Let’s hear it for Logo! (2)

Continuing my re-discovery of Logo, I thought I’d try to implement a backtracking solution to finding a Hamiltonian cycle in…

Let’s hear it for Logo!

Recently I had the occasion of helping my autistic son with some elementary mathematics. He’s very averse to writing, but…

Approximating the sum of an infinite series (3)

In the last post I looked at Aitken’s delta-squared process, and showed its applicability to summing some alternating series. But…

Approximating the sum of an infinite series (2)

Before we begin, some basic definitions. Suppose is a sequence that converges to a limit . We say that the…

Approximating the sum of an infinite series

I started thing about this as I was preparing some material on the use of Matlab for teaching engineering mathematics…

Typesetting music

Recently I’ve been typesetting a little music. My notational needs are simple: mostly single melodic lines, occasional chords or multiple…

The derivative of sin(x)

We know that we can use the limit definition     to compute the derivative of “from first principles”. And…

Tuning and temperament (5): Meantone and the syntonic comma

The Pythagorean comma may be considered as the difference in two ways of tuning 84 semitones: either as 12 fifths,…

Tuning and Temperament (4): Tempering the cycle of fifths

We have seen that 12 justly tuned fifths will overshoot 7 octaves, so in order for them to match up,…

Tuning and temperament (3): Just Intonation and Equal Temperament

We have seen in previous posts on this topic that: The perfect fifth corresponds to a frequency ration of 3/2…