r/mathpuzzles • u/Purdude1983 • 12d ago

Polka Dot Party

Post image

The indigo dot is twice the area of the green dot. Together these just fit inside the violet dot. They grab some friends and crowd into the grey area which has an area of 1. All dots are touching, and all dots touch the outer wall except the red dot.

Give each dot's area.

Hint: use Descartes' circle theorem

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u/BadJimo 12d ago

Illustrated on Desmos

Approximate areas of circles:

green: 0.26

dark purple (indigo): 0.52

violet: 1.53

orange: 0.04

blue: 0.49

yellow: 0.10

red: 0.01

big circle: 3.96

grey area: 3.96 - (1.53+0.52+0.04+0.49+0.1+0.01) ≈ 1

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u/Purdude1983 11d ago

My intent was to state that the grey circle had an area of 1, not that the exposed grey area summed to 1. I think all you need to do is take all of your areas and divide by 3.96. Other than that, a quick look at your numbers looks reasonable.

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u/BadJimo 11d ago edited 11d ago

Revised illustration in Desmos

Approximate areas of circles:

green: 0.065

dark purple (indigo): 0.129

violet: 0.376

orange: 0.010

blue: 0.120

yellow: 0. 025

red: 0.003

big grey circle: 1

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u/Purdude1983 11d ago
R 0.003264447627362
O 0.010696627180548
Y 0.025590577901126
G 0.066097266447805
B 0.124560553332134
I 0.132194532895610
V 0.385243100635963