# The Flying Colours Maths Blog: Latest posts

## "How do I know which method to use?" – How to Integrate

My student frowns as I write down $u = \cos(x)$. "Wait wait wait", he says, "how do you know to do a substitution?" The honest answer is, I just do. I've done integration sum after integration sum for the last 20 years and it comes naturally. However, I know that's

## The Way Of The Mathematical Ninja

The Code of the Mathematical Ninja has been developed over many centuries1, and is considered by most serious mathematicians to be one of the Far East's greatest contributions to maths. Its very existence was - until now - a closely guarded secret, known only by the inner circle of mathematicians

## Free for all Friday

Only a few weeks to the summer break now! Got anything nice planned? Well, what can I help you with this week? Just drop me a comment below and I'll do what I can to answer it.

## A neat number trick: digital roots and modulo-9 arithmetic

This post is inspired by a question asked by Dan - thank you, Dan! So here's the gist of Dan's question: Take a random sum, e.g. 496866 + 446221 = 943087. Add up all the digits in each number (39, 19 and 31). Keep adding up the digits in each

## Secrets of the Mathematical Ninja: Sines and cosines near 45º

This is the one area where I'm better with degrees than with radians - and I suspect that's only because I don't particularly notice when radian angles are close to $\frac{\pi}{4}$, but I do when degree angles are close to 45º. This one's a trickier one than we've been looking

## Free for all Friday

June already? That sounds like it's almost summer. However, bad luck, you still have a few weeks of exams to go. How are they coming along? Well, what can I help you with this week? Just drop me a comment below and I'll do what I can to answer it.

"The race that does not value trained intelligence is doomed." - A.N. Whitehead

## Football, frustration and maths

One of my students scoffed at me the other day for saying I liked football. In particular, I like bad football - the last game I went to see was Maidenhead United against Truro City in the second qualifying round of the FA Cup, and even that was a bit

## Secrets of the Mathematical Ninja: Trigonometry With Small Numbers

Radians - as I've ranted before - are the most natural way to express angles and do trigonometry. No ifs, no buts, degrees are an inherently inferior measure and the sooner they're abolished, the better. (In other news, the campaign to replace the mishmash of units called 'time' by UNIX