a pearlescent shellMaths is everywhere! But it can be hard to find if you don’t know what to look for. Try this mathematical treasure hunt and you’ll soon discover some amazing mathematical secrets!

outdoor hazard iconSafety: If you head outdoors while hunting for these shapes, ask an adult for permission and be aware of your surroundings.

You will need

What to do

  1. A white spiral shell, with a mthematical spiral drawn over the top.

    The logarithmic spiral gets wider and wider as it spirals out

    Time for a treasure hunt! Look at the shapes on the page. Do any of them look familiar?

  2. Have a look around and see if you can find any shapes that look like the shapes on the page. When you spot one, hold up the sheet next to it – how similar are they? If you like, take a picture.
  3. Carry the sheet around with you all day, and when you have a few spare minutes, keep looking.

    A mossy rock with a parabola drawn over it.

    A parabola is the same shape as the path of a ball flying through the air.

  4. Don’t worry if you can’t find them all. Some of these shapes are tricky to find!

What’s happening?

There are mathematical patterns all around us. But you won’t see them if you don’t know what to look for.

A big leaf with a snowflake curve drawn on top of it.

The koch curve is a fractal, which has bumps on bumps on bumps!

Have you ever wondered why shells are the shape they are, or what makes leaves look the way they do? These are questions that scientists still don’t fully understand. But a good first step is to try to find similar shapes.

If a mathematical shape matches a real life object, the two might be connected. But they also might not be. That’s when it’s important to understand more about the maths of the shapes you’re looking at. Here are some short descriptions of the shapes in this activity.

Real-life maths

The logarithmic spiral on this sheet gets 1.618 times wider every time it turns 90 degrees. Many people think this shape is particularly beautiful, but since there’s no way to measure beauty, it’s really up to you to decide!

The Koch curve is an example of a fractal. The first quarter of the line is actually a copy of the whole line itself. With all the wiggles and spikes in the Koch curve, its length is actually infinite!

The witch of Agnesi is named after mathematician Maria Agnesi. In a time when women were not allowed to go to university, Maria wrote excellent maths textbooks. The Pope loved her books and offered her a job as the maths professor at the University of Bologna. Maria wrote about this shape in her textbooks, naming it after a rope used on sailing ships. When translated into English, someone got the word confused, so it is now called the witch of Agnesi, not the rope of Agnesi!

The sine wave is the most simple wave shape in mathematics. When played as a sound it makes a pure tone. Sine waves can be found in ripples on a pond, and even in waves of light.

Parabolas are particularly useful for focusing things. They are used in radio telescopes and solar collectors. And if you throw a ball into the air, it follows a parabolic path.

The cardioid is made by rolling. Imagine using blu-tack to fix a 20 cent coin to a table, then roll a second coin lying flat around the outside of the first. A mark on the edge of the second coin will trace a cardioid.

The tractrix is the solution to a mathematical puzzle about dragging an object behind a tractor with a rope. Surprisingly, it is also used when stretching and bending sheets of metal, to prevent the sheet from breaking.

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