Top 365 Geometry Quotes & Sayings - Page 7

Perfect hexagonal tubes in a packed array. Bees are hard-wired to lay them down, but how does an insect know enough geometry to lay down a precise hexagon? It doesn't. It's programmed to chew up wax and spit it out while turning on its axis, and that generates a circle. Put a bunch of bees on the same surface, chewing side-by-side, and the circles abut against each other - deform each other into hexagons, which just happen to be more efficient for close packing anyway.

I have spent much time in the study of the abstract sciences; but the paucity of persons with whom you can communicate on such subjects disgusted me with them. When I began to study man, I saw that these abstract sciences are not suited to him, and that in diving into them, I wandered farther from my real object than those who knew them not, and I forgave them for not having attended to these things. I expected then, however, that I should find some companions in the study of man, since it was so specifically a duty. I was in error. There are fewer students of man than of geometry.

This king [Sesostris] divided the land among all Egyptians so as to give each one a quadrangle of equal size and to draw from each his revenues, by imposing a tax to be levied yearly. But everyone from whose part the river tore anything away, had to go to him to notify what had happened; he then sent overseers who had to measure out how much the land had become smaller, in order that the owner might pay on what was left, in proportion to the entire tax imposed. In this way, it appears to me, geometry originated, which passed thence to Hellas.

Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison we wish to make, we separate the more inconvenient [elements], we substitute others for them, less troublesome but also less real, and we are surprised to arrive, notwithstanding a painful labour, only at a result contradicted by nature; as if after having disguised it, cut it short or altered it, a purely mechanical combination could give it back to us.

To ride a bicycle is in itself some protection against superstitious fears, since the bicycle is the product of pure reason applied to motion. Geometry at the service of man! Give me two spheres and a straight line and I will show you how far I can take them. Voltaire himself might have invented the bicycle, since it contributes so much to man’s welfare and nothing at all to his bane. Beneficial to the health, it emits no harmful fumes and permits only the most decorous speeds. How can a bicycle ever be an implement of harm?