Category Archives: Geometry

October 7, 2007, 11:52 am

Calculus is older than we thought

It turns out that according to a recent discovery in an ancient manuscript, calculus might first have been discovered not by Newton or Leibniz in the 1700s but by Archimedes a millenium earlier:

For seventy years, a prayer book moldered in the closet of a family in France, passed down from one generation to the next. Its mildewed parchment pages were stiff and contorted, tarnished by burn marks and waxy smudges. Behind the text of the prayers, faint Greek letters marched in lines up the page, with an occasional diagram disappearing into the spine.

The owners wondered if the strange book might have some value, so they took it to Christie’s Auction House of London. And in 1998, Christie’s auctioned it off—for two million dollars.

For this was not just a prayer book. The faint Greek inscriptions and accompanying diagrams were, in fact, the only surviving copies of several works by the…

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November 29, 2006, 3:22 pm

Welcome humor break

I’m grading a geometry lab assignment, on a question which asked the students to list the four possible combinations of effects of an isometry (direct or opposite, has or doesn’t have fixed points) and then classify the four basic isometries according to that list. This group put down:
Picture 1-2

It’s certainly nice to have students with a sense of humor. That doesn’t always happen. (They did go on to classify the isometries correctly, so this isn’t humor instead of a right answer.)

November 1, 2006, 1:36 pm

Characteristics of upper-level math success

I’ve been grading a wheelbarrow-load of papers from my upper-level geometry class this morning. It’s been making me think about the jump from taking calculus to courses beyond calculus. A lot of very good calculus students simply hit the wall when they move on to an "upper-level" course, like linear algebra or geometry. The jump is difficult, I think, because there are certain personality traits that have to be in place for a student to succeed past calculus:

  1. You have to become very tough-minded. This means you have to begin to be ruthless in your assessment of your own work and the work of others. If you can do better, you have to develop the urge to do so and not be content with cutting your losses on a problem and moving on. Same goes for the work your classmates are doing.
  2. You have to become self-confident in your mathematical work. In an post-calculus classroom, the…

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August 29, 2006, 4:10 pm

First day dispatches; or, New Adventures in Sleep Deprivation

Classes started today:

  • The calculus classes were given a biographical sketch assignment to do and send in by email, using mat 135 bio as the subject line so I could use an email filter in Entourage to route it. So far everybody has actually listened to what I said and actually used mat 135 bio as the subject line, and not something else. That’s a good start. Had I given this assignment to previous classes, I might well have half the class using the subject line "here’s my assignment" or just left blank, or emailing me asking me to repeat what the subject line was supposed to be.
  • The calculus class seemed to take this handout pretty seriously. I asked them in the biographical assignment what they planned on doing with their 37 hours of free time, and a lot of them gave just one thing — a part-time job, sports, or even more studying. And yes, I’m keeping these bio sketches on…

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May 4, 2006, 2:47 pm

Taking geometry on the road

Scott Steketee is a developer of Geometers Sketchpad, a dynamic geometry software package which I’ve blogged about before. He and his son are doing a cross-country bike ride to promote Sketchpad and its statistics-oriented cousin Fathom, and they’re going to blog the trip. From the web site, here’s a nice explanation of the connection between cycling and Sketchpad:

I’ve been bicycling since I learned to balance a bike. Not only great for recreation and competition, cycling is the world’s most efficient form of transportation. Bicycling is based on a simple and elegant technology that’s the most effective and environmentally sound method of travel for short trips.

My enthusiasm for bicycling is rivaled by my enthusiasm for The Geometer’s Sketchpad, another easily mastered and elegant technology.

Apparently he’s going to be posting Sketchpad projects along the way as part of the blog….

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