Maths, but not as you know it…
Bayes’ Theorem allows us to assign a probability to an unknown fact. Thomas Bayes himself described an experiment with a billiard table so me and James tried to recreate it. Unfortunately, it didn’t quite go to plan…
Check out James’ channel here: https://www.youtube.com/user/singingbanana
Entries for the first ‘Teddy Rocks Maths’ Essay Competition are now open! This is YOUR chance to write a short article about your favourite mathematical topic which could win you a prize of up to £100. ENTER HERE: https://seh.ac/teddyrocksmaths
All entries will be showcased on tomrocksmaths.com with the winners published on the St Edmund Hall website. St Edmund Hall (or Teddy Hall as it is affectionately known) is a college at the University of Oxford where Tom is based.
Entries should be between 1000-2000 words and must be submitted as Microsoft Word documents or PDF files using the form at https://seh.ac/teddyrocksmaths
The closing date is 12 March 2020 and the winners will be announced in April 2020.
Two prizes of £50 are available for the overall winner and for the best essay from a student under the age of 18. There are no eligibility requirements – all you need is a passion for Maths and a flair for writing to participate!
The winners will be selected by Dr Tom Crawford, Maths Tutor at St Edmund Hall and the creator of the ‘Tom Rocks Maths’ outreach programme. The mathematical topic of your entry can be anything you choose, but if you’re struggling to come up with ideas here are a few examples to get you started:
Where does river water go when it enters the ocean? – Numberphile
Would alien geometry break our brains? – Tom Rocks Maths intern and maths undergraduate Joe Double
How many ping-pong balls would it take to raise the Titanic from the ocean floor?
If you have any questions or would like more information please get in touch with Tom using the contact form here – Good luck!!
I went to visit the National Museum of Mathematics (MoMath) in New York City to walk the Million Millimeter March to celebrate the 1 millionth visitor to MoMath. Puzzle enthusiast and mathematician Peter Winkler (Dartmouth) joined me to provide some fun facts about numbers along the way…
The route is shown below.
The fun facts about numbers explained by Peter Winkler are copied below for reference:
142,857 – a cyclic number. Try multiplying it by 1, 2, 3, 4, 5 or 6 and see what happens!
219,978 – the only 6-digit number such that if you multiply it by 4 it reverses!
322,560 = 9! – 8!
422,481 – the smallest number whose fourth power is itself the sum of three smaller fourth powers: 422,481^4 = 414,560^4 + 217,519^4 + 95,800^4
548,834 – a six-digit number equal to the sum of the sixth powers of it’s six digits: 548,834 = 5^6 + 4^6 + 8^6 + 8^6 + 3^6 + 4^6
604,800 – the number of seconds in a week.
742,900 – the number of different ways to walk from the bottom left to the top right (only moving along grid lines to the right or upward) in a 13×13 grid, always staying below the diagonal.
801,125 – the smallest number that is the sum of two positive squares in at least 2^2^2 ways.
873,613 = 1^1 + 2^2 + 3^3 + 4^4 + 5^5 + 6^6 + 7^7
1,000,000 = the number of visitors to MoMath!
The third video in the fluid dynamics trilogy I made for Numberphile. Rivers contain 80% of pollution which ends up in the ocean, so understanding where the water goes when it leaves the river mouth is of upmost importance in the fight to clean-up our planet.
Watch part 1 on the Navier-Stokes Equations here
Watch part 2 on Reynolds Number here.
Livestream event with Oxplore – the University of Oxford’s digital outreach portal – discussing the BIG question “is school the best place to learn?”. Panelists include geologist Dr Brooke Johnson, historian Dr Sian Pooley, and education specialist Dr Susila Davis.
Calling all state school students with an interest in maths – apply now to join the St John’s College Maths Study Day on March 5th to learn how the MAT (Maths Admission Test) works, dissect a live admissions interview (conducted by me), and hear my talk about Maths and Sport. Free lunch provided and travel support available.
Apply here: https://www.sjc.ox.ac.uk/study/working-schools/study-days/
Fun facts about numbers that you didn’t realise you’ve secretly always wanted to know…
Hands up if you like ice cream? And your favourite brand? I’m not sure I could pick a favourite myself, but Baskin-Robbins is certainly up there. They have a total of 31 flavours of ice cream which means the name of their shops in Japan literally translates as ’31 Ice Cream’. In theory a great idea, but what if they discover a magical new thirty-second flavour…
Aside from frozen goods, thirty-one is also the number of teams in the National Hockey League, with 24 coming from the US and 7 from their Northern neighbours Canada. Each season, the teams battle it out to win the Stanley Cup — the oldest trophy to be awarded in professional sport in North America, and also the one with the infamously large base (see below). Originally, key members of the winning team were engraved on the base, which means its grown a fair few inches over the past 126 years. However, these days the oldest band is removed and replaced with a new one to prevent the trophy from getting any bigger. Less fun no doubt, but perhaps sensible given its already considerable size…
Credit: Michael Miller
Thirty-one is also a Mersenne Prime — the third such one in fact. A Mersenne Prime is a prime number that can be expressed as exactly one less than a power of two: 2^n — 1 for some positive whole number n. To get 31, we take n=5: 2⁵ = 2 x 2 x 2 x 2 x 2 = 32 minus 1 gives 31. A perhaps surprisingly large (and possibly infinite) amount of prime numbers take this form, with the current largest known prime number also being a Mersenne Prime: 2⁸²⁵⁸⁹⁹³³–1 = a number with 24,862,048 digits, aka too many for me to write out here!
Sticking with maths, thirty-two has the very nice property that it can be written as 1 to the power 1 plus 2 to the power 2 plus three to the power three, or in its neatest form: 1¹ + 2² + 3³ = 32. Here’s a challenge for you: can you work out the next largest number that follows the same pattern?
32 can also be written as 2⁴ + 4² = 32 which makes it a Leyland Number. Any number that can be written using two other numbers x and y, in the pattern x to the power y plus y to the power x, is classified as a Leyland Number. Here, we take x = 2 and y = 4 to get: 2⁴ = 2 x 2 x 2 x 2 = 16, plus 4² = 4 x 4 = 16, giving a total of 16 + 16 = 32. Other Leyland Numbers include: 8, 17, 54, 57 and 100 — I’ll leave it to you to figure out the specific values of x and y needed to satisfy the formula x^y + y^x = Leyland Number for each of the cases above.
Outside of the mathematical world, thirty-two is the number of completed piano sonatas by Ludwig van Beethoven; the number of black (or white) squares, and total number of pieces on a chessboard; the number of teeth generally found in an adult human; and the number of described physical characteristics of the historical Buddha, according to the text of the Pāli Canon in the Theravada Buddhist tradition. It’s a pretty long list, but I think it is best enjoyed in its entirety, so here you go:
Let’s start with the bad. Thirty-three is one of the symbols of the Ku Klux Klan, with K being the 11th letter of the alphabet and 3 x 11 or 3 K’s giving 33. It is also believed to be the age of Jesus when he was crucified by the Romans.
On a more positive note, 33 is the longest winning streak ever recorded in NBA history, which was achieved by the Los Angeles Lakers in the 1971–72 season. We also find 33 vertebrae in a normal human spine when the bones that form the coccyx (the tail-like part at the bottom) are counted individually.
Now I don’t say this often — mainly because I think I’m supposed to be impartial when writing these — but this next fun fact is one of my all-time favourites. Long playing records, or LPs as they are more commonly known, are referred to as 33’s in the record industry, because they rotate 33 and a third times per minute when playing on a gramophone. So, next time you see a record player you know what to do…
Counting outtakes from the Numberphile Pi Million Subscribers celebration video. Look out for a familiar face/torso at 4:33…
Jellyfish stingers reach an acceleration 50 times faster than that of a bullet as they are ejected from stinging capsules under high pressure. Uri Shavit at Technion-Israel Institute of Technology has developed a new mathematical model to explain this incredible mechanism which will help to make us better prepared to protect swimmers from jellyfish stings.
This video is part of a collaboration between FYFD and the Journal of Fluid Mechanics featuring a series of interviews with researchers from the APS DFD 2017 conference.
Sponsored by FYFD, the Journal of Fluid Mechanics, and the UK Fluids Network. Produced by Tom Crawford and Nicole Sharp with assistance from A.J. Fillo.
Calling all US-based students, if you have ever thought you would like to have me as your college professor, now is your chance. I am currently in charge of the visiting student mathematics programme at St Edmund Hall, which means anyone accepted onto the programme will have weekly tutorials with yours truly. Information on the course specifics and how to apply can be found on the St Edmund Hall website here.
Courses available include (but are not limited to):
The detailed course synopses, as well as some course materials can be found here.
If you have any questions please get in touch with Tom via the contact form, or the admissions office at St Edmund Hall via admissions@seh.ox.ac.uk.
Photo: Flemming, Heidelberg Laureate Forum
I was recently interviewed by Lucia Taboada for La Redada Podcast about my love of maths and how it is used in today’s world to model everything from penalty kicks to the next TV series you watch on Netflix. The interview was translated into Spanish for the actual podcast so I’ve also included the original recording of my answers in English – enjoy!
La Redada T08 E29: Tom Crawford the Naked Mathematician
Image: Residencia de Estudiantes
