Case of the 'mice problem' for $n=3$ [duplicate]

Solution 1:

The point is to recognize that the spiral is equiangular. The angle between the spiral and the radius is constant at $\frac {\pi} 3$. This means it is a logarithmic spiral of the form $r=ae^{b\theta}$ with $\arctan \frac 1b=\frac \pi 3, b=\frac 1{\sqrt 3}$. If we choose the origin of $\theta$ to go through one of the corners of the triangle we have $a=\frac {\sqrt 3}3l$

If $a_n\to \ell $ then $\hat a_n\to \ell$ [duplicate]

Can mathematical definitions of the form "P if Q" be interpreted as "P if and only if Q"? [duplicate]

Proving the determinant of a tridiagonal matrix with $-1, 2, -1$ on diagonal.

Limits involving factorials $\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}$

Remainder of polynomial product, CRT solution via Bezout

Inverse of a Function exists iff Function is bijective

Open Sets of $\mathbb{R}^1$ and axiom of choice

Distribution of $(XY)^Z$ if $(X,Y,Z)$ is i.i.d. uniform on $[0,1]$

Why do many textbooks on Bayes' Theorem include the frequency of the disease in examples on the reliability of medical tests?

Volume of an n-simplex [duplicate]

Is $\operatorname{lcm}(a,\gcd(b,c))=\gcd(\operatorname{lcm}(a,b),\operatorname{lcm}(a,c))$

Let $(a,b)$ and $(c,d)$ be intervals in $\Bbb R$, and find an injective and surjective function from $(a,b)$ to $(c,d)$