All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
How to do it? (Posted on 2018-09-05) Difficulty: 3 of 5
Provide detailed instructions how to construct a right triangle with edge lengths in geometric progression.

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
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

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information