How many circles can fit inside a circle?

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SUMMARY

The discussion focuses on the mathematical problem of determining how many smaller circles of radius r can fit inside a larger circle of radius R. The equation provided is n = [π/sin^(-1)(r/R)], where [ ] denotes the greatest integer function. Participants seek a proof for this equation, highlighting the challenge of deriving it without external resources.

PREREQUISITES
  • Understanding of basic geometry, specifically properties of circles.
  • Familiarity with trigonometric functions, particularly the sine function.
  • Knowledge of the greatest integer (floor) function.
  • Basic mathematical proof techniques.
NEXT STEPS
  • Research the derivation of the equation for packing circles within a circle.
  • Explore the applications of the greatest integer function in mathematical proofs.
  • Learn about trigonometric identities and their use in geometry.
  • Investigate similar problems in circle packing and their mathematical implications.
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Mathematicians, geometry enthusiasts, students studying circle packing problems, and anyone interested in mathematical proofs and trigonometry.

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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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No.~of~circles,~n=[\frac{\pi}{sin^{-1}(r/R)}]

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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