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Author
sleepsleep

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sleepsleep
i thought bout this when i am pondering about triangle,

if give a 18 meters fence, what is your dimension (height x width) to obtain maximum area,

i think it is 18 / 4 = 4.5

then the answer is 4.5 x 4.5 = 20.25

http://www.calculatorsoup.com/calculators/geometry-plane/circle.php
i lookup a circle calculator and use area as 20.25 and find its C,

r = 2.53885313
C = 15.9520847
A = 20.25

i think it is quite cool, circle done the job using around 16 meters fence only!.

if C is 18 meters like what rectangle got,
r = 2.86478898
C = 18
A = 25.7831008

is circle the best performer?
09 Apr 2016, 21:32
Tyler

Joined: 19 Nov 2009
Posts: 1216
Location: NC, USA
Tyler
If you're only interested in rectanglular shapes, this is an easy minimax problem from calculus 1. The square will always be best.

If you open it up to any and all closed shapes (those that form a loop), then I have no clue. I feel like the answer will probably be that the circle is optimal, but how to prove that is not at all clear to me. Someone message MHajduk.
09 Apr 2016, 21:37
sleepsleep

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sleepsleep
i was thinking that the rectangle only stretch using 4 points, while circle (assume we got 360 degree in every circle) then we stretch 360 points,

but this 360 points is man made, if i try to stretch it using 3600 or 36000 point, assume in bigger circle, maybe i could gain more area?

idk maths a lot, just simple arithmetic and try to pondering and imagine all these concepts.
09 Apr 2016, 21:45
Tomasz Grysztar
Assembly Artist

Joined: 16 Jun 2003
Posts: 7718
Location: Kraków, Poland
Tomasz Grysztar
09 Apr 2016, 21:52
sleepsleep

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sleepsleep
i think i found the right term, polygon calculator

http://www.calculatorsoup.com/calculators/geometry-plane/polygon.php

if n = 5
n = 5 a = 3.6 m
r = 2.47749 m
R = 3.06234 m
A = 22.2974 m2 (quite good, better than rectangle)
P = 18 m
x = 108°
y = 72°

n = 360 a = 0.05 m
r = 2.86472 m
R = 2.86483 m
A = 25.7824 m2 (quite near to circle, 25.7831008)
P = 18 m
x = 179°
y = 1°

i want to try n = 3600, but the calculator only support n till 1000

n = 1000 a = 0.018 m
r = 2.86478 m
R = 2.86479 m
A = 25.783 m2 (quite near to circle, 25.7831008)
P = 18 m
x = 179.64°
y = 0.36°

if polygon n is 1000, the area seems a little bit bigger now,
09 Apr 2016, 21:55
sleepsleep

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sleepsleep
the question is, if i could set n to bigger number, could it somehow beat circle A?
09 Apr 2016, 21:58
Tyler

Joined: 19 Nov 2009
Posts: 1216
Location: NC, USA
Tyler
No. You'll just get closer and closer to the circle.
09 Apr 2016, 22:09
sleepsleep

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sleepsleep

number of sides : 360000
length of sides : 0.00005
area : 25.783100780

yah, doesn't seem to have power to beat circle A,
09 Apr 2016, 22:19
tthsqe

Joined: 20 May 2009
Posts: 724
tthsqe
@Tomasz Grysztar, I love how everyone on that page is in awe of the physicist's intuition, but the only proof on the page is by Green's Theorem and Fourier Series.
10 Apr 2016, 00:01
sleepsleep

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sleepsleep
i got one question,

is the circle/rectangle or etc shapes area calculated based on invisible shape line in mathematics?
the "line" that form the shape never entered into calculation?
10 Apr 2016, 21:30
Tyler

Joined: 19 Nov 2009
Posts: 1216
Location: NC, USA
Tyler
The line is infinitely small in terms of area.
11 Apr 2016, 01:45
sleepsleep

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sleepsleep
thanks Tyler, understood
the pi number is quite interesting,
how they actually reach this number that seems infinite,
11 Apr 2016, 07:15
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