# The Flying Colours Maths Blog: Latest posts

## 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

## 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.)

## 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,

## 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

## Primes or not?

I’m in the process of clearing out old bookmarks, and stumbled on this puzzle from @jase_jwanner: Prime or not prime? No calculators allowed!a. 23567897614^2 - 1b. 34564344^3 -1c. 76543556556625731d. 345643554^{10} - 169 — Jase (@jase_jwanner) August 27, 2016 I shall give you a moment to ponder these, and put my