# Twin and Nearly Twin Pythagorean Triples

Twin and Nearly Twin Pythagorean Triples

A Pythagorean triple is an ordered set of three positive integers that are the side lengths of a Pythagorean triangle, so that +=. A twin Pythagorean triple is a Pythagorean triple in which two elements differ by one. In a twin leg-leg Pythagorean triple, and differ by 1; in a twin leg-hypotenuse or ; in a nearly twin leg-hypotenuse triple, or .

{x,y,z}

2

x

2

y

2

z

x

y

z-x=1

z-y=1

z-x=2

z-y=2

The twin triples ={3,4,5} and ={4,3,5} are called the base twin triples. This Demonstration shows that all twin Pythagorean triples can be calculated by a base twin repeatedly multiplied on the right times by a carefully chosen matrix.

T

1

T

2

n