WISM100: History from Ellipse to Elliptic Curve 2016/17

This page supplements the information in Blackboard and will be updated with suggested reading, course notes, etc.

Important: change in hand in schedule

There will be 2 papers instead of 3, with the following deadlines:

Fri 2 June: deadline for Apollonius
Fri 23 June: deadline for second paper with all the other stuff

Anything handed in after the deadline will suffer a grade deduction of 1 point per working day.

First lecture

First part

Slides about Greek math and Apollonius
a handout with text and translotion from the Conica.
two tasks are suggested near the end of the slides; you have to perform only one.

Second part

Elliptic integrals: intro and addition forumlas NOTE: this is a jpeg image, open in an image viewer and zoom to your preferred level.

Suggested reading for this part:

Stillwell, Mathematics and its History, par. 12.3, 12.4, 12.5, has a easy-going introduction with nice excercises which will show you the necessary techniques. Available online in the UU library.
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!) Euler (site) is highly recommended. His work is indexed using Eneström index numbers, beginning with the letter E. Search for the 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. Euler is a lucid writer so don't hesitate! 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.
Excerpts of Euler's and Fagnano's texts are contained in Dirk Struik's "Source Book in Mathematics" here. Be warned: it has a few typos.

Second Lecture

From elliptic integrals to elliptic functions: Gauss and Abel NOTE: this is a jpeg image again.

Suggested reading:

For down-to-earth stuff: continue reading in Stillwell, see link above.
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 their free site but if you want to print it then take this version with added whitespace.
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 Werke. Currently the University Library has free access: just type "Gauss Werke" in the catalog search bar.
Abel, first part of Recherches sur les fonctions elliptiques available in original French in Crelle's Journal and English translation at the MAA.
Note: I WANT YOU TO STUDY THIS, IN particular paragraph I up to the double periodicity. The functions phi, f and F are defined in the introduction. Referring to the translations: page 6 is quite hard (but can perhaps be skipped), page 7-8 look tough and unrewarding but on p.9 you get to the holy grail.

Third lecture

Slides (pdf) with suggested reading at the end. There is also a worksheet about Riemann surfaces. Note: we made the decision that not all topics of the lectures need to be covered in your paper.