≥ i

... you should try Gröbner bases. Suppose four points \(A,B,C,D\) lie on a common circle. How do the four quadrances to the point \(M:\equ...

It is known since Newton's time that sums of the form \(\sigma_k:=\sum x_i^k\) are polynomial expressions in the coefficients of \(f=\pr...

Suppose \(f = ag + (1-a)h\), a convex combination of pdfs. Then \(f\) is a pdf. Suppose \(X\) has \(f\) as pdf. For any evaluation \(x\) of...

Prop. If \(0,1,z,w\) all lie on a circle centered at \(1/2\) then \(zw\) is the orthogonal projection of \(0\) onto the line through \(z\) ...

By an extremely rational cubic polynomial, I mean a cubic polynomial \(p\) such that both \(p\) and \(p'\) are products of rational lin...

Compute two sequences $\begin{matrix}a_0&\dots&a_{n-1}\\b_0&\dots&b_{n-1}\end{matrix}$ of unsigned integers with $$\begin{a...

This will be a naive discussion about functions roughly of the form $A: \mathbb{R}^2\to\mathbb{R}$ but allowing delta behaviour which I only...