The Secret Life of the Triangle II (the sequel)

Image Credit: Michael Taylor (a triangle formed from odd powers of the trinomial expansion of (a+b+c) to the power n)

A few months ago I wrote The Secret Life of the Triangle. One of the things on my mind, apart from some trigonometry I was teaching, was why there is such a low preponderance of triangles in our environment despite the great structural stability of equilaterals. One thing I didn’t mention was quantum chromodynamics (QCD). The thing is this. The basic building blocks of atomic nuclei are quarks which come in 6 varieties called flavours: up(u), down(d), top(t), bottom(b), charm(c) and strange(s). Although they are all spin 1/2 fundamental particles, they differ in their charge which comes in bundles of 1/3.  The u-quark has charge +2/3 and the d-quark has a charge -1/3. So, for example, a proton is a combination of two up quarks (u) and a down quark (d) giving it an overall charge of 2 x (2/3) -1/3=+1.

The neutron is a combination of two d-quarks and a u-quark giving it an overall charge of 2 x (-1/3) + 2/3=0. Neutral. Hence its name. The quark flavours are held together by gluons which come in three colours; red(r), green(g) and blue(b).  You may think I’m pulling your leg with talk of matter being made up of flavours and colours – but I’m not! And it really is! You, me and all the stuff you see around you is made up of quarks held together by colours. The quark model is one of the most successful models of particle physics. It is truly great (and weird) and was theorized in 1964 by Murray Gell-Mann and George Zweig. In 1968, deep inelastic scattering experiments at the Stanford Linear Accelerator Center (SLAC) showed that the proton contained much smaller, point-like objects and was therefore not an elementary particle. Although initially called “partons” they were soon identified as up and down quarks. On the 11th of November 1974 the c-quark was discovered in what became known as the November Revolution together with its inferred partner, the s-quark. The b-quark was first observed at Fermilab in 1977 where finally the t-quark was also first seen in 1995 with its gigantic mass like that of a gold atom. In all cases, the quarks are not directly “seen”. They are inferred in the observations. The magic is that their inferred properties match so perfectly the theoretical quark model.

And the connection with triangles? Well, the colour force acting between the three quarks in a hadron is, as you expect, always positive. Hence the gluing effect. What’s more is that this force increases, the more you try to separate the quarks! The technical name for this is confinement. It is why hadrons are so stable, like the equilateral triangle. It’s a wonderfully psychadelic, hidden from view, Menage a Trois,  that holds us together. It is at the heart of every raindrop, every leaf. Triangles are everywhere are nowhere. They are there, holding it all together, out of view.

One of the rare times when triangles do make an appearance is Christmas. From the shape of the leaves of Holly or Poinsettia, Parols, Coniferous trees, hexograms, the illuminated edges of the sails of boats, and my favourite… a thick wedge of cake, triangles are everywhere. This year my tribute is to all the triangles we dont see and to whom we own so much – our very existence.