How many circles can fit inside a circle?

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  • #1
Sariaht
357
0
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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  • #2
[tex]No.~of~circles,~n=[\frac{\pi}{sin^{-1}(r/R)}][/tex]

where [ ] represents the greatest integer (or floor) function.
 
Last edited:
  • #3
Can you give a proof please?
 
  • #4
You cant? :smile: And I am too lazy to look it up at the library...
 

Related to How many circles can fit inside a circle?

1. What is a circle of circles?

A circle of circles is a geometric shape made up of multiple circles that are connected together and share a common center point.

2. How is a circle of circles different from a regular circle?

A regular circle is a single circle with a fixed radius, while a circle of circles consists of multiple circles with varying radii that are all connected together.

3. What are the applications of a circle of circles in science?

A circle of circles can be found in various scientific fields, such as biology, physics, and engineering. It can be used to model biological systems, study patterns in nature, and design efficient structures.

4. How is a circle of circles formed?

A circle of circles can be formed by drawing a larger circle and then placing smaller circles along its circumference, with their centers all intersecting at the center of the larger circle.

5. Can a circle of circles have an infinite number of circles?

Technically, yes, a circle of circles can have an infinite number of circles. However, in practical applications, there is always a limit to the number of circles that can be included due to physical constraints.

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