A scientist’s guide to life: how to wrap Christmas presents

This Christmas, don’t be daunted by the pile of wrapping that awaits. Pour yourself a sherry and learn how to wrap presents using geometry, with Sheffield Hallam University mathematician Katie Steckles.

How do most people wrap their presents?

Most people learn to wrap a present by folding a piece of paper around an object, adding a bit of tape and then tucking in the ends. That’s fine, but if you use maths you can make things more efficient and beautiful.

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Can a Maths GCSE help me to wrap presents better?

It can help, but it’s not essential. This is basic geometry. It’s to do with size and shape of the object you’re wrapping. Some shapes are easier to wrap. Others are more difficult.

A scientist’s guide to life: how to wrap Christmas presents © Carlos Ortega
© Carlos Ortega

What’s the best way to wrap a box of After Eights?

That’s a square prism – it’s a square if you look at one end. Let’s say the side of the square is x and the length of the box is L.

Imagine wrapping a piece of paper around the sides of the square. The width of that paper needs to be 4x plus a bit extra for the overlap. We call this extra bit ‘e’. So the width is 4x + e. The length of the paper needs to be (L + x). This means there is just enough paper at the ends to be folded neatly to make a cross shape.

What about a Toblerone?

Ah, the equilateral triangular prism! (Other triangular chocolate bars are available – Editor.) This time the width of the paper is (3x + e) where x is the side of the triangle. The length of the paper is (L + 2h) where L is the length of the Toblerone and h is the height of the triangle measured from the base to the apex.

This means that when you wrap the paper around and fold the ends in, you end up with a perfect triangle shape at each end… which is just incredibly enjoyable!

Need to know…

  1. A bit of simple maths can help you neatly wrap your pressies.
  2. Move the wrapping paper about on squashy presents so that patterns line up.
  3. Wrap big presents first, so you can use offcuts of paper for the smallest gifts.

How should I wrap a bottle?

If d is the diameter of the base of the bottle, then the width of paper you need is (πd + e). We know this because the circumference of a circle is πd. It’s the thing that people learn in school and then immediately forget.

The length should be at least (L + d) so you can tape it shut at the bottom and tie a ribbon around the top, like a Christmas cracker.

What’s your favourite paper?

Something with an unusual pattern. It’s been proven that there are only 17 different types of symmetrical pattern for wrapping paper or wallpaper. Some types of symmetry are more common than others – for example, surprisingly few wrapping paper patterns have reflection or rotation symmetry. I like those ones the best, but they’re not easy to find in the shops!

Read more from A Scientist’s Guide to Life:

How to wrap a jumper?

If you’re wrapping something squidgy like a jumper or a pack of sweets, you can move the paper around so that you match up any symmetrical patterns. This is very satisfying.

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What’s your top tip for Christmas wrapping?

Arrange your gifts in order of size, then wrap them in decreasing size order starting with the biggest ones first. If you do this, you’ll be able to wrap the little gifts using the offcuts left over from wrapping the big ones.