The Flying Colours Maths Blog: Latest posts

When Maths Gets Difficult

I could probably have framed this post as an “Ask Uncle Colin”, but it feels somehow different, so I’m going to do it as a Monday post. My blog, my rules. On Twitter, @sharanjit asked: I had a point in my education where maths went from being easy to suddenly

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Ask Uncle Colin: an unexpected Golden Ratio

Dear Uncle Colin, Why is $\cos(36º)$ equal to $\frac{\phi}{2}$? I find trigonometry difficult and, uh, let’s say I have some demons to banish. Puzzled Educator Noticed That A Golden Ratio Appears Magically Hi, PENTAGRAM, and thanks for your message! I would imagine there are several ways to demonstrate this, but

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A Catriona Shearer Classic

If you’ve read this blog for a while, you’ll know I’m a fan of @cshearer41’s puzzles (her book, Geometry Puzzles in Felt Tip, is available wherever etc). At a recent MathsJam, one jumped out of Chalkdust at us: (Image from Issue 10 of Chalkdust, a magazine for the mathematically curious.)

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Ask Uncle Colin: how many zeros?

Dear Uncle Colin, How many zeros are there on the end of $100!$? I worked it out to be 21, but the answer sheet says it’s 23 – and my calculator just gives an error message. What do you think? - Maybe A Tutor Has Exact, Reasoned Response? Hi, MATHERR,

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Completing the square

Suppose we have $ax^2 + bx + c = 0$. It’d be easier to complete the square if the $x$ term were even, so let’s double: $2ax^2 + 2bx + 2c = 0$ It’s also be nicer if the $x^2$ term were a square, so let’s multiply by $2a$: $4a^2x^2

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Ask Uncle Colin: A Pair Of Toy Trucks

Dear Uncle Colin, I have an exam question I don’t understand! There’s a toy truck of mass 5kg attached (by a rod) to another truck of mass 2kg on a slope at 10 degrees to the horizontal. The resistances to motion are 8N and 6N, respectively, and the whole thing

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Dictionary of Mathematical Eponymy: Volder’s algorithm

One of the questions that occasionally crops up in the hive of scum and villainy I hang out in search of problems to solve is, “how do calculators work out trigonometric values?”. It’s not, typically, the way that the Mathematical Ninja would (find an angle nearby and adjust using heuristics),

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Ask Uncle Colin: integrating a trigonometric product

Dear Uncle Colin, I need to figure out $\int \cos^3(2t) \sin^5(2t) \dt$ and I’m… just going round in circles. So to speak. What do you suggest? - Doing Integration’s Really A Chore Hi, DIRAC, and thanks for your message! It’s very easy to end up going around in circles on

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A Puzzle Full of Nines

A nice puzzle by way of @benjaminleis: This AIME problem is fun: — Benjamin Leis (@benjamin_leis) February 2, 2020 In case you can’t read that, we need to find the sum of the digits in $N = 9 + 99 + 999 + 999\dots999$, where the last number consists

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Ask Uncle Colin: How do I stretch my students?

Dear Uncle Colin, I want to stretch my Year 12 Further Maths class - what extra-curricular topics would you recommend? Something To Really Engage Their Creative Reasoning Hello, STRETCH, and thanks for your message! How excellent to be looking beyond the curriculum for ways to engage and develop your young

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