Теорема о параллелограмме

Горшенин Дмитрий/Param.rkt

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+#lang racket/base
+
+(define (square x) (* x x))
+
+(define (lengths_eq x1 y1 x2 y2 x3 y3 x4 y4)
+(if (equal? (+ (square(- x1 x2)) (square(- y1 y2))) 
+(+ (square(- x3 x4)) (square(- y3 y4)))) 
+(displayln "Lines (1,2) and (3,4) have the same length.") 
+(displayln "Lines (1,2) and (3,4) do not have the same length.")))
+
+(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 (parallel x1 y1 x2 y2 x3 y3 x4 y4)
+(if (equal? (* (- x1 x2) (- y3 y4)) (* (- y1 y2) (- x3 x4))) 
+(displayln "Lines (1,2) and (3,4) are parallel.") 
+(displayln "Lines (1,2) and (3,4) are not parallel.")))
+
+
+(define (is_intersection x1 y1 x2 y2 x3 y3 x4 y4 x5 y5)
+(if (and (equal? (* (- x1 x2) (- y2 y3)) (* (- y1 y2) (- x2 x3)) ) 
+(equal? (* (- x1 x4) (- y4 y5)) (* (- y1 y4) (- x4 x5)) ) ) 
+(displayln "Lines (2,3) and (4,5) meet at point 1.") 
+(displayln "Lines (2,3) and (4,5) do not intersect at point 1.")))
+
+(define (is_midpoint x1 y1 x2 y2 x3 y3)
+(if (and (equal? (* 2 x1) (+ x2 x3)) (equal? (* 2 y1) (+ y2 y3)))
+(displayln "Point 1 is the midpoint of line (2,3).")
+(displayln "Point 1 is not the midpoint of line (2,3).")
+))
+
+
+(define (grobner_decide a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y)
+(if (and (parallel a_x a_y b_x b_y d_x d_y c_x c_y) 
+    (parallel a_x a_y d_x d_y b_x b_y c_x c_y)
+    (is_intersection e_x e_y a_x a_y c_x c_y b_x b_y d_x d_y))
+  (begin 
+  (lengths_eq a_x a_y e_x e_y e_x e_y c_x c_y) 
+  (displayln "This is a parallelogram.") 
+  )
+  (displayln "This is not a parallelogram.") 
+))
+
+
+(define (grobner_decide_coll a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y)
+(if (and (parallel a_x a_y b_x b_y d_x d_y c_x c_y) 
+    (parallel a_x a_y d_x d_y b_x b_y c_x c_y)
+    (is_intersection e_x e_y a_x a_y c_x c_y b_x b_y d_x d_y) 
+    (not (collinear a_x a_y b_x b_y c_x c_y))
+    )
+  (begin 
+  (lengths_eq a_x a_y e_x e_y e_x e_y c_x c_y) 
+  (displayln "This is a parallelogram.") 
+  )
+  (displayln "This is not a parallelogram.") 
+))
+
+
+(define (grobner_decide_mid a_x a_y b_x b_y c_x c_y d_x d_y m_x m_y)
+(if (and (is_midpoint m_x m_y a_x a_y c_x c_y) 
+    (not (perpendicular a_x a_y c_x c_y m_x m_y b_x b_y)))
+    (begin 
+  (lengths_eq a_x a_y b_x b_y b_x b_y c_x c_y) 
+  (displayln "This is a parallelogram.") 
+  )
+  (displayln "This is not a parallelogram.") 
+))
+
+
+
+(grobner_decide 0 0 1 2 4 2 3 0 2 1)
+(grobner_decide_coll 0 0 1 2 4 2 3 0 2 1)
+(grobner_decide_mid 0 0 1 2 4 2 3 0 2 1)

Горшенин Дмитрий/README.md

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+# Теорема о параллелограмме
+## Ссылка на видеоразбор
+https://youtu.be/YGmrNKP__bg
+## Код из сайта
+	START_INTERACTIVE;;
+	(grobner_decide ** originate)
+ 	<<is_midpoint(m,a,c) /\ perpendicular(a,c,m,b)
+   	==> lengths_eq(a,b,b,c)>>;;
+
+	#Parallelogram theorem
+
+	grobner_decide ** originate)
+ 	<<parallel(a,b,d,c) /\ parallel(a,d,b,c) /\
+   	is_intersection(e,a,c,b,d)
+   	==> lengths_eq(a,e,e,c)>>;;
+
+	(grobner_decide ** originate)
+ 	<<parallel(a,b,d,c) /\ parallel(a,d,b,c) /\
+   	is_intersection(e,a,c,b,d) /\ ~collinear(a,b,c)
+   	==> lengths_eq(a,e,e,c)>>;;
+	END_INTERACTIVE;;
+