;;;Generalized Pythagoren theorem
;; "The sum of the area of two squares,whose sides are the
;;  lenghts of the two diagonals of a parallelogram, is equal
;;  to the sum of the areas of four squares, whose sides are
;;  its four sides."
;; Ref. David S. Wise
;; "Proofs without Words II" , by Roger B. Nelson , page 9.
;; Originally from "Mathematics Magazine, Vol.71, no.1 (Feb 1998), p.64
;; Programmed by Takaya Iwamoto
;; Nov 2-7 ,2003
;;;GEN_PYTHAGORAS.LSP
;;
(defun c:gen_pythagoras()
	
	(setup_genpyth)
	(draw_squares)
	(sqr_id)
	(command "_.zoom" "_E")
	(command "_.regen")
	(shaded_pl)
	(copy_whole)
	(move_pl)
	(final_text2)	;;modified
	
	(reset_sysvar)
);;;GEN_PYTHAGORAS
;;;
;;;
(defun setup_genpyth()
	(setup_sysvar)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -3)
	(setq lower_left '(-6 -5) upper_right '(6 5))
	(command "_.zoom" "W" lower_left upper_right)
	(alert "\nDefine your parallelogram ABCD")
	(parlgrm1)
);;;
;draw parallelogram
;                 pnt1: lower left corner
;                 pnt3: upper right corner
;                 theta oblique angle (if = 90. rectangle)
;                 draw lines counter clock wise.
(defun parlgrm1 ()
	;(alert "\nFirst point A of parallelogram ABCD")
    (command "_.point" (setq pnt_a '( 0 0)) )
	(mark_id pnt_a "A" 3 0.25)
		;(command "_.move" (entlast) "" pnt_a PAUSE)
    ;(command "_.point" (setq pnt_b (getpoint pnt_a  "\nSecond corner of rectangle: ")) )
	(command "_.point" (setq pnt_b '( 2.75 0)) )
	(mark_id pnt_b "B" 3 0.25)
		;(command "_.move" (entlast) "" pnt_b PAUSE)
	(command "_.line" pnt_a pnt_b "")
		(setq line_ab (entlast))
    (command "_.point" (setq pnt_c (getpoint pnt_b "\ndiagonal point C:" )) )
	(mark_id pnt_c "C" 3 0.25)
		;(command "_.move" (entlast) "" pnt_c PAUSE)
    (command "_.copy" line_ab "" pnt_b pnt_c)
    (command "_.point" (setq pnt_d (cdr (assoc 10 (entget (entlast)) ))) )
	(entdel line_ab) 
	
    (command "_.pline" pnt_a pnt_b pnt_c pnt_d "cl")
	(setq ABCD (entlast))
	(mark_id pnt_d "D" 3 0.25)
		;(command "_.move" (entlast) "" pnt_d PAUSE)
);;;
;;;
;;;DRAW_SQUARES	---draw 4 squares on 4 sides of the parallelogram
;;;
(defun draw_squares()
	(command "polygon" 4 "Edge" pnt_b pnt_a)
		(setq BAEF (entlast))
	(command "polygon" 4 "Edge" pnt_c pnt_b)
		(setq CBGH (entlast))
	(command "polygon" 4 "Edge" pnt_d pnt_c)
		(setq DCIJ (entlast))
	(command "polygon" 4 "Edge" pnt_a pnt_d)
		(setq ADKL (entlast))
);;;
;;;
;;;
(defun sqr_id()
	(alert "\nMark Grid ID from E to L")
	(setq rev_list (reverse (entget BAEF))	
		pnt_f (cdr (nth 4 rev_list))  pnt_e (cdr (nth 8 rev_list))

		rev_list (reverse (entget CBGH))	
		pnt_h (cdr (nth 4 rev_list))  pnt_g (cdr (nth 8 rev_list))

		rev_list (reverse (entget DCIJ))	
		pnt_j (cdr (nth 4 rev_list))  pnt_i (cdr (nth 8 rev_list))
		
		rev_list (reverse (entget ADKL))	
		pnt_l (cdr (nth 4 rev_list))  pnt_k (cdr (nth 8 rev_list))
		
		
	)
	(mark_id pnt_e "E" 3 0.25)
		;(command "_.move" (entlast) "" pnt_e PAUSE)
	(mark_id pnt_f "F" 3 0.25)
		;(command "_.move" (entlast) "" pnt_f PAUSE)
	(mark_id pnt_g "G" 3 0.25)
		;(command "_.move" (entlast) "" pnt_g PAUSE)
	(mark_id pnt_h "H" 3 0.25)
		;(command "_.move" (entlast) "" pnt_h PAUSE)
	(mark_id pnt_i "I" 3 0.25)
		;(command "_.move" (entlast) "" pnt_i PAUSE)
	(mark_id pnt_j "J" 3 0.25)
		;(command "_.move" (entlast) "" pnt_j PAUSE)
	(mark_id pnt_k "K" 3 0.25)
		;(command "_.move" (entlast) "" pnt_k PAUSE)
	(mark_id pnt_l "L" 3 0.25)
		;(command "_.move" (entlast) "" pnt_l PAUSE)

	(command "_.point" (setq pnt_m (plt pnt_i pnt_j 2.0)) )
		(mark_id pnt_m "M" 3 0.25)
		;(command "_.move" (entlast) "" pnt_m PAUSE)

	;(command "_.copy" pnt_m "" pnt_j pnt_k)
		(setq pnt_mid_mk (plt pnt_k pnt_m 0.5)
			pnt_n (plt pnt_j pnt_mid_mk 2.0))
		(mark_id pnt_n "N" 3 0.25)
		;(command "_.move" (entlast) "" pnt_n PAUSE)
	(make_line_1 "0" 8 pnt_h pnt_i)
	(make_line_1 "0" 8 pnt_n pnt_l)
	(command "_.pline" pnt_n pnt_k pnt_j pnt_m "cl")
	;(make_line_1 "0" 8 pnt_h pnt_i)
	;(make_line_1 "0" 8 pnt_n pnt_l)
);;SQR_ID	writing GRID ID
;;;
;;;SHADED_PL
;;;
(defun shaded_pl()
	(setq upper_right (getvar "EXTMAX") lower_left (getvar "EXTMIN")
		y_b (cadr pnt_b) y_ur (cadr upper_right)
		l_ab (distance pnt_a pnt_b) l_bc (distance pnt_b pnt_c)
		del_y (+ l_bc (max y_ur (- y_ur y_b)))
		new_a (list (- l_bc) del_y) new_b (shift_pnt pnt_b new_a)
		new_c (shift_pnt pnt_c new_a) new_d (shift_pnt pnt_d new_a)
		new_aa (list l_ab del_y ) new_bb (shift_pnt pnt_b new_aa)
		new_cc (shift_pnt pnt_c new_aa) new_dd (shift_pnt pnt_d new_aa)
	)
	(alert "\nTwo ways to divide the parallelogram")
	(command "_.copy" ABCD "" pnt_a new_a)
		(setq new_1 (entlast))
	(command "_.copy" ABCD "" pnt_a new_aa)
		(setq new_2 (entlast))
	(shaded_triangle "layer5" new_a new_b new_d)
		(setq new_ABD (entlast))
	(shaded_triangle "layer1" new_aa new_bb new_cc)
		(setq new_ABC (entlast))
	(command "_.zoom" "E")
	(command "_.delay" 1000)
	(alert "\nFill with shaded triangles and quad")
	(shaded_triangle "layer5" pnt_k pnt_n pnt_l)
		(setq KNL (entlast))
	(command "_.delay" 500)
	(shaded_triangle "layer5" pnt_k pnt_j pnt_d)
		(setq KJD (entlast))
	(command "_.delay" 500)
	(shaded_triangle "layer5" pnt_f pnt_g pnt_b)
		(setq FGB (entlast))
	(command "_.delay" 500)
	(shaded_triangle "layer1" pnt_l pnt_a pnt_e)
		(setq LAE (entlast))
	(command "_.delay" 500)
	(shaded_triangle "layer1" pnt_c pnt_h pnt_i)
		(setq CHI (entlast))
	(command "_.delay" 500)
	(shaded_triangle "layer1" pnt_a pnt_b pnt_c)
		(setq ABC (entlast))
	(command "_.delay" 500)
	(shaded_triangle "layer1" pnt_c pnt_d pnt_a)
		(setq CDA (entlast))
	(command "_.delay" 500)
	(shaded_quad "layer3" pnt_k pnt_j pnt_m pnt_n)
		(setq KJMN (entlast))
	(command "_.delay" 500)

	(command "_.pline" pnt_a "W" 0.02 "" pnt_c "")
	(command "_.delay" 500)
	(setvar "PLINEWID" 0.0)
	
	
);;;SHADED_PL
;;;
;;;COPY_WHOLE
;;;
(defun copy_whole(  / whole dx)
	(setq dx (- (car upper_right) (car lower_left)))
	(alert "\nCopy the whole figure to the right")
		(setq whole (ssget "C" upper_right lower_left ))
		(my_block_def "WHOLE_1" lower_left whole)
		(command "oops")
		(my_block_insert "WHOLE_1" (shift_pnt lower_left (list dx 0)) 1.0)
		(command "_.zoom" "E")
);;;COPY_WHOLE
;;;
;;;MOVE_PL	Move shaded triangles & parallelogram
;;;
(defun move_pl( / n_speed ndiv ncolor layer_name n_repeat)
	(alert "\nMove shaded triangles & parallelogram")
	(setq n_speed 200 ndiv 6 ncolor 1 layer_name "0"  n_repeat 5 )
	;FGB	pnt_f to pnt_e
	(move_ent FGB pnt_f pnt_e n_speed ndiv ncolor layer_name)
	(command "_.delay" 1000)
	;KJMN	pnt_k to pnt_f
	(move_ent KJMN pnt_k pnt_f n_speed ndiv ncolor layer_name)
	(command "_.delay" 1000)
	;KNL	pnt_k to pnt_j
	(move_ent KNL pnt_k pnt_j n_speed ndiv ncolor layer_name)
	(command "_.delay" 1000)
	;KJD	pnt_k to pnt_l
	(move_ent KJD pnt_k pnt_l n_speed ndiv ncolor layer_name)
	(command "_.delay" 1000)
	;ABC	pnt_b to pnt_g
	(move_ent ABC pnt_b pnt_g n_speed ndiv ncolor layer_name)
	(command "_.delay" 1000)
	;CHI	rotate around pnt_i by -90. degrees
	(rotate_ent CHI pnt_i pnt_c -90. n_speed n_repeat ncolor)
	(command "_.delay" 1000)
	;CDA	move pnt_d to pnt_a, then 90 deg rotation abput pnt_a
	
	(rotate_ent CDA pnt_d pnt_c 90. n_speed n_repeat ncolor)
	(command "_.delay" 1000)
	(move_ent CDA pnt_d pnt_a n_speed ndiv ncolor layer_name)
	(command "_.delay" 1000)
);;
;;;
;;;FINAL_TEXT
;;;
(defun final_text()
	(setq dx (- (car upper_right) (car lower_left))
		p1 (list (+ (car new_cc) (* 0.5 l_bc)) (cadr upper_right) )
		p2 (list (* 1.75 dx) (cadr new_dd) )
		text_height (/ (- (cadr new_dd) (cadr upper_right)) 10.)
		text_loc0(shift_pnt p1 (list text_height (* 8.5 text_height)))
	)
	(command "_.rectangle" p1 p2)
	;(setq final_msg (list " The sum of the area of two squares,"
	;		      "whose sides are the lengths of the two"
	;		      "diagonals of a parallelogram, is equal"
	;		      "to the sum of the areas of four squares,"
	;		      "whose sides are its four sides.")
	;)
	(setq final_msg  "A + B = 2 (a + b)")
	;(setq nline 0)
	;(repeat 5
	 ; (setq line_text (nth nline final_msg) 
	;	text_loc (shift_pnt text_loc0 (list 0 (- (* 2 nline text_height))))
	 ;  )
		
	 ;  (textdisplay line_text text_loc 0.75 0. )
	 ;  (setq nline (1+  nline))
	;(princ text_loc)(terpri)
	; );;end of repeat
	(textdisplay final_msg text_loc0 0.75 0.)
	(command "_.zoom" "E")

);;
;;;FINAL_TEXT2
;;;
(defun final_text2()
;draw TEXTS A,B,a b for area identification
	
	(setq dx (- (car upper_right) (car lower_left))
		p1 (list (+ (car new_cc) (* 0.2 l_bc)) (cadr new_aa) )
		p2 (list (* 1.55 dx) (cadr new_dd) )
		text_height (/  (abs (- (cadr new_dd) (cadr new_bb) ) ) 2.5)
		text_loc (shift_pnt p1 '(0.1 0.2))
		dx (- dx text_height)
	)
	(setq mid_lm (plt pnt_l pnt_m 0.5)
		mid_cj (plt pnt_c pnt_j 0.3)
		mid_af (plt pnt_a pnt_f 0.6)
		mid_ak (plt pnt_a pnt_k 0.4)
		mid_cg (plt pnt_c pnt_g 0.6)
		pnt_cj (shift_pnt mid_cj (list dx 0))
		pnt_af (shift_pnt mid_af (list dx 0))
		pnt_ak (shift_pnt mid_ak (list dx 0))
		pnt_cg (shift_pnt mid_cg (list dx 0))
	)
	(command "_.rectangle" p1 p2)
;;change color to yellow
	(set_color "yellow")
	(textdisplay "A" mid_lm text_height 0.)
	(textdisplay "B" mid_cj text_height 0.)
	(textdisplay "a" pnt_af text_height 0.)
	(textdisplay "a" pnt_cj text_height 0.)
	(textdisplay "b" pnt_ak text_height 0.)
	(textdisplay "b" pnt_cg text_height 0.)
	
	(setq final_msg  "A + B = 2 (a + b)")
		
	(textdisplay final_msg text_loc text_height 0.)
	(command "_.zoom" "E")
	(set_color "BYLAYER")

);;