O'Reilly logo

The Mathematical Mechanic by Mark Levi

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

3

MINIMA AND MAXIMA

Max/min problems tend to be well suited for the physical approach. The reason for this is perhaps the fact many physical systems find maxima or minima automatically: a pendulum finds the minimum of potential energy; the light from a pebble on the bottom of the pool to my retina chooses the path of least time; a soap bubble chooses the shape of least volume; a chain hanging by two ends chooses the shape of lowest center of mass, and so on—the list is endless.

Here is a common pattern in finding a physical solution. Let us say we have to minimize a function. The main step is to invent a mechanical system whose potential energy is the given function. The minimum of the function corresponds to the minimum of the potential energy, ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required