but with a detailed analysis of the error in the “proof.” And guess who got to
perform that analysis? Junior faculty members—like me. I learned a lot of ge-
ometry tracing down those errors, but I could have saved a lot of time if this site
had been accessible.- http:// mathworld .wolfram .com/ GeometricConstruction .html.This site has a
reasonable version of how to construct equilateral triangles, squares, regular
pentagons, and Gauss’s heptadecagon. Mathworld has a lot of good stuff—some
of it is highly technical but it’s always a reasonable place to start. I think it’s
mostly written either to sell or support Mathematica, a Wolfram product, which
many mathematicians swear by. As a result, it sometimes reads a little like
something in Math Reviews. - http:// en .wikipedia .org/ wiki/ Carl _Friedrich _Gauss. I admit that Wikipedia has
encountered some problems—since anyone is free to edit it, sometimes the indi-
vidual editing Wikipedia has an agenda and uses Wikipedia to promulgate that
agenda. However, that rarely happens with mathematics—it’s hard to imagine
anyone having an agenda about Carl Friedrich Gauss, the early years. Addition-
ally, there are often a lot of secondary references in Wikipedia that can be used
either to pursue a subject in more depth or to authenticate the material. - http:// www .math .okstate .edu/ ~wrightd/ 4713/ nt _essay/ node17 .html. This site
not only has Gauss’ original conjecture, but several related ones. It helps to know
a little calculus, but most of what is said requires only the knowledge of what
natural logarithms are. - http:// en .wikipedia .org/ wiki/ Fermat _number #Applications _of Fermat
numbers. There is an attractive theorem that states that if 2n1 is a prime, then
n must be a power of two. Fermat primes continue to be studied; a recent in-
triguing result is that no Fermat number can be the sum of its divisors. Num-
bers such as 6 1 2 3 and 28 1 2 4 7 14, which are the sum of their
divisors, are called perfect numbers. Fermat numbers are also useful for gener-
ating sequences of random integers for use in computer simulations. - http:// planetmath .org/ encyclopedia/ TrisectingTheAngle .html.This site con-
tains a plethora of material on this and related problems.
1 5. h t t p : / / w w w - g r o u p s. d c s. s t - a n d. a c. u k / ~ h i s t o r y / B i o g r a p h i e s / W a n t z e l. h t m l. T h i s s i t e
has a number of good biographies, including the best easy-to-find one of Want-
zel. - The actual dialogue is Plato’s Meno, in which Socrates works with an unschooled
servant boy to discover that the square root of 2 is irrational. A good account of the
argument can be found in http:// www .mathpages .com/ home/ kmath180 .html.
Although philosophy was not my best subject in high school (or anywhere else), I
remember my instructor telling us that there was a lot of unconscious humor in
Meno. Socratic dialogues were sometimes the equivalent of a paid appearance by
Paris Hilton—Socrates was paid to conduct a dialogue as entertainment for
the guests at a banquet. The subject of this dialogue was “virtue”—a sly dig at
Meno, who my philosophy instructor told us was something of the Godfather of
his day.
1 7. h t t p : / / w w w - g r o u p s. m c s. s t - a n d. a c. u k / h i s t o r y / B i o g r a p h i e s / L i n d e m a n n. h t m l. A s
mentioned previously, this site has numerous good biographies and secondary
references. It also has terrific internal hyperlinking, so you can jump around
and get a lot of related information.
78 How Math Explains the World