Colin has been a maths tutor since high school, originally for family and friends, then more formally at university and researcher. Listen to this podcast to solve mathematics without headache.
Via @PaulsPrattle (Paul O’Malley): “If you were the ruler of the universe tomorrow what would be the objective in secondary mathematics learning for all kids everywhere?”
Via @aap03102, (Chris Smith)’s newsletter: some love for Simon Plouffe
Puzzle feedback from last time: We hadn’t seen any solutions when we started recording, but some have come in since - we’ll mention those next month. However: Chris pointed out a tweet from @mathsjem (Jo Morgan) showing the clock-hands puzzle in Thompson’s Practical Algebra, published in 1878.
New Puzzle: There are 3 lighthouses. The first shines for 3 seconds and then is off for 3 seconds. The second shines for 4 seconds and then is off for 4 seconds. The third shines for 5 seconds and then is off for 5 seconds. Initially, all three come on together. When is the next time they’re all on at the same time?
Via Jeremy Cote: "I've actually seen [J] in a textbook I've used for my real analysis course, but in that case, it was to represent the natural numbers (1,2,3,...). The book is called Introduction to Analysis, and can be found here.
Stephen Wootton tweets: @WrongButUseful regarding tax there is also the interesting case between £100k - £120k where the tax free allowance is reclaimed thereby giving rise to an effective tax rate higher than the highest rate of income tax! Keep up the podcasts, thank you.
via Adam Atkinson: a picture of a 24-hour clock (photo by Daniele Aurelio of Pavia Mathsjam)
Adam found a book from the 50s or 60s which called the set of integers “J”. “Have you or your loyal listeners ever run into this?”
@divbyzero asks: Technical math terms the general public uses in a nontechnical way: inflection point (a turning point), squaring the circle (difficult task of reconciling two very different things), in the Venn diagram of _ and _ (in the intersection of), exponential growth (grows fast). Others?
This month’s puzzle: In a game show, you have four distinct tokens you have to arrange in an unknown order. Every time you guess, you are told1 how many are in the correct position. What strategy gives you the correct answer in the fewest guesses?
In this month’s Wrong, But Useful, we’re joined by @televisionduck, who is TD Dang in real life. We discuss:
Chalkdust Issue 091 Fun spring cover with Harris spiral, Horoscope is back!, New academic webpage checklist (c.f. Colin’s old webpage, @standupmaths interview, top ten regulars, etc. Write for them!
Talkdust, second best podcast: it’s about maths, puzzles, making the magazine, interviews.
The Queen Elizabeth Prize for Engineering for 2019 has been awarded to engineers Bradford Parkinson, James Spilker, Hugo Fruehauf and Richard Schwartz for their foundational contributions to the creation of GPS. The prize, worth £1,000,000, celebrates the global impact of engineering on humanity.
Dave gave a talk in Exeter and will hopefully give one in Bristol in June.
Humble Pi by @standupmaths – book launch on March 2nd in London, tickets selling fast sold out. You can join the waiting list here.
@honeypisquared (Lucy)’s new podcast – Mathematips
We’ve been shouted out in @aap03102 (Chris Smith)’s newsletter, and on @missradders’s padlet – thanks!
Tax – round up or not?
Rotationally symmetric equations (@robeastaway and @peterrowlett): here, here, and Elliot’s versions here
Puzzle feedback from last time: Gold star for @chrishazell72: for showing that $(a-b)^2 + (b-c)^2 + (c-a)^2 + (a+b+c)^2 = 3(a^2 +b^2 + c^2)$, and that the first child is 6, younger (2yo) born when elder was 3.
New Puzzle (via @cmonMattTHINK): Find the line that touches $y= x^4 – x^3$ at two distinct points. Avoid calculus if possible.
via @fenneklyra: Follow up on “Guess who”: There are 24 people on board, and I had a typo, the first question narrows it down to 12 which means it IS the most efficient one cause you will always have narrowed it down by half. Not sure it’s allowed
Puzzle feedback: @schwartstack and Adam Atkinson both found answers in the region of $3.5 \times 10^{38}$, rather than quadrillions. Gold stars all round. On looking into it more, the Fantasy Flight Games site claims 104 septillion (still several orders of magnitude too small.)
This month’s puzzle: Prove that 3 times the sum of 3 squares is the sum of 4 squares.
This month’s second puzzle: A parent buys a pack of 24 candles. On their first child’s first birthday, they use one candle; on the second, two candles and so on. At some point, a younger sibling arrives, and the candles are used in the same way. On one of the first child’s birthdays, the parent finds they have exactly the right number of candles left for that birthday. How old is the first child, and how old were they when their younger sibling was born?
In this month’s episode of Wrong, But Useful, we’re joined by @ch_nira, who is Dr Nira Chamberlain in real life – and the World’s Most Interesting Mathematician.
Dave has a circle question that stumped his students. Nira turned the tables on some future teachers by making them simulate Aston Villa’s season. Ouch.
@fenneklyra’s Guess Who questions: “White hair OR red hair OR glasses? Yes: Red hair or hat? No: Blond or hat? Then there are only 6 left of which you can make out the next question yourselves”
Dave thanks Adam Atkinson for his help on percentages.
Puzzle feedback: gold stars for @schwartstack, @chrishazell and loyal antipodean listener Sam Steele, who each worked out $P(X=5) = \frac{1}{120}, P(X=4) = 0, P(X=3) = \frac{1}{12}, P(X=2) = \frac{1}{6}, P(X=1) = \frac{3}{8}, P(X=0) = \frac{11}{30}$.
This month’s puzzle: Dave is playing Keyforge, in which a deck consists of 36 cards: twelve from each of three distinct clans. There are 51 distinct cards available for each clan (repeats are allowed), and seven clans. The makers quote quadrillions of possible decks; is this plausible?
Puzzle feedback: @chrishazell wins a green star for implying that he solved the puzzle in episode 59. The expected number of throws were 6 and 4, in some order.
Puzzle: Can you list the integers from 1 to 15 so that each pair of adjacent numbers adds up to a square number? If so, what’s the next number you can do this for?
Ada Lovelace Day: None of us did anything for this this year, shamefully. The Aperiodical is orgainising Noethember, an Inktober in November illustrating mathematical legend Emmy Noether’s life. Matt asks after the Wikiquote editathon, which we discussed here.
Guess who: when there are three people left, should you just guess? Should you take more risks when behind?
Dave isn’t going to Big MathsJam. If that’s an incentive, you can book here.
Parabolic multiplication: Matt describes how to multiply using a parabola, and mentions @realityminus3’s lovely logarithms article.
Puzzle feedback: Gold star to @chrishazell for 8-1-15-10-6-3-13-12-4-5-11-14-2-7-9. For more, [watch @numberphile](https://www.youtube.com/watch?v=G1m7goLCJDY)
From the Chalkdust quiz: Are there more words in Harry Potter and the Order of the Phoenix or entries in the OEIS?
This month’s puzzle: Adapted from a recent MathsJam Shout: you have cards labelled 1, 2, 3, 4, 5 face down in a random order on the table. You predict the order of the cards before turning them over. What’s the probability of getting all five correct? Four? Three? Two? One? None?