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...

 Earth's Curve, Flat Maps, and the Fastest Route Between T...

Imagine, say, that you wanted to travel from New York to Madrid, two cities that are at almost the same latitude. If the earth were flat, the shortest route would be to head straight east. If you did that, you would arrive in Madrid after traveling 3,707 miles. But due to the earth's curvature, there is a path that on a flat map looks curved and hence longer, but which is actually shorter. You can get there in 3,605 miles if you follow the great-circle route. which is to first head northeast,...