| No Solution Yet | Submitted by Danish Ahmed Khan |
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proof
|
 | Comment 1 of 2 |
Claim: for all triangles there are two sides, a and b, such that:
(√5-1)/2<a/b<(√5+1)/2
0.618 < a/b < 1.618
"suppose not"
wlog, label the sides so that in length, they are a <= b <= c.
and wlog scale the triangle so that b = 1.
Now suppose a/b = 0.618 and b/c = 0.618.
Then a = 0.618, b = 1, c = 1.618; c = a+b a triangle with zero area.
If the ratios are even smaller, the result is even worse, say a/b is 0.6
Now a = 0.6, b = 1, c = 1.6666; c > a+b another impossible triangle.
| Posted by Larry on 2025-05-26 14:25:40 |
