Теорема Симсона

Погребицкий Евгений/README.md

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+# Теорема Симсона
+## Ссылка на видеоразбор
+https://youtu.be/_ewjiWIH0VY
+## Код из книги
+	START_INTERACTIVE;;
+	let simson =
+	 <<lengths_eq(o,a,o,b) /\
+  	 lengths_eq(o,a,o,c) /\
+  	 lengths_eq(o,a,o,d) /\
+  	 collinear(e,b,c) /\
+  	 collinear(f,a,c) /\
+  	 collinear(g,a,b) /\
+  	 perpendicular(b,c,d,e) /\
+  	 perpendicular(a,c,d,f) /\
+  	 perpendicular(a,b,d,g)
+  	 ==> collinear(e,f,g)>>;;
+
+	let vars =
+ 	["g_y"; "g_x"; "f_y"; "f_x"; "e_y"; "e_x"; "d_y"; "d_x"; "c_y"; "c_x";
+  	"b_y"; "b_x"; "o_x"]
+	and zeros = ["a_x"; "a_y"; "o_y"];;
+
+	wu simson vars zeros;;
+

Погребицкий Евгений/simson.rkt

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+#lang racket/base
+
+(define (square x) (* x x))
+
+(define (lengths_eq x1 y1 x2 y2 x3 y3)
+(if (equal? (+ (square(- x1 x2)) (square(- y1 y2))) (+ (square(- x3 x1)) (square(- y3 y1)))) 
+#t #f
+))
+
+(define (collinear x1 y1 x2 y2 x3 y3)
+(if (equal? (* (- x1 x2) (- y2 y3)) (* (- y1 y2) (- x2 x3))) 
+#t #f
+))
+
+(define (perpendicular x1 y1 x2 y2 x3 y3 x4 y4)
+(if (equal? (+ (* (- x1 x2) (- x3 x4)) (* (- y1 y2) (- y3 y4))) 0 ) 
+#t #f
+))
+
+
+
+(define (simson o_x o_y a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y f_x f_y g_x g_y)
+(if (and 
+    (lengths_eq o_x o_y a_x a_y b_x b_y) 
+    (lengths_eq o_x o_y a_x a_y c_x c_y) 
+    (lengths_eq o_x o_y a_x a_y d_x d_y) 
+    (collinear e_x e_y b_x b_y c_x c_y)
+    (collinear f_x f_y a_x a_y c_x c_y)
+    (collinear g_x g_y a_x a_y b_x b_y)
+    (perpendicular b_x b_y c_x c_y d_x d_y e_x e_y)
+    (perpendicular a_x a_y c_x c_y d_x d_y f_x f_y)
+    (perpendicular a_x a_y b_x b_y d_x d_y g_x g_y))
+    
+    (begin (displayln "3 Points lie on one line.") (collinear e_x e_y f_x f_y g_x g_y)
+    ) (displayln "3 Points do not lie on one line.")
+))
+
+(simson 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 )