Linked Questions
17 questions linked to/from Examples of unexpected mathematical images
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On the first sequence without triple in arithmetic progression
In this Numberphile video (from 3:36 to 7:41), Neil Sloane explains an amazing sequence:
It is the lexicographically first among the sequences of positive integers without triple in arithmetic ...
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answers
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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 ...
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answers
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Famous examples of "serendipity" in 20th century mathematics
The term "serendipity" is commonly used in the literature to refer to the historical
evidence that very often researchers make unexpected and beneficial discoveries by
chance, while they are ...
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Signs of Kravchuk matrix asymptotically produce a large circular region with hyperbolic sinks. Why?
The Kravchuk matrix of dimension $n+1$ is such that its entries satisfy $$K_{i,j}^{(n+1)}=[x^i](1+x)^{n-j}(1-x)^j\quad\forall0\le i,j\le n.$$ It enjoys properties such as involution and has various ...
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Prominent non-mathematical work of mathematicians
First of all, sorry if this post is not appropriate for this forum.
I have a habit that every time I read a beautiful article I look at the author's homepage and often find amazing things.
Recently I ...
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Lattices on classical combinatorial families
I am asking for examples of lattices defined on classical combinatorial families, such as Permutations, Catalan objects, set partitions or integer partitions, graphs.
I am mosty interested in lattices ...
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Unexpected occurrences of the Sierpinski triangle
The probably most well-known occurrence 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 ...
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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 ...
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11
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1
answer
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Abstract mathematical concepts/tools appeared in machine learning research
I am interested in knowing about abstract mathematical concepts, tools or methods that have come up in theoretical machine learning. By "abstract" I mean something that is not immediately related to ...
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What should we teach to liberal arts students who will take only one math course?
Even professors in academic departments other than mathematics---never mind other educated people---do not know that such a field as mathematics exists. Once a professor of medicine asked me whether ...
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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 ...
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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 $90^\circ$...
CommunityBot
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0
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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 ...
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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 $S$ ...
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answer
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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 ...
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