Geometry

Geometry is one of the oldest branches of maths, used by ancient civilisations to in construct buildings and divide land. It’s also at the heart of cutting-edge science, where physicists use geometry to probe the fabric of the universe. In fact, millions of people use geometry in their work.

The geometry you study at school is called ‘Euclidean geometry’, dealing with shapes and lines in a two-dimensional plane or a three-dimensional space. Euclidean geometry is useful when solving everyday problems, like an interior designer working out the area of a room or a dressmaker using geometrical shapes to make their clothes.

We can’t describe all spaces with Euclidean geometry though. On a flat surface the angles of a triangle add up to 180°, but this isn’t true for a triangle drawn on the surface of a sphere, like the Earth. Manufacturers of car sat-navs programme their GPS devices with an understanding of this non-Euclidean geometry to help us get around.

Mathematicians and physicists have come up with even more weird and wonderful geometries. Albert Einstein’s special theory of relativity uses ‘elliptic geometry’, a four-dimensional version of spherical geometry, to describe our universe. Some physicists working today believe the universe in fact has eleven dimensions!

You don’t need to go to quite those lengths to make use of geometry. Any type of 3D graphics, be it an animated film or the latest video game, relies heavily on geometry. Animators build digital objects like a character’s body from simple polygons and apply geometrical transformations to make them move. Reflections and shadows within an animated scene are also contolled by geometrical rules.

Studying geometry has survived the test of time because it has so many applications. Air traffic controllers directing planes through the sky, an architect creating a skyscraper, and countless others; they’re all using geometry to get the job done. To learn more about geometry, check out these articles in Plus magazine:

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The mathematical mysteries of strange geometries.
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Geometry on the big screen, when maths goes to the movies.
An article from Plus magazine.