updates
Understanding Takens' Embedding theorem
I am having some trouble understanding Takens' embedding theorem, and was hoping that someone with greater knowledge could help out. Formally, the th...
Apr 19, 2026
Archive: Updates
updates
nth prime divided by n
So I was playing around in MATLAB and I plotted the following function; $$f(n) = \frac{p_n}{n}, $$ where $p_n$ denotes the $n^{th}$ prime number (i.e. 5 i...
Apr 19, 2026
updates
Intersection of Common Chords of Three Circles
Three circles intersect pairwise but let's assume there is no point shared by all three of them. There are three pairs of circles. Two circles in any...
Apr 19, 2026
updates
cylindrical coordinate $\theta$ when $r=0$
When we use the cylindrical coordinate system $(r, \theta, z)$ where $r$ is the distance from the point in the $xy$-plane, $\theta$ is the angle with the ...
Apr 19, 2026
updates
Number of right angled triangles formed by vertices of a 14-gon
Here's a question that I found on the website of International Kangaroo Maths Contest. The question goes like this: What is the total number of right...
Apr 19, 2026
updates
Nimbers for Kayles
I have a problem with calculating the nimbers for this game. I know that for Kayles the following is true: \begin{array}{c|c} \hline Hight & Nimber \\...
Apr 19, 2026
updates
Distinct permutations of the word "toffee"
What does distinct permutations mean and how many distinct permutations can be formed from all the letters of word TOFFEE?
Apr 19, 2026
updates
Distribute objects in Concentric Circles
I am attempting to distrubute objects evenly in concentric circles according to the following rules. There will always be 1 object at the centre of the pl...
Apr 19, 2026
updates
Naive Set Theory by Halmos is confusing to a layman like me
I want to be able to express set notations fluently in math fields used in machine learning, so I started reading Naive Set Theory by Halmos. But I have b...
Apr 19, 2026
updates
Finding an orthogonal basis from a column space
I'm having issues with understanding one of the exercises I'm making. I have to find an orthogonal basis for the column space of $A$, where: $$A...
Apr 19, 2026
