# Airplane Weight And World Population

Last week, American mathematicians gathered in San Diego for our annual meeting. The Cole Prize went to Andrew Wiles, who proved Fermat's Last Theorem, which had eluded us for 350 years. The Morgan Prize for research by an undergraduate went to recent Harvard graduate Manjul Bhargava.

Largest prime number

A new largest-known prime was found in November by Joel Armengaud of Paris. Unlike the previous supercomputer discovery of September, this one came on a personal computer, with help from many others on the Internet. It comes from multiplying together 1,398,269 twos and subtracting 1. For more information, see Ivars Peterson's MathLand on the Web.

Old challenge

J. Henry asks whether, on a sinking boat, it helps to make parakeets in the hold fly around. K. Reinecke asks whether an airplane gets lighter when the passengers eat a meal. What causes an airplane to get lighter during flight?

If the hold is sealed, the air supporting the flying parakeets just pushes down on the hold, so it does not help. If a door is open to outside the extra air pressure is dispersed and it does help a bit. Jan Smit explained that the airplane does not get lighter during lunch as long as everything (including the carbon dioxide and heat produced) stays on the plane. Ruth Gatto rightly attributes weight loss to "any loss of liquid, solid, or gas such as fuel, oil, oxygen, external ice dropping off."

Chuck Gahr and Brennie Morgan mention the weakening of gravity as the plane rises farther from the earth (not to mention the gravitational effect of other heavenly bodies). Also, as the plane accelerates downward you feel lighter, and perhaps you are (depending on how you define weight).

New challenge

Estimate what fraction of the people who have ever lived on Earth are alive on Earth today.

* Send answers and new questions to:

Math Chat, Bronfman Science Center, Williams College, Williamstown, MA 01267

or by e-mail to:

Frank.Morgan@williams.edu

The best submissions will receive the book "Flatland."

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