Easy though it may look, this little method encapsulates a basic property of these three-dimensional solids we name polyhedra, which have fascinated mathematicians for over 4000 years. Actually I can go further and say that Euler's components tells us something very deep about form and house. The system bears the name of the famous Swiss mathematician Leonhard Euler (1707 - 1783), who would have celebrated his 300th birthday this year. What is a polyhedron? Earlier than we examine what Euler's components tells us, let us take a look at polyhedra in a bit more element. A polyhedron is a stable object whose floor is made up of numerous flat faces which themselves are bordered by straight strains. Each face is in reality a polygon, a closed shape within the flat 2-dimensional aircraft made up of factors joined by straight strains. Determine 1: The familiar triangle and square are both polygons, but polygons can even have extra irregular shapes just like the one proven on the appropriate.

Polygons aren't allowed to have holes in them, because the figure beneath illustrates: the left-hand form here is a polygon, whereas the proper-hand form is not. Figure 2: The shape on the left is a polygon, but the one on the proper just isn't, because it has a 'hole'. A polygon is called regular if all of its sides are the identical length, and all the angles between them are the same