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<font size=3>Until I came across this I was not aware that there was
something called the Gaon's Theorem. <br><br>
Note that the Gaon apparently felt that knowledge of mathematics was
important, because "Gaon was<br>
putting the notes and explanations in book form to preserve them for
generations to come. <br><br>
<br>
I do not understand why the Gaon's sefer Ayil Meshulash is not used as a
mathematics text during the last year of math in Yeshiva High
Schools. Perhaps it is because it would be most difficult to find
someone who could teach it. >:-} YL <br><br>
The following is from
<a href="http://www2.hmc.edu/www_common/hmnj/journal/26/pdf/articles/26.pdf" eudora="autourl">
http://www2.hmc.edu/www_common/hmnj/journal/26/pdf/articles/26.pdf<br><br>
</a></font><font size=2><b>UNIQUE TOPICS<br><br>
</b></font><font size=3>Some extremely interesting topics arose in this
course<br>
following the students' extensive searching for knowledge<br>
sources. Before I compiled the course, I discovered<br>
the book Ayil Meshulash (Stature of the Triangle)<br>
(1960), written in the 19th century by a student of the<br>
Jewish Torah scholar the Vilna Gaon (Genius from<br>
Vilna). It was based upon notes found after the Gaon's<br>
death, that derived from his oral mathematics teaching.<br>
In this book, subtitled "On the wisdom of triangles<br>
and geometry and some rules of qualities and algebra<br>
author Shmuel Lukenik notes that the Gaon was<br>
putting the notes and explanations in book form to<br>
preserve them for generations to come.<br><br>
The Vilna Gaon, or Rabbi Eliyahu was a master of<br>
Torah, Talmud, Jewish philosophy, Halacha (Jewish<br>
religious law), and Kabbalah (Jewish mysticism). The<br>
bulk of his written work concerns corrections and<br>
emendations of Talmudic texts, and interpretations of<br>
the Shulchan Aruch (code of Jewish law). In the academic<br>
field, the Vilna Gaon wrote on geography (The<br>
Form of the Earth) and grammar (Eliyahu Grammar).<br>
He was also interested in music, claiming that most<br>
of the arguments of the Torah would be incomprehensible<br>
without it (On-line Resources, 2001). According<br>
to some sources, the Vilna Gaon is the author of<br>
"The Gaon's Theorem," a principle of the mathematics<br>
of infinity (Feldman, A., 1999). Other sources<br>
claimed that this theorem was called "Kramer's Theorem,"<br>
Kramer being the Vilna Gaon's family name.<br>
Gerver (1993), however, stated that this supposition<br>
was unlikely, as the author of this article did not<br>
present proof for these two opinions.<br><br>
After reading Ayil Meshulash, I had the idea of including<br>
in the course Jewish and Islamic sources of<br>
mathematics history and integrating them in mathematics<br>
teaching. The result was a collection of materials<br>
included in a chapter entitled "Mathematics in<br>
Judaism and Islam," unique to this course. Every year,<br>
a number of student pairs, both heterogeneous (Jewish<br>
and Bedouin) or homogeneous, work on this chapter.<br><br>
Ayil Hameshulash was frequently chosen for investigation<br>
by these students, as it is both a mathematical<br>
work including mathematical explanations and geometrical<br>
definitions, theorems, and proofs as well as<br>
selected topics in algebra, and an historical document.<br>
Although the book was written 200 years ago, it still<br>
contains explanations that cannot be found today in<br>
any other mathematical work. The students in the<br>
course maintain that this book offers better explanations<br>
than those used today, and often say that they<br>
find it exciting to study such a venerable work. In one<br>
of the lectures, the students compared the Vilna Gaon's<br>
presentation of the right-angle triangle with that of<br>
Israeli mathematics teacher Benny Goren in his book<br>
Plane Geometry - a text currently in wide use in Israeli<br>
schools. Most of the students in the class announced<br>
that they would adopt the former method<br>
in teaching this topic in their classes.<br><br>
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