Geometry is defined as the branch of mathematics which is concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogues. I struggle even to understand that definition! I vividly remember maths lessons at school dealing with shapes. Everyone else loved these lessons, because 2D and 3D shapes would be brought out and all these kinesthetic learners who loved handling things and learning from touch revelled in these practical lessons. I can simply remember agonising over how many sides and faces and edges a square had and wondering who on earth really cared about all these different shapes…
The linguist in me, however, loved the names for these shapes. Triangles obviously had three sides and three angles: the name itself told you that! A pentagon was a five-sided shape because its very name told me so (from pente and gonia, which is Greek for five and angle.
A hexagon in a six-sided polygon for similar reaons (hex is Greek for six). I rather like hexagons, because they tessellate so well:
I also remember feeling a deep satisfaction when I first learned that France is often called ‘the Hexagon’ because of its shape:
Thus, my love of languages kept me going through heptagons, octagons, nonagons, decagons, hendecagons, dodecagons and the like, even when I was entirely bored with counting sides and learning other geometrical terms related to these shapes!
Today, that interest in words (rather than the amazing world of shapes) resurfaced. Garry, in his job as a mechanical engineer, often has to deal with drawings and turn these drawings into a 3D reality. He did it when designing a model of the Buckminster Fullerene (affectionately known as the ‘Bucky Ball’, technically known as a spherical fullerene molecule with the formula C60.) The model, made by Garry, is shown below with Nobel Prize Winner Professor Sir Harold Kroto who discovered this molecule.
Now he is on with a task for church (to be revealed at a later date, hopefully!) which requires similar skill and when I was surveying the drawings, I asked what those ‘plastic-cup like things’ are called. (You can see I struggle with words when I don’t know the correct ones!) He told me these were frusta. Agog with anticipation at discovering a new word, I was back in the world of geometry. A frustum is the portion of a solid (normally a cone, as in this case, or a pyramid) that lies between two parallel plans, cutting it. Confused? It looks like this:
I have no doubt that Garry and others will have great delight in wrestling the properties of this shape into the design they actually want. For me, the joy is in discovering that the Latin word ‘frustum’ simply means a ‘piece cut off‘. A new word to add to my vocabulary. I’ll probably never have cause to use it again, not being an engineer, mathematician, aerospace engineer (where frustum is the common term for the fairing between two stages of a multistage rocket like Saturn V, which is shaped like a truncated cone) or computer graphic designer (where it describes the three-dimensional region which is visible on the screen, formed by a clipped pyramid.) But I will feel immensely satisfied at knowing what these people are talking about in future!