Time as a fourth dimension

We now extend the theorem of Pythagoras to the four dimensions of space-time:

This expression, already given in Equation (15.3), is similar to the 'sum of the squares' Pythagoras formula, except that the fourth term, namely the square of the time component, is negative. In other words, the time component At is represented by an imaginary number iD t, where i =

The interval can have both space and time components.

Everyone agrees on the value of the interval, but observers using different frames of reference will not agree on the relative magnitudes of the space and time components.

It is said that Pythagoras offered 100 oxen in sacrifice to the Muses in thanksgiving for letting him make his great discovery.

T Euclidean space can be defined as a space in which Euclid's definitions and axioms apply.

Had he realised the full significance, perhaps he might have decided that 100 oxen was not enough!

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