Tuesday 30 March 2021

Nature Stoned

Susy Oliveira at the Museum of Contemporary Canadian Art (MOCCA), Toronto 2011:


Sunday 28 March 2021

Thursday 25 March 2021

Saturday 20 March 2021

Tuesday 16 March 2021

Probability for two randomly chosen positive integers to have no common factors

We have previously looked at the evaluation of the Riemann zeta function at 2:



This result can be used to calculate the probability for two randomly chosen positive integers to have no common factors.  It is easy to see that the probability for two randomly chosen positive integers to be both multiples of a prime p is 1/p2.  So the probability that they do not share a common factor of p is 1  1/p2.  Therefore the probability that they do not have ANY common factors is:



Very neat result!

Sunday 14 March 2021

A sequence of prime numbers (from the powers of π)

It's π-day today.  I am going to construct a sequence of prime numbers by applying the floor function to positive integer (n) powers of π,

π n⌋.

Here are the first few:


The next one π 317 is a 158-digit number.

Saturday 13 March 2021

The Angel's Share + Glitch

Ottawa-based piano/percussions duo SHHH!! Ensemble performing Canadian composer John Gordon Armstrong's The Angel's Share:


Video from SHHH!! Ensemble's youtube channel


A glitched drawing:



Saturday 6 March 2021

Tuesday 2 March 2021