Department of Economics, Mathematics and Statistics

# Just for Fun!

On this page I have gathered together a few resources that you might like to look at if you want to discover some interesting mathematics that there isn't time to look at in formal lectures. Difficulty levels vary but mostly you should be able to understand it from the first year onwards.

This is all done in my spare time (ha!) so I can't promise perfection. Do let me know if you find it interesting or if there are any glaring errors (or non-glaring errors of course, those are even worse). Comments, additions, constructive criticism all welcome.

I have tried not to infringe copyright, largely by including few if any photos.

At the end are some external links to mathematical websites.

### The British Museum

The British Museum is so near Birkbeck that it would be a crime not to visit. There are thousands of amazing objects in its collections: the Rosetta Stone, the Lewis Chessmen to name but two. (I believe they're known as the Harry Potter Chessmen nowadays...) There are also many objects of mathematical interest. It is early days yet but my aim is to provide some factsheets about a selection of these artefacts, ideally telling you where to find them and some information about why they are of interest. There will also be some exercises to try if you like that sort of thing, the aim being to use our more sophisticated techniques to look at some of the mathematics raised by the items in question. You might even get inspired to play around a bit with some of the mathematics and see where it leads you. So here we go with the factsheets - to download just click on the pdf icon. Currently the list is rather short!

• The Rhind Papyrus.
• Games at the British Museum

### Mathematical Paper folding

When you're trying to work out the symmetries of a geometric figure it can be useful to have an actual physical model to play with. Paper folding is also very therapeutic especially when you pretend it's vital for studying! All the platonic solids can be made using A4 paper, clever folding and no scissors, glue or artistic abilities required! (Actually that's a slight lie because the dodecahedron I recommend has merely a very good approximation to regular pentagonal sides). If you want to cheat and just cut out nets and stick them together, see the final link. For the purists, note that proper origami only uses square paper, hence my use of the term "paper folding". If you want to stick to that, I have included links to how-to videos for the tetrahedron and cube.

• All the platonic solids (the dodecahedron is an approximation and the icosahedron is less than ideal), but a very good site nonetheless.
• My mother taught me how to make a very sturdy cube using 6 components she called "limping seagulls". Here are my instructions for making them.
• Origami tetrahedron and cube.
• Another icosahedron, which looks pretty hard and I haven't tried it.
• Nets for the five platonic solids are available here (see Section 8). With these you print and cut out the net, then fold and stick together.
• Applets showing many geometric figures

### Impossible Proofs

I sometimes speak about "false" proofs (for example at Business week in 2010, or at Mathematics in Action events organised by The Training Partnership in 2014). Here is the transcript. Try and spot where the "proofs" fall down. If you are really stumped, email me and I'll help you out. Some of the "proofs" I look at are from an excellent book by E.A. Maxwell called â€˜Fallacies in Mathematicsâ€™ (1959). It is sadly out of print but second hand copies are around online. Others are unattributable mathematical "folklore", some I've found online, again it usually wasn't clear who the originators were. And some have come from my own warped mind.

• The British Society for the History of Mathematics (BSHM) puts on regular events and also has its own good links, such as a page on Museums with mathematical exhibits, and where to find history of maths online. I am currently on BSHM council.
• The MacTutor history of mathematics archive, run by the University of St Andrews, features biographies of more mathematicians than you even thought existed.
• Euclid's Elements: now online!
• The USA Mathematical Talent Search. OK so it's not aimed at us, but the puzzles are fun to try and there are 5 new sets each year.
• The Institute of Mathematics and its Applications (IMA) has careers advice and other information for students of mathematics.
• Theorem of the Day. To my extreme joy one of the theorems is mine, from a paper with Michael Giudici.

## Contact details

Phone: +44 (0) 20 7631 6437
Email: s.hart@bbk.ac.uk
Room: 753
Office Hours:Fridays 4:30 - 5:45