The Energy Efficiency of Spheres

Environment-controlling buildings gain or lose their energy as "heat o cool" only through their containing surfaces. Spheres contain the most vololume with the least surface—i.e., have the least possible surface-to-volume ratio. Every time we double the diameter of a spherical structure, we in¬ crease its contained atmosphere eightfold and its enclosing surface onlyily fourfold. When doubling the diameter of our sphere, we are not changiring the size of the contained molecules of atmospher...

 Archimedes Discovers How to Measure Volume

Hieron asked Archimedes to discover, without damaging it, whether a certain crown or wreath was made of pure gold, or if the goldsmith had fraudulently alloyed it with some baser metal. While Archimedes was turning the problem over in his mind, he chanced to be in the bath house. There, as he was sitting in the bath, he noticed that the amount of water that was flowing over the top of it was equal in volume to that part of his body that was immersed. He saw at once a way of solving the proble...

 Mathematical Proof that an Arm's Length of DNA is in Ever...

We know from X-ray diffraction studies that a strand of DNA is 1.5 nanometers (1.5 x 10 to the -9 meters) in radius. Assume a cylinder 1 meter long (the arm's length) with a radius of 1.5 nanometers and work out the volume (length x pi r-squared). A typical animal cell is about 8 micrometers (8 x 10 to the -6 meters) in radius. Assume a spherical cell and calculate the volume (4/3 pi r-cubed). Do it yourself. You will see that the DNA fits easily inside the cell, with plenty of room for all o...

 Dyson Spheres

The mathematician Freeman Dyson, of the Institute for Advanced Study, offers a scheme in which the planet Jupiter is broken down piece by piece, transported to the distance of the Earth from the Sun, and reconstructed into a spherical shell – a swarm of individual fragments revolving about the Sun. The advantage of Dyson's proposal is that all of the sunlight now wasted by not falling upon an inhabited planet could then be gainfully employed; and a population greatly in excess of that which...