Problem 2024. Triangle sequence
A sequence of triangles is constructed in the following way:
1) the first triangle is Pythagoras' 3-4-5 triangle
2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle
3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.
Each triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.
What is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?
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Kirk Roffi
on 11 Dec 2023
Advised to carefully read the problem description and notice that the second to last sentence offers a code structure. -KR
Kshitij Patki
on 20 Mar 2025
wow
Kallen
on 17 Jul 2025 at 17:18
Nice! Fun to relate a geometric procedure to the fibonacci sequence.
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