# Linked Questions

**122**

votes

**6**answers

8k views

### Gaussian prime spirals

Imagine a particle in the complex plane, starting at $c_0$, a Gaussian integer,
moving initially $\pm$ in the horizontal
or vertical directions. When it hits a Gaussian prime, it turns left $90^\...

**71**

votes

**4**answers

2k views

### Can a row of five equilateral triangles tile a big equilateral triangle?

Can rotations and translations of this shape
perfectly tile some equilateral triangle?
I originally asked this on math.stackexchange where it was well received and we made some good progress. Here's ...

**19**

votes

**5**answers

5k views

### Rational points on a sphere in $\mathbb{R}^d$

Call a point of $\mathbb{R}^d$ rational if all its $d$ coordinates are rational numbers.
Q1.
Are the rational points dense on the unit sphere $S :\; x_1^2 +\cdots+ x_d^2 = 1$, i.e. does $S$ ...

**16**

votes

**7**answers

2k views

### Unexpected Occurences of the Sierpinski Triangle

The probably most wellknown occurance of the Sierpinski Triangle is as the odd entries of the Pascal triangle
Some month ago however, there was an article about mathematical models of sandpiles along ...

**12**

votes

**2**answers

2k views

### sequences with a fractal dimension

This is inspired by the self-similarity of the celebrated Golay-Rudin-Shapiro sequence, more exactly, of its alternating partial sums. (This latter one is oeis 020990). The pictures show the 550 first ...

**5**

votes

**1**answer

235 views

### Are lattice points in thin spherical shells uniformly distributed?

Consider the spherical shell (annulus)
$$A(R,r) = \{ x \in \mathbb{R}^3 : R \leq |
x|\leq R+r \}.$$ Think of the limit $R \to \infty$.
Assume that $r$ depends on $R$ as $r(R) = R^{-\delta}$. We are ...

**16**

votes

**0**answers

816 views

### Groups generated by 3 involutions

Let $r(m)$ denote the residue class $r+m\mathbb{Z}$, where $0 \leq r < m$.
Given disjoint residue classes $r_1(m_1)$ and $r_2(m_2)$, let the class transposition
$\tau_{r_1(m_1),r_2(m_2)}$ be the ...

**6**

votes

**1**answer

218 views

### map from 6-vertex model to domino tiling

I am trying to find a correspondence between 6-vertex model and an Aztec Diamond tiling. Here are the building blocks of the 8-vertex model:
There seems to be more than one correspondence. I found ...

**3**

votes

**2**answers

462 views

### notable inductive proofs relating to fractals

what are notable/ prominent inductive proofs relating to fractals?
the motivation for this question is:
fractals are very difficult mathematical objects to work with, and many problems/questions ...

**14**

votes

**1**answer

201 views

### Product of a Laver table and a Hadamard matrix has mostly 0 rows

I recently noticed (while playing around) that the product of a Laver matrix with a Hadamard matrix gives a very sparse matrix. In particular, all but logarithmically few rows are all zero. The ...