My favourite shape…

The content of this post originally appears on Chalkdust’s ‘What’s your favourite shape?’ post.

Möbius strip (Rob Beckett)

My favourite ‘shape’ is the one sided non-orientable surface called the Möbius strip. This can be created by simply twisting a long strip of paper and gluing the ends together. One of the explanations most regularly associated with the Möbius strip is that of MC Escher, who described an ant crawling along its surface. The ant would be able to do this and return to his starting point having not even crossed an edge (or maybe it keeps crawling on indefinitely hoping to find the end!).

In the Numberphile video Möbius bridges and buildings Carlo H Séquin (UC Berkeley) considers using the idea of a Möbius strip to create aesthetic bridges and buildings.

mobius

My favourite function…

The content of this post originally appears on Chalkdust’s ‘What’s your favourite function? Part II’ post.

Rob Beckett’s favourite is a classic:

e^x

My favourite function is the exponential function f(x)=e^x. This is primarily because \frac{d}{dx}(f(x))=e^x, in other words the function is growing at a rate which is equal to its current size. This is a really interesting property which comes from the fact that e=\lim\limits_{n\rightarrow \infty}{(1+\frac{1}{n})^n}. Just like pi is the ratio between the circumference and diameter of circles, the number e is the base rate of growth and it crops up whenever things grow or decay continuously and exponentially. Our exponential function appears when considering bacterial growth rates, populations, radioactive decay and even occurs in the Black-Scholes formula which is used in the financial market.

Chalkdust magazine

I visited UCL for a training course last week and I took the opportunity to catch up with the Chalkdust team, acquiring some copies of their magazine. This is a reasonably new ‘mathsy’ magazine which is being published by students in the mathematics department at UCL.

I’ve not had a proper chance to look thoroughly through it yet, but it looks both professional and full of exciting maths! Congratulations go to the Chalkdust team!

You can view an online version of the magazine in this link if you are interested!