Maximum circles

Geometry Level 3

What is the largest number of circles of radius r = 1 r=1 you can pack around the unit circle S S so that their areas do not overlap?

Details:

Tangency is fine

Packing in this case means placing the outer circles tangent to S S


The answer is 6.

Ilya Andreev by Ilya Andreev , 26, USA

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2 solutions

We can see the two circles around the middle. Since they are tangential the distance between there centers is 2. Hence the centers form an equilateral triangle. So at the center of S two circles take 60 degrees. So it can accommodate 360 60 = 6 circles around \text{We can see the two circles around the middle. Since they are tangential}\\\text{the distance between there centers is 2. Hence the centers form an}\\ \text{ equilateral triangle. So at the center of S two circles take 60 degrees.}\\\text{So it can accommodate }\dfrac{360}{60}=6\text{ circles around}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ramesh Goenka
Feb 15, 2015

https://www.youtube.com/watch?v=QEzlsjAqADA This Ted talk can help :)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice vid! I'll toss this in.

Ilya Andreev - 6 years, 3 months ago

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