Triangle is some of the simplest shapes there are. But this doesn't mean that they are not important!
A triangle is a three-sided polygon and comes in a variety of flavours. Some are to do with the length of the triangle's sides: equilateral — where all the sides (and all the angles) are the same size; isosceles — where two of the sides (and two of the angles) are the same size; and scalene — where none of the sides (or angles) are the same. The angles inside the triangle are also important. The sum of the angles is always 180°. You can have acute triangles, where all the angles are less than 90° and obtuse triangles, where one of the angles is greater than 90°. And of course you can get right-angled triangles — one of the most important mathematical shapes inspiring Pythagoras' Theorem and trigonometry.
But triangles aren't just mathematically significant, they are also fundamental to the way we build our environments, both physical and virtual. Triangles are special because they are exceptionally strong. Out of all the two-dimensional shapes we can make out of straight struts of metal, only a triangle is rigid. All other shapes can be deformed with a simple push if the shape is hinged at the corners (for example, a rectangle can be pushed over into a parallelogram). But not the trusty triangle, which explains its ubiquitous use in construction, from pylons to bracing.
Triangles are also special because they are the simplest polygon — a common approach to a tricky geometrical problem, such as analysing a complex surface, is to approximate it by a mesh of triangles. This approach is also used in the real world to achieve some of the exotic shapes we now see in modern architecture, such as the curved shape of 30 St Mary's Axe, aka the Gherkin, or the canopy over the courtyard in the British Museum.
The method of triangulation is also vital in building our virtual world. The CGI characters we see in film and on TV are usually approximated by an incredibly fine mesh of triangles, as this makes it easier to digitally store and manipulate them.
Triangles — the simple shapes that make our mathematical, physical and digital worlds go round.
You can read more about triangles in the following articles on Plus magazine:
- Pylon of the month explores triangle strength;
- Perfect buildings: The maths of modern architecture explores the role of triangles in architecture;
- It's all in the detail explores the role of triangles in the virtual world.