Puzzle time - square or circle?

[Aqua Letifer]

Circle.

[jon-nyc]

Circle.

|| ||

[taiwan_girl]

||I guess circle, but just by eyeball it.||

[Axtremus]

||Circle
See "proof" in this PDF file. ||

[Klaus]

@jon-nyc said in Puzzle time - square or circle?:

Circle.

Jon, you can eyeball that your ratio cannot be correct. According to your calculation, the circumference of the circle would be more than twice that of the square. But they are very close.

Your solution idea looks very good but I can spot two blunders.

[Klaus]

I’ll say this much: If your solution says the perimeters differ by more than 2%, then it’s wrong.

[Klaus]

@Axtremus your solution looks promising, too, but you also made a very trivial error near the end.

[jon-nyc]

Oops.

Perimeter of square = 4*2a, a=(4/5) * r
= 8 * (4/5)*r
= 6.4r

So square is bigger by <2%

[Klaus]

Precisely. Ax has the same solution when he fixes the little bug.

I found this interesting, because eye-balling seems to give a different solution.

[Axtremus]

@Klaus said in Puzzle time - square or circle?:

@Axtremus your solution looks promising, too, but you also made a very trivial error near the end.

Ah, indeed I have, that’s when the tawny port kicked in.