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Symmetry

12 13 sphericAl the perfect 3dimensional symmetry Just as the circle is the perfect figure in 2dimensions, an ideal sphere is a perfect, radially symmetric, 3d body. Both were known as such by the Ancient Greeks, and were considered divine the philosopher Xenophanes went so far as to replace the old pantheon of Gods with a single deity, which he assumed to be spherical. Pythagoras was the first to teach that the Earth itself was spherical in shape more recent cosmologists have suggested that the entire, expanding cosmos has the overall symmetry of a sphere. Interestingly, this shape appears at the very opposite extremes of scalestars, planets, moons, the Oort cloud and the globular clusters of galaxies are spherical 1, and so are small water droplets. Each owe their symmetrical regularity to the fact that they are shaped by a single dominant force the latter to surface tension, all of the former to gravity which itself is spherically symmetric. The action of surface tension is also responsible for the spherical shape of a host of microscopic creatures 2. These tend to be virtually fluid in composition and have to maintain an internal pressure that is in balance with that of their surrounding medium. In fact most spherical creatures tend to be very small where the distorting effects of gravity are minimised, and to live in water. The great majority of these have little or no motivity. In practical terms a sphere represents the smallest surface area for a given volume, which is why so many fruit 3 and eggs 4 are this shape. Since it minimises surface area, and presents the same profile on every side, the sphere also offers a natural defense against predation. Hence the evolved response in those species which, whilst not spherical to begin with, roll themselves up into balls when attacked 5. 2. 1. 3. 4. 5.
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