# The Flying Colours Maths Blog: Latest posts

## Ask Uncle Colin: Meeting Graphs

Dear Uncle Colin, I’m told that the graphs of the functions $f(x) = x^3 + (a+b)x^2 + 3x -4$ and $g(x) = (x-3)^3 + 1$ touch - and I need to express $a$ in terms of $b$. Can you help? - Can’t Understand Basic Introductory Calculus Hi, CUBIC, and thanks

## Dictionary of Mathematical Eponymy: Ivory’s Theorem

I… I… I… *Looks up Ito’s Lemma* *Reaches for bargepole, then doesn’t touch it.* I… I… I… Oh! It says here, there’s a thing called Ivory’s Theorem1! What is Ivory’s Theorem? Despite the main paper I could find about it calling it “the famous Ivory’s Theorem”, it was fairly tricky

## Ask Uncle Colin: An Area To Find

Dear Uncle Colin, I need to find the area between the curves $y=16x$, $y= \frac{4}{x}$ and $y=\frac{1}{4}x$, as shown. How would you go about that? Awkward Regions, Exhibit A Hi, AREA, and thanks for your message! As usual, there are several possible approaches here, but I’m going to write up

## The Mathematical Ninja and the Unknown Powers

The Mathematical Ninja peered at the problem sheet:   Given that $(1+ax)^n = 1 - 12x + 63x^2 + \dots$, find the values of a and n   Barked: “$n=-8$ and $a=\frac{3}{2}$.” The student sighed. “I get no marks if I just write down the answer.” Snarled: “You get no

## Ask Uncle Colin: A Missing Digit

Dear Uncle Colin, A seven-digit integer has 870,720 as its last six digits. It is the product of six consecutive even integers. What is the missing first digit? Please Reveal Our Digit! Underlying Calculation Too Hi, PRODUCT, and thanks for your message! There are several approaches to this (as usual)

## Barney’s Wedge

Once upon a MathsJam, Barney Maunder-Taylor showed up with a curious object, a wedge with a circular base. Why? Well, if you held a light above it, it cast a circular shadow. From one side, the shadow was an equilateral triangle; along the third axis, a rectangle. A lovely thing.

## Ask Uncle Colin: An Infinite Product

Dear Uncle Colin, I have to show that $\Pi_1^\infty \frac{(2n+1)^2 - 1}{(2n+1)^2} > \frac{3}{4}$. How would you do that? Partial Results Obtained Don’t Undeniably Create Truth Hi, PRODUCT, and thanks for your message! That’s a messy one. I can see two reasonable approaches: one is to take the whole thing

## Regions of a circle

On a recent MathsJam Shout, an Old Chestnut appeared (in this form, due to @jamestanton): If you’ve not seen it, stop reading here and have a play with it - it’s a classic puzzle for a reason. Below the line are spoilers. Counting is hard The first thing you’d probably

## Wrong, But Useful: Episode 70

In this episode, we're joined by special guest co-host @sophiebays, who is Dr Sophie Carr in real life, and the world's most interesting mathematician1. We discuss: The Big Internet Math-Off. My favourite pitch wasn’t really in the contest! I also liked Alex’s wobbly table and Anna’s FURNACE. Number of the

## Ask Uncle Colin: Why is $e$ not 1?

Dear Uncle Colin, If $e = \left( 1+ \frac{1}{n} \right)^n$ when $n = \infty$, how come it isn’t 1? Surely $1 + \frac{1}{\infty}$ is just 1? - I’m Not Finding It Natural, It’s Terribly Yucky Hi, INFINITY, and thanks for your message. You have fallen into one of maths’s classic

Sign up for the Sum Comfort newsletter and get a free e-book of mathematical quotations.

No spam ever, obviously.

##### Where do you teach?

I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.