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Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

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The incircles of 3, 4, 5 and of 5, 12, 13 right angled triangles have radii 1 and 2 units respectively. What about triangles with an inradius of 3, 4 or 5 or ...?

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If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle?

Few and Far Between?

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This open investigation follows on from the problem Generating Triples. It can be taken to many levels of complexity.

The well-known Pythagorean Triple ${3,4,5}$ has the property that the two smaller numbers differ by 1.
 
Can you find any more Pythagorean Triples where the two smaller numbers differ by 1? Investigate your findings.

 

For more investigations see our Stage 5 pages.