By Petr Beckmann

The historical past of pi, says the writer, notwithstanding a small a part of the historical past of arithmetic, is however a replicate of the historical past of guy. Petr Beckmann holds up this reflect, giving the heritage of the days whilst pi made growth -- and likewise while it didn't, simply because technology was once being stifled through militarism or non secular fanaticism.

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For most of that time, topology was pursued as an intellectual challenge, with no expectation of it being useful. After all, in real life, shape and measurement are important: A doughnut is not the same as a coffee cup. Who would ever care about five-dimensional holes in abstract 11-dimensional spaces, or whether surfaces had one or two sides? Even practical-sounding parts of topology, such as knot theory, which had its origins in attempts to understand the structure of atoms, were thought to be useless for most of the nineteenth and twentieth centuries.

In the 1960s, physicists Murray Gell-Mann and Yuval Ne’eman independently showed that a specific group, referred to as SU(3), mirrored a behavior of subatomic particles called hadrons—a connection that ultimately laid the foundations for the modern theory of how atomic nuclei are held together. The study of knots offers another beautiful example of passive effectiveness. Mathematical knots are similar to everyday knots, except that they have no loose ends. In the 1860s Lord Kelvin hoped to describe atoms as knotted tubes of ether.

But it was Joseph Fourier, at the beginning of the nineteenth century, who recognized the great practical utility of these series in heat conduction and began to develop a general theory. Thereafter, the list of areas in which Fourier series were found to be useful grew rapidly to include acoustics, optics, and electric circuits. Nowadays, Fourier methods underpin large parts of science and engineering and many modern computational techniques.