╨╧рб▒с>■ /1■ . ье┴Y ┐мbjbjєWєW *С=С=м ]ЦЦЦЦЦЦЦккккк╢$кA╢цццццццц$ўЇыд,Цццццц,АЦЦцццАААцЪЦцЦцккЦЦЦЦцАЖАЦЦц┌@;>Ъз┴ккАTo Whom It May Concern:
My name is Jacob Lewis, and I am submitting a paper for submission to the journal. The
paper, entitled "Geodesics on Surfaces of Constant Gaussian Curvature Using
Mathematica," is attached in MS-Word format. I began this paper in the fall of 2000, and
I revised it in the fall of 2001. I was an undergraduate at Columbia University when I
wrote the paper and when I revised it. Professor Charles Doran will be my reference for
the paper. A letter from him should appear shortly.
All of the figures and equations should be embedded in the attached file. If there are
any problems with viewing the text, figures, or equations, please let me know. The
paragraphs below are intended be the information about the author and the abstract,
respectively. The abstract also appears within the submission itself.
I hope this submission meets the criteria of the editorial board, and I look forward to
hearing from you.
Sincerely,
Jacob Lewis
----------------------------
I am currently a senior math major at Columbia University. I am also in a
double degree program with the Jewish Theological Seminary of America,
where I am a modern Jewish studies major. This article began as a final
project for a Differential Geometry class taught by Professor Charles Doran in
the fall of 2000. Following graduation, I plan to teach mathematics in the New
York City public schools, then return to school to become a mathematician.
Abstract: We describe surfaces and geodesics without assuming
prior knowledge of differential geometry. This involves selecting and
presenting basic definitions and theorems. Included in this
discussion are definitions of surface, coordinate patch, curvature,
geodesic, etc. This summary closes with a proof of the
length-minimizing properties of geodesics. Examples of surfaces of
constant gaussian curvature are given and plotted in Mathematica.
We also describe geodesics on these surfaces and plot select
examples.
****************Т
Dear Editors,
Jacob Lewis was a star student in my differential geometry
class last year
here at Columbia. On the strength of his final paper and
other coursework
he received an "A+". I suggested at the time that he
consider the VIGRE
program here at Columbia, and, even though he's a "general
studies" student
rather than a regular student at the College, he won a
place in this
mathematical extension of the highly competitive Rabi
scholar program.
His paper is a fine blend of mathematical exposition and
rigor, with
attention to the sort of "hands-on" computational details
that are so
often lacking in such work. Students who read his paper
will doubtless
feel compelled to try out the routines with their own
Mathematica programs
--- making the paper a very nice "teaser" advertising a
course in differential
geometry to those undergraduates in their final semester of
a calculus
sequence.
I highly recommend Jacob's paper for publication in your
online journal.
Best regards,
Chuck Doran
P.S. My name/address as it should appear:
Charles F. Doran
Department of Mathematics
Columbia University
New York, New York 10027
doran@math.columbia.edu
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