The tutor shows that yesterday’s formulas to generate Pythagorean triples are valid. In yesterday’s post I showed a way to generate Pythagorean triples x, y, z from an odd number n: x n y (n²-1)/2 z (n²+1)/2 Let’s make sure …
Math: Pythagorean triples: proof of yesterday’s generating formulas Read more »
The tutor continues his discussion about Pythagorean triples. Back in my January 7, 2016 post I brought up Pythagorean triples, which are all-integer solutions to x² + y² = z² The equation above is based on the familiar a² + …
Math: number theory: a formula for generating Pythagorean triples Read more »
Continuing about Pythagorean triples, the tutor considers the isosceles case. In my previous post I discussed all-integer solutions to the Pythagoras equation a^2 + b^2 =c^2 Such solutions are often called Pythagorean triples. Presently we consider the possibility of Pythagorean …
Math: Are there (integer) Pythagorean triples with two equal sides? Read more »
The tutor gives a few integer solutions to a2+b2=c2. All-integer solutions to a2+b2=c2 are called Pythagorean triples. They are comparativeley rare. Here are three sets I know: 3,4,5 5,12,13 8,15,17 From the sets above, infinitely more can be generated: multiplying …