How many circles can fit inside a circle?

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    Circle Circles
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Discussion Overview

The discussion revolves around the problem of determining how many smaller circles can fit inside a larger circle, focusing on the mathematical formulation and potential proofs related to this arrangement. The scope includes mathematical reasoning and exploratory inquiry.

Discussion Character

  • Mathematical reasoning, Exploratory

Main Points Raised

  • One participant proposes an equation for the number of smaller circles that can fit inside a larger circle, given by n=[\frac{\pi}{sin^{-1}(r/R)}], where [ ] denotes the floor function.
  • Another participant requests a proof for the proposed equation.
  • A subsequent reply expresses skepticism about the ability to provide a proof and indicates a lack of motivation to seek it out.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as there is a request for proof that remains unaddressed, and no agreement on the validity of the proposed equation is established.

Contextual Notes

The discussion lacks detailed assumptions regarding the arrangement of the circles and does not clarify the conditions under which the proposed equation holds true.

Sariaht
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A circle with the radius R cuts the centers of circles with the radius r that does mearly touch each other, What is the equation for the number of circles in the circle?
 
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[tex]No.~of~circles,~n=[\frac{\pi}{sin^{-1}(r/R)}][/tex]

where [ ] represents the greatest integer (or floor) function.
 
Last edited:
Can you give a proof please?
 
You cant? :smile: And I am too lazy to look it up at the library...
 

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