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