Why oranges don’t have ‘segments’

In the aisle of Tesco I stood like one thunderstruck. It was not the print of a man’s naked foot that took me aback, as it did Crusoe, but a tin of ‘Mandarin segments in juice’.

These days we get our entertainment where we can, and I had toyed with buying tinned goods against the next disruption of trade, as Margaret Thatcher had stocked up with 20 tins of fruit in 1974 against inflation.

But I had wondered that very morning what to call the shape made by cutting the top off a boiled egg. That is a spherical cap, I learnt. One thing led to another, and the next thing I knew was that a slice taken out of a spherical Christmas pudding (such that the straight sharp edge is the pud’s diameter) is called a spherical wedge. The flat sides of the slice are semidisks.

So, staring at the tin of mandarin segments, I suddenly realised that these too were in reality spherical wedges. I (and Tesco) had wrongly been calling them segments all my life. A segment of a circle (the geometers tell us) is a bit broken off its edge (as it were), with a straight line cutting the circumference at two points. It is the two-dimensional version of the top of the egg.

A spherical segment is like a pineapple slice. A spherical wedge is the correct name for one of the 20 parts of a Terry’s chocolate orange. These spherical wedges are a kind of ungula, taking their name from a horse’s hoof imagined as a cone cut off at an angle.

With pizza (which children are given to eating), a slice seen from above is a sector. A spherical sector is a conical shape, with the sharp end at the centre of the sphere and its outer surface the shape of a spherical cap.