Category Archives: Maths

The solution to the algebra puzzle…

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The solution to Puzzle #4 is now up. Either follow the links from the puzzle itself HERE, or, if you have seen the question already, click HERE to go straight to the solution.

As I mentioned previously, I think this is a good puzzle for mathematics learners at GCSE level or for those setting out on A-level courses, both for checking up on basic algebraic understanding and for illustrating some specific problem-solving skills. I have summarised the key learning points that I think the puzzle raises on the solution page.

 

New Puzzle

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I have put a new puzzle up. Nothing too tough this time. A classic algebra puzzle, which I have found to be pretty good as a test of how well GCSE/A-level students understand some basic points of algebra, while illustrating some important problem solving skills.

#4: Hidden depths…
A classic algebra puzzle.
Published: 02/06/2015
Difficulty: *
Maths knowledge required: GCSE algebra [i.e. 14-16 year olds]. Although KS3 would do…

Click HERE to access the puzzle.

The solution will go up in a day or two.

Fractal Follow-up

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There have been a few nice follow-ups on my fractals based on iterating the factorial function:

Steve Kass also directed me to this page, in which academic multitasker in computer science, neuroscience, philosophy and future studies Anders Sandberg presents some lovely alternative Gamma function fractals (posted in February). Intriguingly, the author has also co-written an academic paper on the science of tie-knots (apparently inspired by a costume from The Matrix Reloaded), which identifies “266,682 distinct tie-knots that seem tie-able with a normal neck-tie”. Surely worth a read.

In other news, I recently passed my PhD viva, which is probably for the best. Among other things, this means that my putative article on “How to fail your PhD” will have to be put on ice indefinitely.

Diabolical Digits

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The other day, I did a mini-investigation into an interesting maths tweet from Cliff Pickover. Here’s another:

 

This fact is beautiful, but is it surprising?

Click here to find out.

 

Political Pi

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The seat totals of the four largest political parties at the general election (excluding Northern Ireland and the speaker), 330, 232, 56, 8, appear in sequence, starting from the eighty-eight million, five hundred and eight thousand, three hundred and seventy-ninth digit of π, counting after the decimal point.

To think that the election result was staring us in the face all the time. If only we had known where to look, we could have saved ourselves all that bother with the polls…

(Actually, √2 is even more helpful, giving us the DUP seat total as well. 330, 232, 56, 8, 8 appear in sequence, starting from the one billion, forty million, one hundred and thirty-two thousand, five hundred and seventy-third digit of √2, counting after the decimal point.)

Search for other numbers hidden in mathematical constants here.

Election predictions and statistical independence

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Here’s an article on predicting the UK election: CLICK HERE

In the piece, I raise some queries about two very interesting articles from the excellent election news site May2015. The articles (here and here) suggest that David Cameron faces an extremely difficult task to remain as prime minister, based on the mathematics of how national polls will translate into parliamentary seats. I wonder whether the statistics support the level of confidence with which this conclusion is presented.