2
votes
0answers
30 views

Packing circles in circle vs semicircle vs quarter of circle

Consider $N$ disjoint circles with radius $1$ packed into a larger circle $C$. Let $R$ be the smallest possible radius of $C$, allowing the best packing density. Now take the $N$ unitary circles ...
2
votes
1answer
60 views

Packing circles into circle of diameter 7

How many unit circles can you fit inside a circle of diameter 7 such that no circle overlaps any other circle? Please explain the concept or any tricky process regarding this problem.
6
votes
2answers
120 views

Unequal circles within circle with least possible radius?

It is the classical will-my-cables-fit-within-the-tube-problem which lead me to the interest of circle packing. So basically, I have 3 circles where r = 3 and 1 circle where r = 7 and I am trying to ...
2
votes
2answers
115 views

Square covered with circles

I have a square 800x800 and i need to fully cover it with the least number of circles possible, each circle has a radius of 150. QUESTIONS: - What pattern would be the best to use? Clover, diamon or ...
1
vote
1answer
928 views

How many circles of radius r fit in a single bigger circle of radius R?

Is there any formula to calculate how many circles of radius r fit in a single bigger circle of radius R? I'd apreciate if it didn't involve advanced math, like calculus (unless there is no other way, ...
6
votes
0answers
586 views

The number of circles that will fit inside the area of larger circle?

Let's say circle $\omega_1$ has a diameter $X$. Let $X>Y$; $Y\in \mathbf{R}^{+}$. How many circles with diameter $Y$ will fit inside $\omega_1$? Is there a formula for this?
3
votes
2answers
242 views

Applonius Circle/ Ford Circle / Infinite GP / Circle Packing

All the smaller circles are mutually tangent and continue to infinity. What is sum of radii of all the smaller circles?
2
votes
1answer
115 views

Circle Packing: Unsolved Problem in Geometry?

Graham and Sloane minimize the second moment of the centres of a number discs in order to maximize their compactness. They use computational geometry techniques to find the optimal packings for ...
2
votes
1answer
57 views

Approximate radius of a group of n packed circles

I am looking for a formula to estimate the radius of a circle which would hold n number of circles with some radius r. I understand this is part of the packing problem which does not have a definite ...
1
vote
1answer
117 views

What is the relative behaviour when a center circle surrounded by 6 circles is (recursively) replaced by 6 circles

Start with a given "inner" circle of arbitrary radius (blue) centered at C. Surround it by 6 circles of equal radius. This concerns to known issues of circle packing and is a frequently treated ...
1
vote
1answer
96 views

Smallest Circle that encircles $4$ circles

I want to calculate the radius of the smallest circle (radius $R$) that can hold $4$ circles (with radii $a, b, c, d$) inside it, such that: No circles overlaps one other. $a \ge b \ge c \ge d.$ ...
3
votes
0answers
516 views

Circle Packing Algorithm

I have question related to circle-packing. The problem is to find the circle of minimum radius enclosing four non-overlapping circles of arbitrary radius. I have to write a program in C for this ...
3
votes
1answer
1k views

Packing squares into a circle

I need determine the maximum number of squares of the given size that can be packed into a circle of the given radius. Squares can be rotated. I'm not sure how complex this problem is and i can find ...
0
votes
2answers
1k views

Find, inside a large circle, the maximum number of small circles placed 60 degrees to each other and

... starts with a small circle in the center of the large circle. The above picture shows a program I wrote to actually draw the circles out. But you can see that this method does not yield maximum ...
12
votes
1answer
220 views

A question on circles

Given that a lamp-post can light a surrounding circle of radius 100 m, what is the minimum number of such lamp-posts required to light a circular ground of radius 1000 m.