There's an easy proof of this: you can colour the vertices red and blue so that no vertices joined by an edge are the same colour, and there are an odd number of vertices.
So any lap visiting each vertex once has to end on a different colour to the start.
Here's an image showing the colouring property, by David Eppstein. If you start on blue, you have to finish on red, and vice versa.
Another one. Here, flocks of arrowheads are tracing out the Herschel graph.
The Herschel graph is something I keep returning to, because our building is named after its inventor.
Here's a closeup of the handwriting one. I wandered round the department knocking on doors, asking people to write some mathematical notation. It was fascinating seeing the different symbols and conventions used in different disciplines.
What can you spot in this snippet?
Art* is going on walls!
On the right is one of the Truchet pieces I shared above, and the other is made up of handwriting samples I gathered from colleagues. It feels good to finally put something out with this!
... and some more.
Just published a new thing to thingiverse: the Seven Triples puzzle
Look upon my works, ye mighty, and despair!
(I'm trying to learn #blender)
When I stack them on top of each other, this is what it looks like. What do you notice?
Does anybody need a set of orthogonal whiteboard markers? #3dprinted
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