Provide detailed instructions how to construct a right triangle with edge lengths in geometric progression.
(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 (377^2233^2) 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 nearinteger third side of 58981.
But why settle for a nearinteger value? By paity of reasoning, just select 3 and 5 as the Fibonacci numbers: (5^23^2) = 4^2, and we are done.
Edited on September 5, 2018, 12:32 pm

Posted by broll
on 20180905 12:14:59 