/sci/ - Science & Math » Thread #14292305

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Anonymous Thu 10 Mar 04:10:52 2022 No.14292305 View Reply Original Report

Quoted By: >>14294514 >>14294527 >>14294598 >>14294631 >>14294751 >>14294820

If the blue and green areas are equal and the radii of both circles are 1, what is the exact distance between the circles' centers?

Anonymous

Anonymous Thu 10 Mar 2022 04:14:55 No.14292308 Report

Quoted By:

tree fiddi

Anonymous

Anonymous Thu 10 Mar 2022 04:16:23 No.14292311 Report

Quoted By: >>14293161 >>14293180

A little more than 1?

Anonymous

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Anonymous Thu 10 Mar 2022 15:05:11 No.14293161 Report

Quoted By:

>>14292311
*DING DING DING*
we have a winner

Anonymous

Anonymous Thu 10 Mar 2022 15:14:30 No.14293180 Report

Quoted By: >>14294522

>>14292311
A little less than 1

Anonymous

Anonymous Fri 11 Mar 2022 02:24:22 No.14294514 Report

Quoted By: >>14294526 >>14294527

>>14292305
How would you go about solving this?

Anonymous

Anonymous Fri 11 Mar 2022 02:26:35 No.14294519 Report

Quoted By: >>14294592

Actually answer might be 1?

Anonymous

Anonymous Fri 11 Mar 2022 02:28:00 No.14294522 Report

Quoted By:

>>14293180
Or yeah, less than 1

Anonymous

Anonymous Fri 11 Mar 2022 02:30:14 No.14294526 Report

Quoted By: >>14294542 >>14294552

>>14294514
use the equation for a half circle and do calculus

Anonymous

Anonymous Fri 11 Mar 2022 02:30:25 No.14294527 Report

Quoted By: >>14294542 >>14294552

>>14292305
>>14294514
Looked up "circle intersection area" on my search engine and the following came up.
https://mathworld.wolfram.com/Circle-CircleIntersection.html
>In order for half the area of two unit disks to overlap, set... and solve numerically, yielding d = 0.8079455 (OEIS A133741).
https://oeis.org/A133741

Anonymous

Anonymous Fri 11 Mar 2022 02:35:16 No.14294542 Report

Quoted By:

>>14294526
>>14294527
I tried to hold a tape measure up to my phone screen

Anonymous

Anonymous Fri 11 Mar 2022 02:39:38 No.14294552 Report

Quoted By:

>>14294526
>>14294527
It looks like the center section goes past each circles center, is that irrelevant? As long as the areas are equal, that can be used to find the circles center? And then the messurement of the center to the edge?

Anonymous

Anonymous Fri 11 Mar 2022 03:01:39 No.14294592 Report

Quoted By: >>14294789

>>14294519
Come on. That is trivially false

Anonymous

Anonymous Fri 11 Mar 2022 03:04:26 No.14294598 Report

Quoted By:

>>14292305
Uh, something something Nyquist?

Anonymous

Anonymous Fri 11 Mar 2022 03:21:49 No.14294631 Report

Quoted By:

>>14292305
G + B = pi
W + B = pi
W = G
QED

Anonymous

Anonymous Fri 11 Mar 2022 05:05:10 No.14294751 Report

Quoted By: >>14295298

>>14292305
Let x be the angle between the radii of one circle touching each intersection point.

x-sin(x) = pi/2

Distance between centers = 2cos(x/2)

It's not analytically solvable.

Anonymous

Anonymous Fri 11 Mar 2022 05:24:44 No.14294789 Report

Quoted By:

>>14294592
yeah that guy is a big retard

Anonymous

Anonymous Fri 11 Mar 2022 05:52:41 No.14294820 Report

Quoted By: >>14295089

>>14292305
>what is the exact distance between the circles' centers?
two?

did you mean to ask what is the distance "?" ?

Anonymous

Anonymous Fri 11 Mar 2022 09:17:27 No.14295089 Report

Quoted By:

>>14294820
They're one and the same. About as far as my drunk ass can get.

Anonymous

Anonymous Fri 11 Mar 2022 12:36:40 No.14295298 Report

Quoted By: >>14295994 >>14295996 >>14296007

>>14294751
Let cos(x) = C and sin(x) = S since I'm on mobile. Distance is D.

2D^2 = 1 - C
C^2 = (1 - 2D^2)^2
From equation (1) S^2 = 1 - C^2 = (x - pi/2)^2

1 - (x - pi/2)^2 = (1 -2D^2)^2

This is analytically solvable. Liar.

Anonymous

Anonymous Fri 11 Mar 2022 19:09:32 No.14295994 Report

Quoted By:

>>14295298
>2D^2 = 1 - C
Incorrect. 2D^2 = 1+4C

Anonymous

Anonymous Fri 11 Mar 2022 19:10:32 No.14295996 Report

Quoted By:

>>14295298
>2D^2 = 1 - C
Incorrect. 2D^2 = 4+4C

Anonymous

Anonymous Fri 11 Mar 2022 19:12:50 No.14296007 Report

Quoted By:

>>14295298
Please explain, you think x-sin(x) = pi/2 is analytically solvable? I'd like to see you try.

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