Code Competition Round 1

The Pythagorean Theorem

By Christine

The Pythagorean Theorem, discovered by greek mathematician Pythagoras, is a famous mathematical equation showing the relation between the legs and hypotenuse of a right triangle. It shows that a² + b² = c².

The Theorem:

Let a and b be the legs of a right triangle and c be the hypotenuse:

Then a² + b² = c².

Proof of the Theorem:

In the diagram above, the area of the large square is (a + b)², though it is also equal to c² + 4 • 1/2 • a • b, since c² is the area of the small square and 1/2 • a • b is the area of each triangle, and there are 4 right triangles in the large square. Using the distributive law, it would be written like this:

(a + b)²
= (a + b)(a + b)
= (a + b)a + (a + b)b
= a² + ab + b² + ab
= a² + 2ab + b²

So
a² + 2ab + b² = c² + 2ab

and
a² + 2ab + b² - 2ab = c²

So
a² + b² = c²

3, 4 and 5 is a Pythagorean Triple because it satisfies the equation a² + b² = c².

© Christine 2018