_r "_c")
	(command "_.pline" pnt_i pnt_k pnt_s "_c")
	(command "_.pline" pnt_h pnt_k pnt_s "_c")
	
	(command "_.layer" "_set" "0" "")
 ;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.50)
	(regapp "my_point")
	
	(make_point "layer8" 0 pnt_a "A"  1 chr_size)
	(make_point "layer8" 0 pnt_b "B"  4 chr_size)
	(make_point "layer8" 0 pnt_c "C"  2 chr_size)
	(make_point "layer8" 0 pnt_d "D"  4 chr_size)
	(make_point "layer8" 0 pnt_e "E"  4 chr_size)
	(make_point "layer8" 0 pnt_f "F"  3 chr_size)
	(make_point "layer8" 0 pnt_g "G"  3 chr_size)
	(make_point "layer8" 0 pnt_h "H"  4 chr_size)
	(make_point "layer8" 0 pnt_i "I"  1 chr_size)
	(make_point "layer8" 0 pnt_j "J"  4 chr_size)
	(make_point "layer8" 0 pnt_k "K"  4 chr_size)
	(make_point "layer8" 0 pnt_l "L"  2 chr_size)
	(make_point "layer8" 0 pnt_m "M"  1 chr_size)
	(make_point "layer8" 0 pnt_n "N"  4 chr_size)
	(make_point "layer8" 0 pnt_o "O"  1 chr_size)
	(make_point "layer8" 0 pnt_p "P"  2 chr_size)
	(make_point "layer8" 0 pnt_q "Q"  1 chr_size)
	(make_point "layer8" 0 pnt_r "R"  4 chr_size)
	(make_point "layer8" 0 pnt_s "S"  1 chr_size)

	;;;zoom to the extent
	(command "_.point" pnt_r1)
	(command "_.point" pnt_r2)
	(command "_.text" '(-1.5 -5.5) chr_size 0. "Dissection  #2")
	(command "_.text" "" "Proof by :  J.E.Boettcher")

	(command "_.zoom" "_EXTENT")
	(setq n_speed 100 n_div 8)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -2)
);dissect_2
;;;
;;;added the next on May 01,2007
;;;
;;;Abe_origami_a	H.Abe's origami solution
;;;
(defun C:Abe_origami_a()
	(setup_Abe)
	(make_jpg)
	(make_jpg)
	(shade_abe)
	(make_jpg)
	(make_jpg)
;move BCH upward
	(alert "       Step 1:\n Move Triangle BCH \n to point A")
		(move_ent trig_1 pnt_b pnt_a n_speed 10 1 "0")
	(make_jpg)
	(make_jpg)
;move CGD & EDGH to the left
	(alert "       Step 2:\n Move  CEH & EDGH\n to point B")
	(setq ss (ssadd)
			ss (ssadd trig_3 ss)
			ss (ssadd quad_4 ss)
		)
		(move_ent ss pnt_c pnt_b n_speed 10 1 "0")
	(make_jpg)
	(make_jpg)
	(command "_.zoom" "E")
	(command "_.regen")
;copy the whole things to the right
	(alert "\nCopy all to the right.")
	(command "_.copy" "all" "" pnt_b '(7.5 0))
	(command "_.zoom" "E")
	(command "_.regen")
	(make_jpg)
	(make_jpg)
;move BCH downward to the original position
	(alert "       Step 1:\n Move Triangle BCH \n back to the original location")
		(move_ent trig_1 pnt_a pnt_b n_speed 10 1 "0")
	(make_jpg)
	(make_jpg)
;move CGD & EDGH to the left
	(alert "       Step 2:\n Move  CEH & EDGH\n back to the original location")
		(move_ent ss pnt_b pnt_c n_speed 10 1 "0")
	(make_jpg)
	(make_jpg)
	(reset_sysvar)

)
;;;
;;;
;;;
;;;Abe_origami_b	H.Abe's origami solution-variation
;;;
(defun C:Abe_origami_b()
	(setup_Abe)
	(make_jpg)
	(make_jpg)
	(command "_.delay" 500)
	(shade_abe)
	(make_jpg)
	(make_jpg)
	(command "_.delay" 500)
;rotate BCH around B
(alert "       Step 1:\n Rotate Triangle ABC \n around point A")
		(rotate_ent trig_1 pnt_b pnt_c 90. 25 25 1)
	(make_jpg)
	(make_jpg)
	(command "_.delay" 500)
;rotate CGD around D
(alert "       Step 2:\n Rotate  CEH & EDGH\n around point D")
	(setq ss (ssadd)
			ss (ssadd trig_3 ss)
			ss (ssadd quad_4 ss)
		)
		(rotate_ent ss pnt_d pnt_c -90. 25 25 1)
	(make_jpg)
	(make_jpg)
	(command "_.delay" 500)
	(command "_.zoom" "E")
	(command "_.regen")
;copy the whole things to the right
	(alert "\nCopy all to the right.")
	(command "_.copy" "all" "" pnt_b '(7.5 0))
	(command "_.zoom" "E")
	(command "_.regen")
	
	(make_jpg)
	(make_jpg)
	(command "_.delay" 500)
;rotate BCH to the original position
	(alert "       Step 1:\n Rotate Triangle BCH \n back to the original location")
		(rotate_ent trig_1 pnt_b pnt_a -90. 25 25 1)
	(make_jpg)
	(make_jpg)
	(command "_.delay" 500)
;rotate CGD & EDGH back to the original locationt
	(alert "       Step 2:\n Rotate  CEH & EDGH\n back to the original location")
		(rotate_ent ss pnt_d pnt_a 90. 25 25 1)
	(make_jpg)
	(make_jpg)
	(command "_.delay" 500)
	(make_jpg)
	(make_jpg)
	(command "_.delay" 500)
	(reset_sysvar)

)
;;;
;;;
(defun setup_Abe()
	(setup_sysvar)
	;;;mark the points
	(set_txstyle "arial")
	(setq chr_size 0.25   n_speed 50	ndiv 6	)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -2)
	(setq pnt_a '(0 5) pnt_b '(0 0) pnt_c '(5 0)
		pnt_d '(5 5) pnt_e '(5 2)
		pnt_f '(3 5) pnt_i '(0 3)
		pnt_g (inters pnt_c pnt_f pnt_d pnt_i nil)
		pnt_h (inters pnt_c pnt_f pnt_b pnt_e nil)
		low_left '(-1.75 -0.25) up_right '(5.5 7.0)
	)
	(command "_.zoom" "_W" low_left up_right)

;;mark grid ID
	(mark_id pnt_a "A"  3 chr_size)
	(mark_id pnt_b "B"  3 chr_size)
	(mark_id pnt_c "C"  1 chr_size)
	(mark_id pnt_d "D"  1 chr_size)


	(command "_.pline" pnt_a pnt_b pnt_c pnt_d "cl")

;;draw a line from B to a point E on CD
	(alert "\nLine BE")
	(make_line_1 "0" 1 pnt_b pnt_e)
	(mark_id pnt_e "E"  1 chr_size)
;;draw a line from C to a point F on AD perpendicular to line BE
	(alert "\nLine CF perpendicular to BE.")
	(make_line_1 "0" 1 pnt_c pnt_f)
	(mark_id pnt_f "F"  2 chr_size)
;;intersecting point is H.
	(alert "\nH is the point of intersection.")
	(mark_id pnt_h "H"  3 chr_size)
;;draw a line DG D normal to line CF.
	(alert "\nLine DG normal to CF")
	(make_line_1 "0" 0 pnt_d pnt_g)
	(mark_id pnt_g "G"  3 chr_size)
		
	;(command "_.zoom" "E")
	(command "_.regen")
);setup_Abe
;;;
;;;
;;;
(defun shade_abe()	
  ;;;draw shaded triangles & quadrilaterals
	(setq trig_1 (shaded_triangle "layer2" pnt_b pnt_c pnt_h)
	 	trig_2 (shaded_triangle "layer3" pnt_d pnt_f pnt_g)
	 	trig_3 (shaded_triangle "layer4" pnt_c pnt_e pnt_h)
		quad_4 (shaded_quad "layer5" pnt_e pnt_d pnt_g pnt_h)
		;;quad_5 (shaded_quad "layer9" pnt_a pnt_b pnt_h pnt_f)
	)
;;;shade polygon DHGFE by 45 deg by 0.2 inch cross hatch
		(command "_.pline" pnt_a pnt_b pnt_h pnt_f "_cl")
		(setq pl_ABHF (entlast))
		(command "_.hatch" "_U" 45. 0.2 "_N" pl_ABHF "")
	
);;
;;;
;;;CIRCLE_TEXT		text in a circle
;;;
(defun circle_text(text text_size circle_center  / 
			circle_radius qtr_text half_text text_pnt)
	(setq   qtr_text (* 0.25 text_size)
		half_text (* 0.5 text_size)
		circle_radius (* 0.75 text_size)
		text_pnt (shift_pnt circle_center (list (- qtr_text) (- half_text) ))
	)
	(make_circle_1 "0" 0 circle_center circle_radius)
	(textdisplay text text_pnt text_size 0.)
);;
;;;
;;;
(defun c:Abe_origami()
	(setup_Abe)
	(circle_text "1" 0.25 '(2.4 1.25))
	(circle_text "2" 0.25 '(3.5 2.9))
	(circle_text "3" 0.25 '(4.1 4.3))

)
;;;
(princ)