Professor Stewart's Hoard of Mathematical Treasures (65 page)

Euler wrote widely about almost everything that had even the slightest connection with mathematics.

If that doesn’t sound very mathematical, it can be stated more technically: any smooth vector field on a sphere has a singular point. Hope that helps.

Throughout this book, ‘doughnut’ refers to an American one, with a hole. British doughnuts are, or used to be, a single lump, generally filled with jam. Two nations divided by a common culinary heritage. Younger readers may not understand this footnote - all doughnuts have holes, don’t they?

Such procedures are often likened to trapdoors, where it is easy to go in but hard to get out. I’m inclined to compare them to catflaps. Our cat Harlequin knows how to go out of a catflap, by pushing, but most of the time she imagines that the way to get back in is to reverse the procedure, and sit outside trying to pull the flap open. It wouldn’t surprise me if she took that to the logical extreme and tried to come in tail first. She forgets the secret short cut, and we lie in bed listening to the racket thinking: ‘Harley! Push!’

Fermat proved this theorem before Gauss invented modular arithmetic, but not from that point of view.

This is the time-honoured formula for: ‘Somebody told me this, but I can’t provide a shred of evidence.’

When I was doing a lecture tour of Oregon, I once stayed in the Sylvia Beach Hotel, whose rooms have literary themes: the Oscar Wilde room, the Agatha Christie room. Mine was the Dr Seuss room, with a 15-foot (5-metre) Cat in the Hat painted on one wall.

Look up
glaber
in Latin.

This is the only time that the old-fashioned ‘division’ symbol ÷ will appear in this book. Oops.

He would also have realised that he need dig only along an arc of a circle, centre Buccaneer Bay and radius 99 nautical perches.

Or earlier. The warp drive was invented in 2063 by Zefram Cochrane of Alpha Centauri, but the early version used a fusion plasma as an energy source. By the 22nd century and the first series of Star Trek, the warp drive was powered by a gravimetric field displacement manifold (or warp core) that used antimatter to create energy. In 1994, in our own universe, the physicist Miguel Alcubierre discovered a ‘warp drive’ that does not conflict with relativity, yet allows faster-than-light travel. The trick is the oft-repeated science fiction mantra that ‘while there is a limit to the speed with which matter can travel through space, there is no limit to the speed with which space can travel through space’. Alcubierre found a solution of Einstein’s equations for gravity in which the space ahead of a spacecraft contracts while the space behind expands. The spaceship surfs this wave, carried along by a warp bubble of entirely normal space, relative to which it is stationary. Unfortunately, it takes a lot of negative-energy matter to build an Alcubierre drive, and we don’t have any.

This is the kind of energy that things acquire when they move, and in classical mechanics it is half the mass times the square of the speed.

However, uncharged particles are not always the same as their antiparticles. The neutron, an uncharged particle, is made from quarks, which individually have non-zero charges. The antineutron is made from the corresponding antiquarks, so the neutron and antineutron are different.

The CAT scanner was pioneered by EMI, primarily a recording company. It is suspected that the millions of dollars came from the sale of Beatles records.

As of 2006, the International Astronomical Union declared that Pluto is no longer considered a ‘planet’, but a ‘dwarf planet’ or ‘plutoid’. Not all astronomers approve of this.

‘Clump’ is a metaphor: they don’t look like the asteroid belts in Star Wars, and what clumps is the distances, not the asteroids themselves. Actually, nowhere in the asteroid belt looks like an asteroid belt in Star Wars. If you stood on a typical asteroid and looked around for the nearest one, it would be about a million miles (1.6 million kilometres) away. No exciting chase scenes, then.

As of 1 April 2009. See The Extrasolar Planets Encyclopaedia at
www.exoplanet.eu
for the latest information.

That is, it is item HR8799 in the Yale Bright Star Catalogue. The HR prefix refers the earlier Harvard Revised Photometry Catalogue, and most of the stars listed in the Yale catalogue come from this.

Except when checking that it has only one side, by colouring it. Then the ink doesn’t soak through. If it did, an ordinary cylinder would have one side. Because of difficulties like this, mathematicians approach the whole topic differently, talking of ‘orientations’ rather than ‘sides’.

More properly the Journal für die reine und angewandte Mathematik (Journal for Pure and Applied Mathematics).

Whose total population far exceeds that of the world’s baseball-playing countries.

In Terry Pratchett’s Discworld novel Pyramids, there is an Ephebian philosopher named Xeno, who proved that an arrow cannot hit a running man. Other philosophers agreed, with the proviso that ‘it is fired by someone who has been in the pub since lunchtime’. Xeno also claimed that the tortoise is the fastest animal on the Disc, but actually it is the ambiguous puzuma, which travels close to the speed of light. If you see a puzuma, it’s not there.

Indeed, a continuum, which according to Cantor is a bigger kind of infinity than that of the whole numbers (see Cabinet, page 160).

It is also the name of the principal villain in Stargate SG-1, a Goa’uld System Lord, in case that’s more familiar.

It was probably suggested by John of Palermo, but it is the emperor’s question all the same, just as the Great Pyramid was indisputably built by the pharaoh Khufu. Emperors are like that. Hans Christian Anderson’s story of the emperor’s new clothes is completely unconvincing: any little boy who dared to contradict the emperor would have ended up in jail. The cliché ‘the emperor has no clothes’ affirms the imperial status - what people usually mean is that the clothes contain no emperor, which isn’t quite the same thing.

You can give a slipstick to a pig, but it’s still a pig.

Stress the third syllable, arithmetic, not arithmetic. An older term is ‘arithmetic progression’.

Who appears to be pseudonymous.

That is, do you allow both attributes, or only one?

The group of p-adic integers has no faithful group action on a manifold. Hope that helps.

Look up the Latin funiculus.

That is, Olaf Tryggvason, the son of Tryggve Olafsson, who was king from 995 to 1000. Before the game of dice, Olaf had proposed marriage to Sigrid the Haughty, the Queen of Sweden, in an attempt to unite Scandinavia. She wasn’t keen.

Who seems to have been Olof the Treasurer, from the dates. As it happens, he was the son of Eric the Victorious and Sigrid the Haughty. It’s a small world.

According to which a monkey did write the collected works of Shakespeare, though not - to begin with - on a typewriter. It performed the feat indirectly, by producing descendants that evolved into . . . Shakespeare. This is a far more efficient approach.

I’m not counting
x
₀
here, although that’s an integer too. However, it’s an arbitrary starting-point, which is a reason - not a terribly good one, but a reason nonetheless - for omitting it from the count. I mention this only because dozens of readers will write to me about it if I don’t. Anyway, if I included
x
₀
, then 42 would become 43, and the gratuitous link to Hitch Hiker wouldn’t work.

To play the game you will need to make a set of cards - I don’t know anywhere that sells them. It’s worth the effort.

They thought it was a bar.

Abbott Abbott = A
²
?

He also sees the circles ‘edge on’. Just as we see only a 2D projection - or a stereo pair of projections - of a 3D object.

Alas! Poor Pluto.

17 May, 2.46 p.m.

17 May, 2.47 p.m.

Except when you’re trying to stuff it into the cat basket, to take it to the vet.

This was unfair to pigs, and ignored a long tradition of political piggery, including the book Lipstick on a Pig: Winning in the No-Spin Era by Someone Who Knows the Game by Victoria Clarke, an Assistant Secretary in George W. Bush’s administration. See:
en.wikipedia.org/wiki/Lipstick_on_a_pig
.

I made this up, but it wouldn’t surprise me to find it’s been used for centuries in parts of Lincolnshire.

In A
Brief History of Time
, where he mentions editorial advice that every formula halves a book’s sales. So he could have sold
twice as many
. Ye gods.