flat assembler
Message board for the users of flat assembler.
Index
> Heap > maximum area for rectangle 
Author 

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/geometryplane/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 

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
Here are some nice proofs : http://math.stackexchange.com/questions/4808/whydoesacircleenclosethelargestarea


09 Apr 2016, 21:52 

sleepsleep
i think i found the right term, polygon calculator
http://www.calculatorsoup.com/calculators/geometryplane/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
the question is, if i could set n to bigger number, could it somehow beat circle A?


09 Apr 2016, 21:58 

Tyler
No. You'll just get closer and closer to the circle.


09 Apr 2016, 22:09 

sleepsleep
i google for advance polygon calculator
http://www.icalculator.info/mathematics/advancedpolygoncalculator.html 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
@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
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
The line is infinitely small in terms of area.


11 Apr 2016, 01:45 

sleepsleep
thanks Tyler, understood
the pi number is quite interesting, how they actually reach this number that seems infinite, 

11 Apr 2016, 07:15 

< Last Thread  Next Thread > 
Forum Rules:

Copyright © 19992020, Tomasz Grysztar.
Powered by rwasa.