flat assembler
Message board for the users of flat assembler.

Index > Heap > maximum area for rectangle

Author
Thread Post new topic Reply to topic
sleepsleep



Joined: 05 Oct 2006
Posts: 8885
Location: ˛                             ⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣Posts: 334455
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?
Post 09 Apr 2016, 21:32
View user's profile Send private message Reply with quote
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.
Post 09 Apr 2016, 21:37
View user's profile Send private message Reply with quote
sleepsleep



Joined: 05 Oct 2006
Posts: 8885
Location: ˛                             ⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣Posts: 334455
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.
Post 09 Apr 2016, 21:45
View user's profile Send private message Reply with quote
Tomasz Grysztar
Assembly Artist


Joined: 16 Jun 2003
Posts: 7718
Location: Kraków, Poland
Tomasz Grysztar
Post 09 Apr 2016, 21:52
View user's profile Send private message Visit poster's website Reply with quote
sleepsleep



Joined: 05 Oct 2006
Posts: 8885
Location: ˛                             ⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣Posts: 334455
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,
Post 09 Apr 2016, 21:55
View user's profile Send private message Reply with quote
sleepsleep



Joined: 05 Oct 2006
Posts: 8885
Location: ˛                             ⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣Posts: 334455
sleepsleep
the question is, if i could set n to bigger number, could it somehow beat circle A?
Post 09 Apr 2016, 21:58
View user's profile Send private message Reply with quote
Tyler



Joined: 19 Nov 2009
Posts: 1216
Location: NC, USA
Tyler
No. You'll just get closer and closer to the circle.
Post 09 Apr 2016, 22:09
View user's profile Send private message Reply with quote
sleepsleep



Joined: 05 Oct 2006
Posts: 8885
Location: ˛                             ⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣Posts: 334455
sleepsleep
i google for advance polygon calculator
http://www.icalculator.info/mathematics/advanced-polygon-calculator.html

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

yah, doesn't seem to have power to beat circle A,
Post 09 Apr 2016, 22:19
View user's profile Send private message Reply with quote
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.
Post 10 Apr 2016, 00:01
View user's profile Send private message Reply with quote
sleepsleep



Joined: 05 Oct 2006
Posts: 8885
Location: ˛                             ⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣Posts: 334455
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?
Post 10 Apr 2016, 21:30
View user's profile Send private message Reply with quote
Tyler



Joined: 19 Nov 2009
Posts: 1216
Location: NC, USA
Tyler
The line is infinitely small in terms of area.
Post 11 Apr 2016, 01:45
View user's profile Send private message Reply with quote
sleepsleep



Joined: 05 Oct 2006
Posts: 8885
Location: ˛                             ⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣⁣Posts: 334455
sleepsleep
thanks Tyler, understood Smile
the pi number is quite interesting,
how they actually reach this number that seems infinite,
Post 11 Apr 2016, 07:15
View user's profile Send private message Reply with quote
Display posts from previous:
Post new topic Reply to topic

Jump to:  


< Last Thread | Next Thread >
Forum Rules:
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
You can attach files in this forum
You can download files in this forum


Copyright © 1999-2020, Tomasz Grysztar.

Powered by rwasa.