Pythagorean Triangles with Consecutive Values

This Demonstration shows the values of a right triangle with integer sides for which the difference between the lengths of the hypotenuse and the long leg is equal to one, as well as the more complicated case where the difference between the long leg and the short leg is one.

THINGS TO TRY

SNAPSHOTS

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DETAILS

The values can be computed from the following expressions; here is a positive integer.
For the first case,
;
.
For the second case,
;
.
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