# Frank Morgan's Math Chat - BRIGHTEST MOON FOR THOUSANDS OF MILLENNIA?

February 17, 2000

QUESTIONABLE MATHEMATICS. Eric Brahinsky saw in an article on "New molecule has explosive future" on January 31 in the San Antonio Express-News, reprinted from the New York Times: "According to Plato, the tetrahedron (four triangles) represents fire, the cube (four squares) symbolizes earth, the octahedron (eight triangles) stands for air, the icosahedron (20 triangles) represents water and the dodecahedron (12 pentagons), the universe." Of course, the cube has six faces, not four.

Readers are invited to send in more examples of questionable mathematics from the media.

THE CODE BOOK, by Simon Singh, author of the best seller Fermat's Enigma, was criticized in the March Notices of the AMS for numerous inaccuracies. I must say, however, that I found it a beautiful and fascinating popular explanation of the history and mathematics of codes, and that the inaccuracies involved matters I either missed or forgot anyway.

OLD CHALLENGE. Was there any validity to the claim that the full moon of December 22, 1999 was the brightest that we shall see for millions of years?

ANSWER. There are a number of reasons for a bright moon:

1. The moon is full.

2. The moon is at its closest approach to the earth in its orbit ("perigee").

3. The full moon is high in the nighttime sky, particularly at Winter solstice (when the sun, opposite the moon, is low in the daytime sky).

All three of these factors coincided on December 22, 1999. This had last happened 133 years earlier on December 21, 1866. But MILLIONS of years? Well, the moon is gradually moving farther from Earth, so future occasions might not be quite as bright. Of course we have not even mentioned the most important factor--the weather--and there are other factors too.

NEW CHALLENGE. Propose a new system for selecting Presidential candidates.

Send answers, comments, and new questions by email to Frank.Morgan@williams.edu, to be eligible for Flatland and other book awards. Winning answers will appear in the next Math Chat. Math Chat appears on the first and third Thursdays of each month. Prof. Morgan's homepage is at www.williams.edu/Mathematics/fmorgan.

THE MATH CHAT BOOK, including a \$1000 Math Chat Book QUEST, questions and answers, and a list of past challenge winners, is now available from the MAA (800-331-1622).