Barney Maunder-Taylor, Author at Maths Tutor Bournemouth

WHAT’S SPECIAL ABOUT THE NUMBER 2025?

16 January 2025 by Barney Maunder-Taylor

or: Why is the square of the nth triangular number equal to the sum of the first n cubes?

SUGGESTED LEVEL: Further Maths A-level or anyone at any level if you love numbers!

Every New Year brings a new number for us all to wonder about: is this year a prime number? A square number? Something else?? As I write we are at the start of 2025 and the interest has been far higher than usual. So: why is 2025 such a very cool number?

SHORT ANSWER (read on if this makes no sense – I will explain!):
$2025=(1+2+3+4+5+6+7+8+9)^2=1^3+2^3+3^3+4^3+5^3+6^3+7^3+8^3+9^3$.
You can easily use a calculator to check that it’s true, but my maths brain really wants an intuitive way to see why this works – ideally using geometry (“shapes”) so I can picture the result!

TOP FIVE MATHEMATICAL SPIRALS

1 November 202415 August 2024 by Barney Maunder-Taylor

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 use your favourite free graph sketching software (e.g Geogebra or Desmos). For A-level Further Maths students: the polar equation is $r=aθ$ where the parameter a makes the (constant) separation distance between each coil larger or smaller.

4) LOGARITHMIC SPIRAL: a spiral in which

CIRCLE THEOREMS

1 November 20245 August 2024 by Barney Maunder-Taylor

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?

17 June 2024 by Barney Maunder-Taylor

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?

18 December 202320 August 2023 by Barney Maunder-Taylor

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 spotting patterns, and algebra is the language we use to write down patterns. A simple example: $A=l \times w$ is a formula to tell you how big a rectangle is. ANY rectangle. At GCSE, it is reasonable to develop clever tools to avoid having to use algebra; but at A-level, we must embrace algebra: it’s our friend and is there to make maths easier! An example:

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 it works.

INTUITIVELY:
Let’s see if we can find a rule for dividing by $\frac{1}{2}$.

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

18 December 20231 June 2022 by Barney Maunder-Taylor

How Hard is a 2000 piece Jigsaw 1000 pieces?

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

Barney Maunder-Taylor