# Sam Hartburn

sam@samhartburn.co.uk

• #### Excircles and excentres

The incircle of a triangle is fairly well known as the circle inscribed in the triangle – it’s tangent to each of the three sides, which means that it touches each one but doesn’t cross any of them. But did you know that triangles have three more circles that are (sort of) tangent to all…

• #### The Nine Point Centre

How many centres do you think a triangle has? There are more than you might think. Maybe you learned about a few at school – the centroid, incentre and circumcentre are the classic ones that most people learn. But there are a few (actually, more than a few) more than that.

• #### How Many Moves can a Knight Make?

Imagine you’re a knight moving around on a chessboard, and you’re not allowed to visit any square that you’ve already been to. How quickly are you likely to get stuck?

• #### Mathober 2023 Prompt 5: Supergraph

A series of blog posts of 100ish words for Mathober.

• #### Mathober 2023 Prompt 4: Section

A series of blog posts of 100ish words for Mathober.

• #### Mathober 2023 Prompt 3: Internal

A series of blog posts of 100ish words for Mathober.

• #### Mathober 2023 Prompt 2: Symmedial

A series of blog posts of 100ish words for Mathober.

• #### Mathober 2023 Prompt 1: Kiss

I’ve decided to join in with Mathober: a month of prompts for mathematical creativity. I’m planning to do 100-or-so word blog posts. I know I won’t post daily (and I’m already behind) so it might take me into November, December or even beyond. I’m fine with that! Prompt 1 is Kiss.

• #### Can You Turn This Pattern into a Knight’s Tour?

Did you notice that, in the video for More Than Nine Million Billion Ways, the order in which the attempts at random knights tours appear makes a knight’s tour itself? This video explains where it comes from. (Spoiler: it isn’t randomly generated!)

• #### Is a Shape With 1000 Sides the Same as a Circle?

I recently found out about a shape I’d never heard of before: a chiliagon.

• #### More Than Nine Million Billion Ways

If you make random knight’s moves around a chessboard, how likely is it that you’ll find a path that visits every square without visiting any of them more than once? This video discusses some of the maths around that idea, including a song about one knight’s attempt to do it.

• #### Maths Tourism: A Spiral on Brighton Seafront

A few weeks ago I visited Brighton seafront. While there, I spotted several lovely mathematical sights, including this spiral.