Invented on May 18th, 2007 (by Oleg Ivrii and Zavosh Amir-Khosravi) a "rigorous" defintion of CoolStuff is against our philosophy, so I will only give some guidelines what qualifies stuff to be cool:
- The process of CoolStuff is to learn mathematics by application. Here at CoolStuff, we believe that to understand a subject is to see it used in action.
- By its nature, it is elementary, simple, elegant and intuitive. Sometimes, it could even be accessible to highschool students if it did not use a simple fact from topology or abstract algebra. Nevertheless, CoolStuff benefits from its highly intelligent audience.
- CoolStuff does not belong to a single subject, it draws from all of mathematics. By its nature, it cannot be found in a university classroom, which tries to partition all of mathematics into "subjects".
- CoolStuff should be able to stand by itself as a final result, with no applications in mind (even though, applications make it even more cool).
- When it is a well-known theory, the focus is on showing examples rather than dunking theorems one by one.
Of course, classical university education has its merits too :-).
CoolStuff is now organized by Yuri Burda. Contact (in person, or by email) if you are interested in giving a talk.
Previous CoolStuff Seminars can be found at the following link: http://www.math.toronto.edu/oleg/css/coolstuff.html
Ruler and Compass Constructions for Cheapskates
Omar Antolín Camarena
University of Toronto
11:00 — 13:00 (Thursday, Mar. 25, 2010
BA6180, Bahen Center, 40 St George St
Buying both a ruler and compass for your geometric constructions can be very expensive. Fortunately Lorenzo Mascheroni proved in his Geometria del Compasso (1797) that you don't need the ruler at all!: any construction that can be done with both ruler and compass can be done with compass alone. Of course the big savings would be in doing away with the compass, but it's easy to see there is much you won't be able to do with only a ruler. The good news is that Jakob Steiner proved in 1833 that you only need to borrow someone else's compass once!: any construction possible with ruler and compass can be carried out with ruler alone, provided you start with a piece of paper that has a circle and its centre already drawn.
Dates in this series
- · Thursday, Jan. 07, 2010:
Quasiconformal Distortion (Oleg Ivrii)
- · Thursday, Jan. 28, 2010:
An introduction to combinatorial species (Brad Hannigan-Daley)
- · Thursday, Feb. 04, 2010:
Flipping functions: bundlish things and their classifying gadgets (Omar Antolín Camarena)
- · Thursday, Feb. 25, 2010:
The ADHM Construction of Instantons (Jonathan Fisher)
- · Thursday, Mar. 25, 2010:
Ruler and Compass Constructions for Cheapskates (Omar Antolín Camarena)
- · Thursday, Jan. 20, 2011:
Blaschke Worlds (Oleg Ivrii)
- · Thursday, Apr. 28, 2011:
Blaschke Worlds (Oleg Ivrii)