Pythagorean Triples
Essay Preview: Pythagorean Triples
Report this essay
Pythagorean Triples are a set of three integers that consist of a, b, c which form the sides of a right angled triangle. The smallest Pythagorean triple is the set of numbers 3, 4, and 5. Pythagorean Theorem relationship of the sides of a right triangle is attributed to the Greek mathematician and philosopher Pythagoras (ca.585-ca. 500 B.C.E.), and it bears his name (Allen G. Bulman (2005) p.471). He felt that everything could be explained by numbers (Michael Petrov 2011). Pythagorean triple is a set of three positive whole numbers a, b, and c that are the lengths of sides of a right triangle.
These formulas represent every Pythagorean triple. Given a Pythagorean Triple, we can recover d, r, and s using d = GCD (a, b, c), r = sqrt ([c + a]/ [2d]), s = sqrt ([c – a]/ [2d]). The radius is always a whole number, and is given by the formula s(r-s) d. The other formula is a+ b=c. The five Pythagorean Triples: (6,8,10) (9,12,15) (12,16,20) (15,20.25) (18,24,30). That were generated will be verified by the Pythagorean Theorem (Allen G. Bluman 2005 p.471).
(6,8,10) c=a^2+b^2
=6^2+ 8^2
=36+64
= 100
c=√100
(9,12,15 c=a^2+b^2
=9^2+ 〖12〗^2
=81+144
c=√225 = 15
(12,16,20)〖 12〗^2+ 〖16〗^2=〖20〗^2
144+256
400=400
√400=40
((15,20,25)
a^2+b^2=c^2
〖15〗^2+ 〖20〗^2
=225+400
c =√625
(18,24,30)