I really really like this zoom into a Menger sponge made by Reuben Thomas of functor.co.
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The minch, the mound and the light-gigaminch
On Wednesday 27th November 2013, friend of The Aperiodical and standup mathematician Matt Parker tweeted a link to his latest YouTube video.
In the video Matt apologises for some remarks on the imperial number system that he made in an earlier Number Hub video about the A4 paper scale. He then goes into some of the quirkiness of the many imperial number units used for measuring length. It is an unusual ‘apology’, although very entertaining.
This got me thinking about how I think about lengths, and I tweeted that I often think in ‘metric-imperial’ units of length, or multiples of exactly 25mm in my job as a civil and structural engineer – a metric inch, if you like. Colin Wright suggested the name ‘minch’ for these units; there are then two score minch to the metre.
Daydream by Nonotak Studio
[youtube url=http://www.youtube.com/watch?v=UY7l_UgHhBQ]
via NotCot.org
Dynamic generation of maths questions
I was recently asked about my MSc dissertation (by someone who may choose to ‘out’ themselves here, but as it was a personal email I won’t name them). In my dissertation, for a Masters degree in computing in 2003-4, I developed a system for pre-processing MathML code using PHP to include pseudo-randomised values in the questions for an e-assessment tool. The title is ‘Asking Questions With MathML: dynamic treatment of XML and pseudo-randomised mathematics assessment’.
The query was from someone who is training to be a maths teacher and is doing some web development. They had seen mention of my MSc dissertation topic on this blog and asked where they could read more about the underlying web technologies. Here, basically, is what I replied.
Interesting Esoterica Summation, volume 8
Mathematicians! Stop what you’re doing! I’ve almost certainly got something more interesting for you here. It’s been a good while since I last updated you on the contents of my Interesting Esoterica collection, and I have a proportionate number of mathematical curiosities to entertain and bewilder you with.
In case you’re new to this: every now and then I encounter a paper or a book or an article that grabs my interest but isn’t directly useful for anything. It might be about some niche sub-sub-subtopic I’ve never heard of, or it might talk about something old from a new angle, or it might just have a funny title. I put these things in my Interesting Esoterica collection on Mendeley. And then when I’ve gathered up enough, I collect them here.
In this post the titles are links to the original sources, and I try to add some interpretation or explanation of why I think each thing is interesting below the abstract.
Some things might not be freely available, or even available for a reasonable price. Sorry.
What do these three pictures have in common?
What do these three pictures have in common?
The first is the bust of Nefertiti, an Egyptian queen. The bust is now in the Neues Museum in Berlin and is one of the most beautiful works of art. Nefertiti is translated as “a beautiful woman has come”. The word nefer is in this case translated as ‘beautiful’.
The second is a drawing of a Grecian urn by Keats. Keats’ Ode on a Grecian Urn ends with the line “Beauty is truth, truth beauty,”.
The third picture is part of the Moscow Mathematical Papyrus from ancient Egypt.
Probability of dealing four perfect hands of cards in a world of random shufflers
A couple of months ago (really? Two years?! Man!) I posted about an extraordinary coincidence: in a game of whist at a village hall in Kineton, Warwickshire, each of four players had been dealt an entire suit each. My post ‘Four perfect hands: An event never seen before (right?)‘ discussed this story. What really interested me was that the quoted mathematical analysis — and figure of 2,235,197,406,895,366,368,301,559,999 to 1 — appears to be correct; what lets down the piece is poor modelling. The probability calculated relies on the assumption that the deck is completely randomly ordered. Apart from the fact that new decks of cards come sorted into suits, whist is a game of collecting like cards together, so a coincidental ordering must be made more likely. Still unlikely enough to be worthy of mention in a local paper, maybe, but not “this is the first time this hand has ever been dealt in the history of the game”-unlikely.
Anyway, last week I was asked where the quoted figure 2,235,197,406,895,366,368,301,559,999 to 1 actually comes from. Here’s my shot at it.