Intereting Posts

Poincaré Inequality
Prime elements in the gaussian integers
$\Bbb RP^2$ as the union of a Möbius band and a disc
Continuously deform 2-torus with a line through one hole to make it go through both
Known bounds and values for Ramsey Numbers
What is $-i$ exactly?
Computing $\sum_{n=1}^{\infty} \left(\psi^{(0)}\left(\frac{1+n}{2}\right)-\psi^{(0)}\left(\frac{n}{2}\right)-\frac{1}{n}\right)$
Evaluate $\int_{0}^{\infty} \mathrm{e}^{-x^2-x^{-2}}\, dx$
Good Textbook in Numerical PDEs?
roots of a polynomial inside a circle
Is irrational times rational always irrational?
Representation of $e$ as a descending series
$m \times n$ persons stand in $m$ rows and $n$ columns
Crafty solutions to the following limit
Volume of Pyramid

This is an offshoot of this question.

A $4*4*4$ cube must have exactly one red cube in every $1*1*4$ segment of the cube. By “segment” I mean any row, column or depth. There will thus be $16$ red cubes in total.

How many unique cubes are there which have this property?

- Calculating $\sin(10^\circ)$ with a geometric method
- Simple proof that equilateral triangles have maximum area
- How to draw ellipse and circle tangent to each other?
- Division of regular tetrahedron
- What's behind the Banach-Tarski paradox?
- How to prove there are exactly eight convex deltahedra?

A cube with this property is unique if it cannot be transformed into another cube with this property via rotations of the cube along one or more of its three central axes.

An example: Let’s take a smaller cube of size $2*2*2$. Such a cube has two solutions where every segment has exactly one red cube. But the solutions are not unique, as one could be turned into the other by a simple $90^\circ$ rotation of one face of the cube.

- Compute center, axes and rotation from equation of ellipse
- Drawing a thickened Möbius strip in Mathematica
- How to sort vertices of a polygon in counter clockwise order?
- How did Archimedes find the surface area of a sphere?
- Volume of a pyramid, using an integral
- Are rotations of $(0,1)$ by $n \arccos(\frac{1}{3})$ dense in the unit circle?
- Area of a triangle in terms of areas of certain subtriangles
- Traversing the infinite square grid
- Why is Volume^2 at most product of the 3 projections?
- Geometrical interpretation of a group action of $SU_2$ on $\mathbb S^3$

- $K\subseteq \mathbb{R}^n$ is a compact space iff every continuous function in $K$ is bounded.
- Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
- Evaluate $\int_0^{\pi/4} \frac {\sin x} {x \cos^2 x} \mathrm d x$
- Peano Arithmetic before Gödel
- The “find my car” problem: proper interpretation and solution?
- The problem of the most visited point.
- Derived subgroup where not every element is a commutator
- Why is the group action on the vector space of polynomials naturally a left action?
- Complex projective line hausdorff as quotient space
- What is the connection between linear algebra and geometry?
- Finding subgroups of a free group with a specific index
- Evaluate $\int_0^{\pi} \frac{\sin^2 \theta}{(1-2a\cos\theta+a^2)(1-2b\cos\theta+b^2)}\mathrm{d\theta}, \space 0<a<b<1$
- Rigorous proof of an infinite product.
- Polynomial irreducible – maximal ideal
- Do the sequences from the ratio and root tests converge to the same limit?