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Topic: [HM] L'Hopital, Pythagoras, Ptolemy and Hilbert
Replies: 25   Last Post: Jul 19, 2000 9:37 PM

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 James A Landau Posts: 217 Registered: 12/3/04
Re: [HM] L'Hopital, Pythagoras, Ptolemy and Hilbert
Posted: Mar 18, 2000 2:51 PM

> I need some examples of results which are not named after the people who
> derived them - ie [sic] - L'Hopital's rule, found by his tutor Johann
> Bernoulli.

HEINE-BOREL THEOREM. Heine's name was connected to this theorem by A.
Schoenfliess, although he later omitted Heine's name. The validity of the
name has been challenged in that the covering property had not been
formulated and proved before Borel. (DSB, article: "Heine")

PELL'S EQUATION was so named by Leonhard Euler (1707-1783) in a paper of
1732-1733, even though Pell had only copied the equation from Fermat's
letters (Burton, page 504).

WILSON'S THEOREM was given its name by Edward Waring (1734-1798) for his
friend, John Wilson (1741-1793). The first published statement of the theorem
was by Waring in his Meditationes algebraicae (1770), although manuscripts in
the Hanover Library show that the result had been found by Leibniz.

The above quotes are from URL http://members.aol.com/jeff570/mathword.html

> Where on earth (!) can I find information about how man's conception
> of the size of universe has changed throughout history?

This question is discussed, although maybe implicitly, in most books about
the history of astronomy. Some of the high points:

Someone---I cannot recall whom or when---deduced that the universe was
finite. If it were infinte (and stars were distributed randomly) then any
line of sight will reach a star and the night sky will not be dark

One of the arguments against a heliocentric solar system was that nobody had
observed the stellar parallax that would result from the earth's going around
the sun. Once the Copernican theory was accepted, it necessarily was
accepted that the "fixed stars" were so far away their parallax was too small
to be observed

Then during the 19th century the first stellar parallaxes were observed, and
it became obvious that the universe was measured in light years or parsecs

Circa 1920 Henrietta Leavitt discovered the relationship between the period
and the brightness of Cephieid variables, which gave the first means of
measuring distances beyond what could be done by parallax. This "yardstick",
as modified by Baade just after World War II, is still in use today.

The Theory of Relativity brought up a new question: is the universe closed or
open? That is, does the universe have Riemannian geometry ("closed") or
Euclidean/Lobachevskian geometry ("open")

James A. Landau