MathsNet: The Death of Distance: from Pythagoras to Galileo

The Death of Distance: from Pythagoras to Galileo
An event at the Dome, November 29th, 2000

Ancient Greeks

Calculation from 1000 - 200 BC

The Babylonian basis of mathematics was inherited by the Greeks and independent development by the Greeks began from around 450 BC.
The major Greek progress in mathematics was from 300 BC to 200 AD. After this time progress continued in Islamic countries. Mathematics flourished in particular in Iran, Syria and India. This work did not match the progress made by the Greeks but in addition to the Islamic progress, it did preserve Greek mathematics.

Thales seems to be the first known Greek philosopher, scientist and mathematician.

Thales

(Read a detailed account here of how the book Euclid's Elements, thought to have been writen about 300BC, has survived to this day.)

The Parthenon, 447-432 BC
Dedicated to Athena Parthenos, the great Parthenon was designed by the architects Ictinus and Callicrates.

In building the Parthenon, The Greeks made great use of a rectangle whose sides are in the "golden proportion" (1 : 1.618 which is the same as 0.618 : 1).
Though no original plans of the temple exist, it appears that the temple was built on a square-root-of-5 rectangle, that is, it is 5 times as long as it is wide. These are also the dimensions of the longest side view of the temple. Also, the front elevation is built on a Golden Rectangle, that is, it is Phi times as wide as it is tall.

The golden ratio

A knotted rope
The Egyptians measure their fields with lengths of knotted rope. The size of the farmer's field is used to work out how big his harvest will be, and how much tax he should pay.

Pythagoras (c. 582-c. 500 BC) was a Greek philosopher and mathematician, whose doctrines strongly influenced Plato. Born on the island of Sámos, Pythagoras was instructed in the teachings of the early Ionian philosophers Thales, Anaximander, and Anaximenes. Pythagoras is said to have been driven from Sámos by his disgust for the tyranny of Polycrates. About 530 BC Pythagoras settled in Crotona, a Greek colony in southern Italy, where he founded a movement with religious, political, and philosophical aims, known as Pythagoreanism.
See

Pythagoras

Bridges
The earliest bridges were probably formed by laying one or more logs across a brook or by stretching ropes or cables across a narrow valley. Such bridges are still employed. The single-span bridge is an outgrowth of these elementary forms. The stepping-stone crossing, improved by logs laid on the stones to connect them, is the prototype of the multiple-span bridge. Wooden piles driven into a river bottom to form bridge supports made it possible for the log or beam structure to span wider streams. Such trestle bridges are still used extensively to cross valleys or streams where they will not interfere with shipping. Use of stone piers as intermediate supports for wooden members marked another advance in the construction of wooden-beam bridges. The use of boats instead of fixed piers produced the pontoon bridge. Wooden-beam bridges appear to have been the most common type known to the ancients, although according to tradition a brick-arch bridge was built about 1800 BC in Babylon.