Welcome to this week’s Math Munch!

The things we have lined up for you this week have to do with a part of math called topology.  Topology is like geometry in many ways, except the shapes you study aren’t rigid.  Instead, you can twist, stretch, squish, and generally deform them in any way you like, so long as you don’t rip any holes or attach things that weren’t already attached.  One of the reasons why topology is interesting is that you get to play with new and fascinating shapes, like…

… knots!  This nifty site, Knot Theory Online, is full of interesting information about the study of mathematical knots and its history and applications.  For some basic information, check out the introduction to knots page.  It talks about what a knot is, mathematically speaking, and some ways that mathematicians answer the most important question in knot theory: is this knot the unknot?  The site also has some fun games in which you can play with transforming one knot into another.  Here’s my favorite: The Hunt for the Elusive Trefoil Knot.

Knots can also be works of art – and this site, Knot Plot, showcases artistic knots at their best.  Here are some images of beautiful decorative knots.

A really cool thing about knot theory is that it is a relatively new area of mathematical research – which means that there are many unsolved knot theory problems that a person without a lot of math training could attempt!  Here’s a page of “approachable open problems in knot theory,” compiled by knot theorist and Williams College professor Colin Adams.

One of a topologist’s favorite objects to study is one that you might encounter at breakfast – the torus, or donut (or bagel).  To get a sense for what makes a torus topologically interesting and for what life might be like if you lived on a torus (instead of a sphere, a topologically different surface), check out Torus Games.  Torus Games was created by mathematician Jeff Weeks.  You can play games that you’d typically play on a plane, in flat space – such as Tic-Tac-Toe, chess, and pool – but on a torus (or a Klein bottle) instead!

A maze – on a torus!

By the way, you can find Torus Games and other cool, free, downloadable math software on our new page – Free Math Software.  You’ll find links to other software that we love to use – such as Scratch and GeoGebra, and another program by Jeff Weeks called Curved Spaces.

All this talk of tori making you hungry?  Go get your own tasty torus (bagel), and try this fun trick to slice your bagel into two linked halves.  This topologically delicious breakfast problem was created by mathematical artist George Hart.

Bon appetit!  (Literally, this time.)