# Numbers of circle a circle

"When you attract a circle in an aircraft of distance $1$ you can flawlessly border it with $6$ various other circles of the very same radius."

BUT when you attract a circle in an aircraft of distance $1$ and also attempt to flawlessly border the main circle with $7$ circles you need to transform the distance of the border circles.

Just how can I locate the distance of the border circles if I intend to make use of extra that $6$ circles?

ex-spouse : $7$ circles of distance $0.4$

$8$ circles of distance $0.2$

Imagine there are $n \geq 3$ circles bordering your device circle. After that the scenario would certainly resemble :

Whence $\cos(x)=\frac{r}{r+1}$. The angle $x$ is fifty percent of the interior angle of the equivalent normal polygon, so $x=\frac{n-2}{2n} \cdot 180^\circ$. You can after that address for $r=\dfrac{\cos(x)}{1-\cos(x)}$.

As an example

- when $n=4$ we have $r=\dfrac{\cos(45^\circ)}{1-\cos(45^\circ)}=1+\sqrt{2}=2.41421\ldots$.
- when $n=6$ we have $r=\dfrac{\cos(60^\circ)}{1-\cos(60^\circ)}=1$.
- when $n=8$ we have $r=\dfrac{\cos(67.5^\circ)}{1-\cos(67.5^\circ)}=0.619914\ldots$.

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