Ten Interesting 2D Shapes To Show Your Class

Squircle

A Squircle is a cross between a square and a circle, and this humble shape can be found all over the place, from the design of car dashboards to icons on your phone. Squircles are not just squares with the edges rounded off – they are actually plotted using equations such as

x 4 + y 4 = r 4

where r is the minor radius of the Squircle.
Find out more: What is the area of a Squircle? – Stand-up Maths Video.

Megagon

Image Credit: https://en.wikipedia.org/wiki/Megagon#/media/File:Megagon.svg

This shape might look exactly like a circle whereas in fact it is a regular Megagon, with 1 million straight sides. It is a great shape name to impress your friends with, but doesn’t serve any practical purposes which we know of—yet.

Find out more about Megagons.

Annulus

An Annulus is a ring shape which is formed from two circles with the same centre. This is quite a common shape, both in abstract maths questions and in real life applications such as engineering, where is it used to model the cross sections of pipes. The name Annulus comes from Latin and means ‘Little Ring’.

Find out more about an Annulus.

Balbis

Image Credit: https://upload.wikimedia.org/wikipedia/commons/3/37/Balbis_hydrant_example.jpg

The most common example of a Balbis is the capital letter ‘H’. A Balbis is made up of a straight line in the middle, with two other straight lines meeting it at right angles. The word Balbis is from Ancient Greek, describing posts which are joined by a rope to start or finish a race. A practical example of a Balbis is an Antennae.

Aperiodic Monotile

Penrose Tiles are two famous tiles which can be used to tile a flat surface aperiodically, meaning there are no repeating patterns. In 2023 there was big maths news – an Aperiodic Monotile had been discovered for the first time. There is now a single tile known as the ‘Hat’ which can form an aperiodic tiling - no longer do you need a pair of tiles. Even better, the Aperiodic Monotile was first discovered by an amateur mathematician.

Watch the Numberphile Video on the Discovery of the Aperiodic Monotile.

Polyomino

If you know what a domino is, then you’ve met an example of a Polyomino. A domino is formed by joining two squares together, but what about if you had three, four or more squares? If you have five squares they are called Pentominoes, and if you ignore rotation and reflection, then there are twelve distinct Pentominoes. (If you’ve ever played the game Blokus then you will be familiar with the Pentominoes.) The number of distinct polyominoes increases rapidly, for example there are 369 octominoes (8 squares) and 1285 nonominoes (9 squares).

Pentomino Image credit: https://www.cimt.org.uk/resources/puzzles/pentoes/pentoint.htm

Lune

Take two circles which overlap – the resulting crescent shapes are called Lunes. A famous Lune is the ‘Lune of Hippocrates’ where the Lune has the same area as the shaded triangle:

Image: The Lune of Hippocrates

Arbelos

Now that we’re talking about circles, there’s also the Arbelos which is formed from three Semi-Circles. If you were to join the three vertices they would form a straight line.

Here is a cool sculpture of an Arbelos:

Arbelos Image Credit: https://en.wikipedia.org/wiki/Arbelos#/media/File:Arbelos_sculpture_Netherlands_1.jpg

Golden Triangle

A Golden Triangle is an Isosceles triangle where the ratio of the two differing side lengths is the Golden Ratio. Interestingly, one of the Penrose Tiles (the kite) is made from two Golden Triangles stuck together. A Golden Triangle is sometimes called a Sublime Triangle – could this be the most beautiful triangle you’ve ever seen?

Silver Rectangles

Chances are, you use Silver Rectangles all of the time. Every A4 sheet of paper is a Silver Rectangle, as are all the other A-Series rectangles such as A1, A2 and A3. The sides of these rectangles are in the ratio

and they have some incredibly useful properties such as the A0 paper size being exactly one metre squared. All the A-sized rectangles are also similar, meaning that you can scale your photos to different sizes without any strange distortions. Can you guess what the next paper size up from A0 is? It is labelled 2A0, as it’s double the area of A0!

Be Careful! Mathematicians also talk about the Silver Ratio which has a different value of

Check out the Metallic numbers: Beyond the golden ratio article on Plus.