August, 2019

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

Read More

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

Read More

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)

Read More

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.

Read More

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

Read More

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

Read More

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

Read More

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

Read More

Dictionary of Mathematical Eponymy: Hoberman Sphere

What are they? I thought, until I looked closely, that we had a Hoberman sphere in the children’s toybox. We don’t: we have something closely related to it, though. The Hoberman mechanism comprises a series of pairs of pivoted struts arranged end to end. Each pair looks a little like

Read More

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.

On twitter