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Dan
  • Member for 1 year, 8 months
  • Last seen more than a week ago
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I like math questions that:

  • can be expressed concisely
  • contain few or no numbers
  • are challenging
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40
Conjecture: If circular coins of any sizes are in a convex polygonal frame, with each coin touching exactly one edge, then all the coins can move
Jan 11, 2023
31
On average, how many uniformly random real numbers $u$ are needed for their sum to exceed $1$, if $u_1$ is in $(0,1)$ and $u_k$ is in $(0,eu_{k-1})$?
Feb 23, 2023
25
Does there exist a continuous function $f(x)$ such that $f(0)=0$ and $0<\lim_{n\to\infty}\prod_{k=1}^n f(k/n)<\infty$?
Nov 16, 2022
24
Find the area of the region enclosed by $\frac{\sin x}{\sin y}=\frac{\sin x+\sin y}{\sin(x+y)}$ and the $x$-axis (comes from a probability question)
Apr 15
21
Conjecture: Given any five points, we can always draw a pair of non-intersecting circles whose diameter endpoints are four of those points
Nov 28, 2023
16
Are there general principles that allow us to easily determine whether coins in simple arrangements in a frame can move?
Jan 12, 2023
15
Conjecture: If equal size circular coins are in a convex polygonal frame, with each coin touching exactly one edge, then all the coins can move
Jan 12, 2023
15
Will a unit disk be completely covered by randomly placed disks of area $\pi,\frac{\pi}{2},\frac{\pi}{3},\dots$ with probability $1$?
Nov 20, 2023
14
Regular $n$-gon with diagonals: bounds on area of largest cell?
Dec 17, 2022
14
A disc contains many random points. Each point is connected to its nearest neighbor. What is the expectation of average cluster size?
Jan 15
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70
Geometry question about a six-pack of beer
48
Geometry question about a six-pack of beer
46
Can a disk of area $1$ be completely covered by six disks of areas $\frac12,\frac13,\frac14,\frac15,\frac16,\frac17$?
45
Regular polygon of radius $1$ with diagonals: mysterious ring of radius $1/e$?
45
Intuition is silent: Find the probability that the smallest circle enclosing $n$ random points on a disk lies completely on the disk, as $n\to\infty$.