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 How to do it? (Posted on 2018-09-05)
Provide detailed instructions how to construct a right triangle with edge lengths in geometric progression.

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 re(2): A Start- I concur | Comment 3 of 11 |
(In reply to re: A Start- I concur by Steven Lord)

The 3,4,5 triangle qualifies.

More specifically, approximations to the golden ratio (as suggested by the equation b^2 = b + 1) exist between successive members of the Fibonacci Series. e.g. 377=233*phi. With these numbers, the third side has a value of (377^2-233^2) or around 296.38. Checking: 296 =  1.27*233, 377=1.27*296, as required.

So for example, we could select side lengths of 75025 and 46368 and obtain a near-integer third side of 58981.

But why settle for a near-integer value? By paity of reasoning, just select 3 and 5 as the Fibonacci numbers: (5^2-3^2) = 4^2, and we are done.

Edited on September 5, 2018, 12:32 pm
 Posted by broll on 2018-09-05 12:14:59

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