In Pursuit of the Unknown Read Free

There is someevidence that Pythagoras may have visited Egypt as a young man, and some have conjectured that this is where he learned his theorem. The surviving records of Egyptian mathematics offer scant support for this idea, but they are few and specialised. It is often stated, typically in the context of pyramids, that the Egyptians laid out right angles using a 3–4–5 triangle, formed from a length of string with knots at 12 equal intervals, and that archaeologists have found strings of that kind. However, neither claim makes much sense. Such a technique would not be very reliable, because strings can stretch and the knots would have to be very accurately spaced. The precision with which the pyramids at Giza are built is superior to anything that could be achieved with such a string. Far more practical tools, similar to a carpenter’s set square, have been found. Egyptologists specialising in ancient Egyptian mathematics know of no records of string being employed to form a 3–4–5 triangle, and no examples of such strings exist. So this story, charming though it may be, is almost certainly a myth.
    If Pythagoras could be transplanted into today’s world he would notice many differences. In his day, medical knowledge was rudimentary, lighting came from candles and burning torches, and the fastest forms of communication were a messenger on horseback or a lighted beacon on a hilltop. The known world encompassed much of Europe, Asia, and Africa – but not the Americas, Australia, the Arctic, or the Antarctic. Many cultures considered the world to be flat: a circular disc or even a square aligned with the four cardinal points. Despite the discoveries of classical Greece this belief was still widespread in medieval times, in the form of orbis terrae maps, Figure 4 .
    Who first realised the world is round? According to Diogenes Laertius, a third-century Greek biographer, it was Pythagoras. In his book Lives and Opinions of Eminent Philosophers , a collection of sayings and biographical notes that is one of our main historical sources for the private lives of the philosophers of ancient Greece, he wrote: ‘Pythagoras was the first who called the Earth round, though Theophrastus attributes this to Parmenides and Zeno to Hesiod.’ The ancient Greeks often claimed that major discoveries had been made by their famous forebears, irrespective of historical fact, so we can’t take the statement at face value, but it is not in dispute that from the fifth century BC all reputable Greek philosophers and mathematicians considered the Earth to be round. The idea does seem to have originated around the time of Pythagoras, and it might have come from one of his followers. Or it might have been common currency, basedon evidence such as the round shadow of the Earth on the Moon during an eclipse, or the analogy with an obviously round Moon.

    Fig 4 Map of the world made around 1100 by the Moroccan cartographer al-Idrisi for King Roger of Sicily.
    Even for the Greeks, though, the Earth was the centre of the universe and everything else revolved around it. Navigation was carried out by dead reckoning: looking at the stars and following the coastline. Pythagoras’s equation changed all that. It set humanity on the path to today’s understanding of the geography of our planet and its place in the Solar System. It was a vital first step towards the geometric techniques needed for mapmaking, navigation, and surveying. It also provided the key to a vitally important relation between geometry and algebra. This line of development leads from ancient times right through to general relativity and modern cosmology, see Chapter 13 . Pythagoras’s equation opened up entirely new directions for human exploration, both metaphorically and literally. It revealed the shape of our world and its place in the universe.
    Many of the triangles encountered in real life are not right-angled, so the equation’s