WISM103: History from Ellipse to Elliptic Curve 2018/19
This page supplements the information in Blackboard and will be
updated with suggested reading, course notes, etc.
Students work in pairs on three assignments.
We will announce two assignments each lecture.
Each pair selects three out of the six assignments to work on. We
encourage you to explore the historical and social aspects of
mathematics as well as to understand the mathematics at a more
intuitive level than you have become accustomed to in regular
Results are to be
handed in in the form of one article-style paper. A (perhaps limited)
level of integration of the individual assignments is preferred but
this is not strictly necessary.
Several people have asked if it is ok to hand in by email, and indeed
Anything handed in after the deadline will suffer a grade deduction of
1 point per working day or part thereof. We will consider the weekend
as 1 working day.
Assignments and content of lectures
First lecture Fri 12 April
Lecture slides (careful, 23MB) and
two assignments in the pdf
For your information and benefit: a digital copy of the Dictionary
of Scientific Biography is available from the University Library and
is accessible through WorldCat.
Second lecture Fri 26 April
Assignments are in the last two sheets.
- If you want more about the Bernoulli's and the paracentric
isochrone then have a look at
Bos, The lemiscate of Bernoulli,
in: Lectures in the History of Mathematics, 1993, or
Blåsjö, Transcendental Curves in the Leibnizian
Calculus, 2016, par. 7.3 and 8.3.
It is not my intention to lay too much stress on this topic, but it
may give you a clear idea of the much more geometric way of
thinking in the 17th century.
As an original source (Learn from the Masters!) see Euler
(site) e.g., paper E251
"De integratione aequationis differentialis
mdx/√(1-x4)=ndy/√(1-y4)". There is an
English translation and you can also see a scan
of the original. You
could also look around the site for other articles of Euler's under
the subject "Elliptic functions".
Fagnano's article Teorema da cui si
deduce una nuova misura degli Archi Elittici... is available but
much harder to read.
Gauss: a very enjoyable article by David
Cox: "The arithmetic-geometric mean of Gauss"
in l'enseignement mathematiques, vol.30, 1984,
p.275-330. It covers more than only Gauss and agM. Be sure to
read section 3, Historical remarks. And
yes, it's in English! Download it from
free site but if you want to print it then
take this version with added
Reading Gauss himself is a bit steep because (a) mostly Latin
(b) not finished, publishable work and (c) leaves a lot of work
to the reader. But, if you like, follow any reference of your
liking from the
secondary literature (e.g., Cox) into the Gauss
Third lecture Friday 3 May
Suggestions for literature:
The 6th assignment refers to this article The war of the frogs and the mice
Friday 10 May
Deadline for handing in your worked assignments