The fourth dimension

We can express the mathematics of relativity neatly by employing a new geometry, which embodies time as a fourth dimension.

Pythagoras' theorem. Courtesy of Greek Post Office.

Mathematicians have been familiar with multi-dimensional geometries for a long time, but now we use it to represent physical reality.

The theorem of Pythagoras is carried forwards into this geometry. The concept that the length of a straight line can be expressed in terms of the sum of the squares of perpendicular components is expanded to four dimensions. The idea that such a length is 'invariant', i.e. independent of the coordinate axes, plays an important role in practical calculations.

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