Here are sets of 3 Pythagorean triangles with equal perimeters and area in arithmetic progression.

Note that the perimeters are multiples of 120.

Why does it work with the multiples of 120? 38 more words

Here are sets of 3 Pythagorean triangles with equal perimeters and area in arithmetic progression.

Note that the perimeters are multiples of 120.

Why does it work with the multiples of 120? 38 more words

Let be the sides of triangle such that are in A.P.

Prove that the cotangent of the interior angles are also in A.P.

Find three numbers in arithmetic progression such that

(1)

(2)

(3)

, ,

where the common difference is

(1) ………..

(2) ………..

(3) ………..

, , are in A.P., that is, … 69 more words

We want , , to be in arithmetical progression

and the sum to be a square number

Here are the first few solutions:

**(14, 26, 34)** 38 more words

In part 1, I started a discussion on the ordered triples of integers whose squares form an arithmetic progression.

In other words,

, or equivalently… 113 more words

Let’s look at ordered triples of integers whose squares form an arithmetic progression.

In other words,

, or equivalently

The solutions are of the form… 66 more words