| ... the problem of which polygons are constructible
| with straightedge and compass was very well known at the
| time, and the result was acclaimed. Gauss gave considerable
| details in Art. 354 of the Disquisitiones Arithmeticae.
|
| Gauss presumably thought his result was important, since
| it was his first Tagebuch note (March 30, 1796) and
| since he had the 17-sided polygon inscribed on his tombstone.
In a similar fashion, Carl Pomerance -- in a recent paper dedicated to
the memory of his friend and teacher, Paul Erdo"s -- states that:
"Fermat numbers are connected with an ancient problem of Euclid:
for which 'n' is it possible to construct a regular 'n'-gon with
straightedge and compass? Gauss showed that a regular 'n'-gon is
constructible if and only if 'n' >= 3 and the largest odd factor
of 'n' is a product of distinct, prime Fermat numbers. Gauss's
theorem, discovered at the age of 19, followed him to his death:
a regular 17-gon is etched on his gravestone." [1]
I have read this myth many times before, so I shall take this opportunity
to refer to it - yet rather briefly:
Eric Temple Bell tells this story properly - around 50 years ago!
"There is a baseless legend that Gauss's tombstone is inscribed
with the diagram of his construction for the regular polygon
of 17 sides. It may possibly be true that at one time Gauss,
remembering the tomb of Archimedes with its diagram of the
quadrature of the sphere, described by Cicero, wished such a
memorial." [2]
as does Oystein Ore in his well-known "Number Theory and its History"
- published in 1948.
"It has been told that Gauss proposed, perhaps not too seriously,
that a polygon with 17 sides be inscribed on his grave, emulating
the tombstone of Archimedes, which was decorated by a figure of
a sphere and the circumscribed cylinder, suggesting his formula
for the area of a sphere. On Gauss's simple grave in Go"ttingen
there is no such polygon, but it does appear on the monument in
his native town of Brunswick." [3]
On Tue, 8 Dec 1998, Samuel S. Kutler wrote:
| Do you mean that he [Gauss] WANTED to have the 17-sided polygon
| inscribed on his tombstone?
William Dunham goes further, and states:
"Gauss was so proud of this discovery that, even after a lifetime
of extraordinary mathematical achievement, he requested that a
regular 17-gon be inscribed upon his tombstone. (Unfortunately,
it was not.)" [4]
And, on Wed, 9 Dec 1998, referring to Sam's suggestion, Franz Lemmermeyer
wrote:
| That would be wrong too. Gauss only remarked that this was a
| result _worthy_ of being inscribed on one's tombstone, but that
| doesn't qualify as a wish, especially when you note that he
| said this when he wasn't even 20.
Which is the precise quotation for Gauss's remark?...
| BTW, I've heard it said that there is a statue of Gauss
| in Goettingen on which a 17gon is inscribed.
To my knowledge, the regular 17-gon is inscribed on a monument of Gauss
just located in Braunschweig (and not in Goettingen).
References quoted:
[1] Pomerance, Carl:
"A tale of two sieves", _Notices of the AMS_, vol 43, no 12, pp 1473-1485,
December 1996. Also online at:
http://www.ams.org/notices/199612/pomerance.html
or
http://www.ams.org/notices/199612/pomerance.pdf
[2] Bell, Eric Temple:
"Mathematics: Queen and Servant of Science", New York: McGraw-Hill, 1951.
This book is an integration and amplification of two earlier volumes by
the same author: "The Queen of the Sciences" (1931), and "The Handmaiden
of the Sciences" (1937).
[3] Ore, Oystein:
"Number Theory and its History", New York: McGraw-Hill Book Company, Inc.,
1948.
[4] Dunham, William:
"Journey Through Genius: The Great Theorems of Mathematics", John Wiley
& Sons, Inc. (1990); Penguin Books, 1991.
Further comments would be appreciated.
With best regards,
Julio Gonzalez Cabillon