Intereting Posts

Prove this inequality: $\frac n2 \le \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+…+\frac1{2^n – 1} \le n$
A finite group which has a unique subgroup of order $d$ for each $d\mid n$.
How fundamental is Euler's identity, really?
Modular Arithmetic – Find the Square Root
Concavity of the $n$th root of the volume of $r$-neighborhoods of a set
What is exactly the difference between a definition and an axiom?
Algorithm for constructing primes
Inverse of a Function exists iff Function is bijective
How to find a vector potential (inverse curl)?
Sum of irrational numbers, a basic algebra problem
Probability that $n$ vectors drawn randomly from $\mathbb{R}^n$ are linearly independent
Why is the volume of a parallelepiped equal to the square root of $\sqrt{det(AA^T)}$
What is the intuitive way to understand Dot and Cross products of vectors?
Behavior of Gamma Distribution over time
How many field structures does $\mathbb{R}\times \mathbb{R}$ have?

At Probability that one part of a randomly cut equilateral triangle covers the other, the case with flipping allowed was quickly solved. The case without flipping seems more difficult and hasn’t been adressed, so I’m posting it as a separate question:

What is the probability that randomly cutting an equilateral triangle will allow one part to cover the other if you’re not allowed to flip the parts?

The cuts are distributed according to Jaynes’ solution to the Bertrand “paradox”: random straws thrown from afar, with uniformly distributed directions and uniformly distributed coordinates perpendicular to their direction.

- Centre in N-sided polygon on circle
- How is the number of points in the convex hull of five random points distributed?
- What is the probability of having a pentagon in 6 points
- Expected size of subset forming convex polygon.
- Randomly dropping needles in a circle?
- Probability of the Center of a Square Being Contained in A Triangle With Vertices on its Boundary

A succinct characterisation of the cuts that allow one part to cover the other would already constitute significant progress.

- Sums of independent Poisson random variables
- Probability of men and women sitting at a table alternately
- Conditioning on a random variable
- Continuous uniform distribution over a circle with radius R
- How to solve probability when sample space is infinite?
- Expected value of maximum of two random variables from uniform distribution
- Conditional expectation for a sum of iid random variables: $E(\xi\mid\xi+\eta)=E(\eta\mid\xi+\eta)=\frac{\xi+\eta}{2}$
- Probability of two events
- Choose a random number between 0 and 1 and record its value. Keep doing it until the sum of the numbers exceeds 1. How many tries do we have to do?
- Intuitive reason why sampling without replacement doesnt change expectation?

- Number of Multiples of $10^{44}$ that divide $ 10^{55}$
- What does double vertical-line means in linear algebra?
- What do higher cohomologies mean concretely (in various cohomology theories)?
- How to find the gradient for a given discrete 3D mesh?
- $\mathcal{B}^{-1}_{s\to x}\{e^{as^2+bs}\}$ and $\mathcal{L}^{-1}_{s\to x}\{e^{as^2+bs}\}$ , where $a\neq0$
- Prove any orthogonal 2-by-2 can be written in one of these forms…
- How to get determinant of $A$ in terms of tr$(A^k)$?
- The derivative of a linear transformation
- The commutator subgroup of a quotient in terms of the commutator subgroup and the kernel
- Image of complex circle under polynomial
- What is the least value of $k$ for which $B^k = I$?
- Generalization of Cayley-Hamilton
- Why doesn't using the approximation $\sin x\approx x$ near $0$ work for computing this limit?
- Linear independence of function vectors and Wronskians
- How do I show that the derivative of the path $\det(I + tA)$ at $t = 0$ is the trace of $A$?