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1561

What is the roundest country?

We can define roundness in many ways. For example, as you may know, the circle is the shape that given a fixed perimeter maximizes the area. This definition has many problems. One of the problems is that countries generally have chaotic perimeters (also known as borders), so they tend to be much longer than they seem…

1562

What makes music sound “good?”

When listening to music, however, we are not just listening to a series of disconnected instants. Instead, the way things sound depends on the notes we have heard. In other words, we integrate over time . One of the most important functions of a musical scale is to limit the overall pitch content of what we're hearing…

1584

The Relativistic Rocket

Thanks to Alan R. Wilson for correcting a two-word typo involving GPS satellites. Thanks to Aron Yoffe for suggesting the newtonian comparison. Thanks to Tom Fuchs for suggesting the analogy to the stone thrown upwards. Fuel numbers added by Don Koks, 2004. Updated by Phil Gibbs, 1998. Thanks to Bill Woods for…