## Maths on a Mug #16

#mathsonamug pic.twitter.com/Rd0IAC9YHw — Sean Elvidge (@seanelvidge) November 17, 2016 Perhaps a “simple” #mathsonthemug this time. Simple, but very important. This is Bayes’ theorem: $P(A|B) = \frac{P(B|A)P(A)}{P(B)}.$ This relates the probability of observing $$A$$ given that $$B$$ is true where $$A$$ and $$B$$ are events, we also require that the probability of $$B$$ does not equal

## Maths on a Mug #15

#mathsonamug #maths #newpoundcoin pic.twitter.com/lMQm5uOUyl — Sean Elvidge (@seanelvidge) November 4, 2016 Keeping with the theme of yesterdays blog post about the new pound coin and shapes of constant diameter here is a nice little result known as Barbier’s theorem. Simply, it says that for any curve of constant diameter (width; $$w$$) the perimeter of that shape

## Maths on a Mug #14

#mathsonamug #maths #puzzle pic.twitter.com/jbbehLQbp7 — Dr. Sean (@seanelvidge) January 29, 2016 A question I really like because of the logical way of thinking about the answer. First we assume that we do not allow the trivial answer where $$n=m=q=0$$. Then rewrite the equation as: $2^n + 3^m = 5^q+1.$ Now $$2^n$$ must be even for

## Maths on a Mug #13

#mathsonamug #maths pic.twitter.com/zzl8CjKZ3o — Dr. Sean (@seanelvidge) January 26, 2016 A classic! This is my favourite result from Graph Theory. The branch of mathematics invented by Euler, this theorem is known as Euler’s Formula. It is a remarkable fact that for any planar graph (edges only intersect at their endpoints) the number of faces (regions

## Maths on a Mug #12

#mathsonamug #maths pic.twitter.com/7GmWSFAfYP — Dr. Sean (@seanelvidge) January 25, 2016 One of the more common things that I’ve been asked recently. Mostly this comes from people who have watched the incredibly successful Numperphile video, but the result was well known before then. There are a number of ways to ‘prove’ this result, giving rise to

## Maths on a Mug #11

#mathsonamug #maths pic.twitter.com/REPJ4xFhT9 — Dr. Sean (@seanelvidge) January 22, 2016 Primes. Primes. Primes. The hunt continually goes on for the next biggest. Well, yesterday, we found a new largest. $$2^{74207281}-1$$ is the 49th Mersenne Prime that has been found. It is 22,338,618 digits long (click the link to download the whole number, be warned though, the file is

## Maths on a Mug #10

#mathsonamug #maths pic.twitter.com/YV2iIOuinu — Dr. Sean (@seanelvidge) January 21, 2016 Another University of Birmingham Mathematics department mug. The ‘Blakelet’ named after Professor John Blake at the University is a based upon a 1971 paper investigating the velocity and pressure fields for Stokes’s flow due to a point force.

## Maths on a Mug #9

#mathsonamug #maths pic.twitter.com/Af8IJ9uGbw — Dr. Sean (@seanelvidge) January 20, 2016 Fermat’s Last Theorem is a celebrated result in mathematics, simply it says that: There are no three positive integers $$a,\,b,\,c$$ such that $$a^n+b^n=c^n$$ for any value of $$n>2$$. For the value $$n=2$$ this is the well known Pythagoras theorem. A simple theorem to state, but

## Maths on a Mug #8

#mathsonamug #maths pic.twitter.com/gDWvKSfTlN — Dr. Sean (@seanelvidge) January 19, 2016 This is the first post related to my work at the moment. I’ve been using a branch of statistics called ‘Extreme Value Theory’ in order to come up with a statistical analysis of extreme space weather events. This approach has been used in a variety

## Maths on a Mug #7

#mathsonamug #maths pic.twitter.com/wSbBxEd9bm — Dr. Sean (@seanelvidge) January 18, 2016 I saw someone solving a Sudoku on the train this morning, which made again think about the minimum number of ‘clues’ required to solve a puzzle. It has been proven that you need at least 17 clues to have a unique, solvable, solution.