Dave Richeson

How do you place incoming mathematics students?

Our department is looking for a better method of placing incoming students in mathematics courses. Currently we have a placement exam that determines whether a student should begin in a calculus I course or in a calculus/precalculus hybrid course (our lowest-level math class). The exam consists of 25 precalculus questions. It does a pretty good…

Ancient number systems in XeTeX

I am teaching a history of mathematics class this semester. We are beginning with a brief discussion of ancient number systems: Egyptian, Babylonian, Mayan, Chinese, Incan, Greek, Roman, and Hindu-Arabic. As I was writing up the first homework assignment it occured to me that I should investigate whether these numbers could be typeset using LaTeX. It…

Mathematics departments at liberal arts colleges

I’m often curious about how other mathematics departments do things—how they structure their curriculum, run the Putnam Exam, handle research projects, etc. This invariably leads to a lot of web searching. So I decided to put together a collection of links to mathematics departments at schools like mine (a small liberal arts college). Because I…

Plato’s approximation of pi?

Today I came across an assertion that Plato used as an approximation of . Indeed, it is not a bad approximation: (although it is not within Archimedes’s bounds: ). Not only had I not seen this approximation before, I had not heard of any value of attributed to Plato. I investigated a little further and…

Puzzler: a squarable region from Leonardo da Vinci

It is famously impossible to square the circle. That is, given a circle, it is impossible, using only a compass and straightedge, to construct a square having the same area as the circle. I will let you read elsewhere about the exact rules behind compass and straightedge constructions. The punchline is that if you begin…

Angle trisection using origami

It is well known that it is impossible to trisect an arbitrary angle using only a compass and straightedge. However, as we will see in this post, it is possible to trisect an angle using origami. The technique shown here dates back to the 1970s and is due to Hisashi Abe. Assume, as in the…

An interesting multivariable calculus example

Earlier this semester in my Multivariable Calculus course we were discussing the second derivative test. Recall the pesky condition that if is a critical point and , then the test fails. A student emailed me after class and asked the following question. Suppose a function has a critical point at and . Moreover, suppose that…

Parametric curve project for multivariable calculus

I’m teaching two sections of Multivariable Calculus this semester. Each class has 3 hours of lecture and a 1 hour 20 minute lab each week. Last week the students were learning about parametric equations. So in lab I wanted to give them some hands-on experience with 2-dimensional parametric curves. Their assignment was to create a…