Re: [HM] Steiner-Lehmus Theorem
Julio Gonzalez Cabillon (jgc@adinet.com.uy)
Wed, 30 Dec 1998 01:33:06 -0200
At 08:58 AM 29/12/1998 -0500, Samuel S. Kutler wrote:
|
| In doing Euclid's geometry, many theorems have converses
| that are very easy to prove by reductio. Of course the Steiner-Lehmus
| theorem is the converse of an easy-to prove theorem, but it, the S-L
| theorem, is quite difficult for a novice:
|
| Any triangle with equal angle bisectors is isosceles.
|
| Did you try this one out on your students. H.S.M. Coxeter (with Greitzer)
| writes that this theorem
|
| always excites interest.
|
| He calls Jacob Steiner
|
| the great Swiss geometer.
|
| About C. L. Lehmus, they write that the theorem was sent in 1840
|
| by C. L. Lehmus (whose name would otherwise have been forgotten
| long ago).
|
| to Steiner.
|
| Is there any information at all about Lehmus?
The German mathematician Daniel Christian Ludolf Lehmus was born in Soest
on July 7, 1780, and died in Berlin on January 18, 1863.
D.Ch.L. Lehmus, who is not as unknown as Coxeter and Greitzer seem to
suggest, wrote many (many) books and papers on Zahlenrechnung, Arithmetik,
Algebra, hoeheren Analysis, Geometrie, mechanischen Wissenschaften (zum
Leitfaden fuer den Lehrer, zur Ergaenzung fuer den Schueler) ...
I would be very happy to send you a 'bibliolist' if you are interested. Just
recall, for instance, that Lehmus was one of the contributors of Crelle's
Journal since its very first issue (in 1826).
Have a very fine and prime 1999 [ = T(35) + T(36) + T(37) ]
Julio Gonzalez Cabillon