Curvature is of critical importance in numerous contexts. An example is shown in the figure above, a map of the Silverstone Formula 1 racetrack. The sharp bends (high curvature) force drivers to reduct speed drastically.

## Archive for January, 2023

### Curvature and the Osculating Circle

Published January 26, 2023 Occasional Leave a CommentTags: Geometry

### The Cosmology of the Divine Comedy

Published January 19, 2023 Irish Times Leave a CommentTags: Astronomy, Cosmology, Topology

If you think poetry and maths are poles apart, think again. Around the sixth century, Indian poet and mathematician Virahanka codified the structure of Sanskrit poetry, formulating rules for the patterns of long and short syllables. In this process, a sequence emerged in which each term is the sum of the preceding two. This is precisely the sequence studied centuries later by Leonardo Bonacci of Pisa, which we now call the Fibonacci sequence [TM241 or search for “thatsmaths” at irishtimes.com].

### Adding a Point to Make a Space Compact

Published January 12, 2023 Occasional Leave a CommentTags: Topology

The real line is an example of a locally compact Hausdorff space. In a Hausdorff space, two distinct points have disjoint neighbourhoods. As the old joke says, “any two points can be *housed off* from each other”. We will define local compactness below. The one-point compactification is a way of embedding a locally compact Hausdorff space in a compact space. In particular, it is a way to “make the real line compact”.

### Summing the Fibonacci Sequence

Published January 5, 2023 Occasional ClosedTags: Arithmetic, Number Theory