TOP FIVE MATHEMATICAL SPIRALS

RECOMMENDED LEVEL: A-level 5) ARCHIMEDEAN SPIRAL: the spiral you see if you roll up a carpet and look side-on. Constant separation distance between each coil. See my video of how to draw one here or

CIRCLE THEOREMS

IN THIS VIDEO: all eight Circle Theorems needed for GCSE maths demonstrated and explained. NOTE: students of IGCSE ("International GCSE") also need to know the Intersecting Chords Theorem (not covered in this video).

WHAT SHAPE OF CYLINDER IS BEST?

THE TIN OF TUNA ON THE LEFT: is the traditional shape: quite wide and not very tall. I was intrigued to see recently (2024) that one producer of tuna (can on the right!) has recently

KEY DIFFERENCES BETWEEN GCSE MATHS AND A-LEVEL MATHS?

Thinking of taking A-level maths? Here are some key differences you'll find from the style of GCSE maths, all designed to make our life easier not harder: 1)  EMBRACE THE ALGEBRA! Maths is ultimately about

WHAT’S THE POINT OF A “RECIPROCAL”?

A QUICK REMINDER: The reciprocal of a number is: either: turn it upside down or (equivalently): one divided by that number. So the reciprocal of $\frac{2}{3}$ is $\frac{3}{2} = 1.5$ and the reciprocal of $5$

WHAT’S THE POINT OF USING GREEK LETTERS IN MATHS?

AT GCSE: introducing Greek letters (α, β, γ, δ, ...) leaves the more familiar Roman letters (a, b, c, d, ...) free to represent other quantities and unknowns. To start with, here are two Greek

WHY DO YOU “KEEP, CHANGE, FLIP” WHEN DIVIDING FRACTIONS?

Aimed at: KS3, GCSE and A-level First we will see why it seems to make sense that you can divide by a fraction by simply flipping it upside down and multiplying; then we will prove

HOW MUCH HARDER IS A 2000 PIECE JIGSAW THAN A 1000 PIECE JIGSAW?

First of all, it's easy to see that a 2000 piece jigsaw is more than twice as hard as a 1000 piece jigsaw. To see why: imagine having two 1000 piece jigsaws that are of

Quote of the week: DIFFERENTIATION IS A SKILL. INTEGRATION IS AN ART.

I was delighted to find this quote at the start of Seán M. Stewart's book "How to Integrate it".One of the main differences between GCSE and A-level maths is the introduction of calculus. This branch

WHAT’S THE POINT OF INTEGRATION BY SUBSTITUTION?

A PUZZLE: which of these shapes is larger: a square of side 7cm or a circle or diameter 8cm? Well that's easy to answer if you know that the area of a circle is $A=\pi

TOP TEN SAMPLING METHODS

A quick reminder: if there are 1200 students at our school, it would be very time-consuming (if not impossible) to interview them all for your Sociology project. Here the population is everyone at the school,

PRODUCT OF PRIME FACTORS – A CALCULATOR SHORTCUT!

Expressing a positive integer (whole number) as the product of prime factors is a bit like dismantling a machine to see what it's made of. Let's try it with 26390. Drawing a Prime Factor Tree

WHAT IS THE “AVERAGE” IN MATHS?

An average is simply a way of picking out a typical value from a set of objects (usually numbers). There are infinitely many different ways to pick a "typical value", but here are some of

HOW MANY SQUARES ARE THERE IN THIS GRID?

Before we see the quickest way to answer the question (scroll down if you are an expert!), let’s see some different possible approaches: GCSE APPROACH: There are 16 little squares.There is the one large square

Regression: lines (and planes) of best fit.

Let's suppose we have some data for height and weight of some adult humans. We suspect the weight depends on the height - so taller people tend to weigh more than shorter. How can we

What does “MATH ERROR” mean?

SHORT ANSWER: this means you have just asked the calculator to do a sum it doesn't like. The three most common reasons for getting this error message are: 1) you have tried to divide by

WHAT’S ZERO TIMES BY INFINITY?

SHORT ANSWER: 0 x ∞ = anything you like! Intrigued? Read on... LONG ANSWER: the question seems absurd: after all, zero multiplied by anything is zero, yet any multiple of infinity is always infinity. But

THE GREATEST MISTAKE IN THE HISTORY OF MATHS:

This must surely be the exclusion of women from maths for most of our history, due to mathematics (and academia in general) being seen as an unsuitable activity or as simply “too hard” for women.

USING MATHS TO CHECK WORLD RECORD ATTEMPTS: PETE’S DIABOLO HIGH THROW

My friend Pete can throw a diabolo ridiculously high - check out this video of him in action! Pete thinks his throw is higher than the “official” world record of 23.92metres so asked me if

HIPPASUS

HIPPASUS: was an Italian born mathematician who lived around 500BC. Legend has it that Hippasus was drowned at sea after daring to suggest that some numbers cannot be written as one whole number divided by

Strange but True: IRRATIONAL NUMBERS

The first numbers we discover in childhood are the Natural Numbers: 1, 2, 3, … Next come the Integers (whole numbers) – which also include Zero and the negatives: ... -3, -2, -1, 0, 1,

WHY THE ANGLES IN A TRIANGLE ADD TO 180°

Given any triangle: Rotate so that the longest side lies horizontally along the base. Extend the base, and draw a parallel line going through the uppermost corner (these two lines are shown in light blue).

What’s special about ZERO?

(or: Much ado about Nothing) Zero doesn’t actually exist. Think about it: by definition it isn’t anything, it’s nothing!! Even so, here are 5 facts every mathematician should know about Zero: