/sci/ - Science & Math » Thread #13685908

23KiB, 514x539, Area enclosed.png

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Anonymous Sun 26 Sep 18:57:10 2021 No.13685908 View Reply Original Report

Quoted By: >>13686933 >>13687111

The area enclosed by this curve is pi/2. I wrote a program to prove that numerically, but it's impossible to prove.

Anonymous

Anonymous Sun 26 Sep 2021 19:21:08 No.13685972 Report

Quoted By: >>13686012

The area is 4 times the area enclosed by r = sqrt(costheta) from 0 to pi/2

That area is equal to 1/2 integral(costheta dtheta) from 0 to pi/2

That is 1/2

Total area = 2

Anonymous

Anonymous Sun 26 Sep 2021 19:33:43 No.13686012 Report

Quoted By: >>13686023

>>13685972
no. it's pi/2. you fail.

Anonymous

Anonymous Sun 26 Sep 2021 19:40:48 No.13686023 Report

Quoted By: >>13686034 >>13686084

>>13686012
each "circle" is strictly larger than a circle with radius 1/2

A circle with radius 1/2 has area pi/4

Ergo two circles with radius 1/2 would have area pi/2 total. But as we said each of these "circles" clearly is larger than a radius 1/2 circle, so the total area must be >pi/2

You fucking retard

Anonymous

Anonymous Sun 26 Sep 2021 19:43:34 No.13686034 Report

Quoted By: >>13686037 >>13686059 >>13686084

>>13686023
>"circles" clearly is larger than a radius 1/2 circle,

they aren't circles and they are larger than 0.5 by 0.1. pi/2 is a long way from 2.

Anonymous

Anonymous Sun 26 Sep 2021 19:44:12 No.13686037 Report

Quoted By:

>>13686034
Ah so you admit they are larger than pi/4 each, so pi/2 is clearly too low

Moron

Anonymous

Anonymous Sun 26 Sep 2021 19:49:43 No.13686059 Report

Quoted By: >>13686084

>>13686034
Also these aren't ellipse, but an ellipse with one axis 0.5 and one axis 0.6 has an area of 3pi/10 which is about 0.95 which is VERY close to 1

Anonymous

Anonymous Sun 26 Sep 2021 19:57:20 No.13686084 Report

Quoted By:

>>13686059
>>13686034
>>13686023

you are right, thanks

Anonymous

Anonymous Mon 27 Sep 2021 00:46:04 No.13686933 Report

Quoted By:

>>13685908
>impossible to proof
loo up Cauchy's integral formula

Anonymous

Anonymous Mon 27 Sep 2021 01:48:51 No.13687111 Report

Quoted By:

>>13685908
$\int_0^\pi (\cos\theta)(\sin d\theta)/2$

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