Теорема Пифагора в картинках
Отсюда
Вариант 1
Вариант 2
I like this proof of Pythagoras' Theorem (image taken from www.wisfaq.nl):
The key to understanding this is to realize that the inner quadrilateral must be a square - the sides are equal in length (obviously) and each of its angles is 90∘ because the two angles on either side sum to 90∘, and the sum of the three angles is 180∘. The area of this square is c2.
The outer square's area is (a+b)2, which is c2 plus 2ab which is the total area of the four triangles, each of area 12ab.
(a+b)2=c2+2ab
a2+b2+2ab=c2+2ab
a2+b2=c2, which is Pythagoras' theorem.
Вариант 3
A well-known visual to explain (a+b)2=a2+2ab+b2:
$(a+b)^2 = a^2+2ab+b^2$
Вариант 1
Вариант 2
I like this proof of Pythagoras' Theorem (image taken from www.wisfaq.nl):
The key to understanding this is to realize that the inner quadrilateral must be a square - the sides are equal in length (obviously) and each of its angles is 90∘ because the two angles on either side sum to 90∘, and the sum of the three angles is 180∘. The area of this square is c2.
The outer square's area is (a+b)2, which is c2 plus 2ab which is the total area of the four triangles, each of area 12ab.
(a+b)2=c2+2ab
a2+b2+2ab=c2+2ab
a2+b2=c2, which is Pythagoras' theorem.
Вариант 3
A well-known visual to explain (a+b)2=a2+2ab+b2:
$(a+b)^2 = a^2+2ab+b^2$