Pythagorean Theorem
Relationship between the lengths a, b and c of the sides of a right triangle such that a2 = b2 + c2, where a represents the length of the hypotenuse and b the lengths of the two sides of the right angle.
This is a concrete representation of the use of the Pythagorean theorem, where : [latex]{2}^{2} + {3}^{2} = (\sqrt{13})^{2}[/latex]
A Pythagorean triangle is a right triangle whose side lengths are expressed as whole numbers.
The triple of numbers obtained is a Pythagorean triple.
These measures can be determined by choosing two whole numbers m and n, with m > n, and applying the following relationship :
A Pythagorean triangle is a right triangle whose side lengths are expressed as whole numbers.
The triple of numbers obtained is a Pythagorean triple.
These measures can be determined by choosing two whole numbers m and n, with m > n, and applying the following relationship :
- a = k(m[latex]^{2}[/latex] – n[latex]^{2}[/latex])
- b = k(2mn)
- c = k(m[latex]^{2}[/latex] + n[latex]^{2}[/latex])
- Pythagorean triples can be determined by replacing k with the sequence of whole numbers. If m = 5, n = 2 and k = 3, we obtain : a = 42, b = 40 and c = 58. This can be verified as follows : [latex]42^{2} + 40^{2} = 58^{2}[/latex] and 1764 + 1600 = 3364.