N circles around a circle.

BrowserUk has asked for the wisdom of the Perl Monks concerning the following question:

Perl content: I will be writing a perl script to perform the calculations for any given inner circle size.

Starting with a circle of a supplied size, I want to arrange a given number (usually smaller) circles around the periphery of the given circle such that they all touch central circle and two of the smaller circles either side. Anyone know or have pointers to a formula?

Eg. Given an inner circle of 100 units, and the desire to arrange 8 circles around its periphery, what diameter do the 8 circles need to be so that they just touch the inner circle and each other?

Thanks.

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Comment on N circles around a circle.

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Re: N circles around a circle. by tybalt89 (Monsignor) on Feb 20, 2017 at 03:20 UTC
`sub r_outer { ($R_center * sin( $pi / $n)) / (1 - sin $pi / $n) }` [download] semi-tested :)	[reply] [d/l]
Re^2: N circles around a circle. by pryrt (Abbot) on Feb 20, 2017 at 14:04 UTC
For the curious, the derivation for this is the same as for this geometry@SE post, except that here, the angle θ is known (θ = 2π/N) and you are trying to solve for r, rather than the other way around.	[reply]
Re^2: N circles around a circle. by BrowserUk (Patriarch) on Feb 20, 2017 at 05:56 UTC
Perfect. Thank you.	[reply]
Re: N circles around a circle. by choroba (Cardinal) on Feb 20, 2017 at 03:23 UTC
Reminds me of Circles of Apollonius we did at high school. ($q=q:Sq=~/;[c](.)(.)/;chr(-\|\|-\|5+lengthSq)`"S\|oS2"`map{chr \|+ord }map{substrSq`S_+\|`\|}3E\|-\|`7**2-3:)=~y+S\|`+$1,++print+eval$q,q,a, [download]	[reply] [d/l]


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