Lately I’ve been thinking a lot about Euler and his many contributions to mathematics. So, just for fun I decided to make a Geogeba applet showing the “Euler Line.” In 1763 Euler proved that three different centers of a triangle—the centroid, the orthocenter, and the circumcenter—are collinear. This line is called the Euler line. The centroid…

# Tag: geometry

## The geometry of meandering rivers

I regularly watch the Science Friday video podcast. This week they had an interesting piece on potamology (OK, I just learned that word and wanted to use it in my post: potamology is the scientific study of rivers). The podcast showcased the work Christian Braudrick and Bill Dietrich of University of California, Berkeley, who achieved…

## Kindergarten mathematics

This is a call for help. My son’s kindergarten teacher has invited parents to come in and talk about their careers. I’d like to go in and talk about math. I’d like to have some interactive hands-on mathematics activities for the kids to do. I also want them to be activities outside the typical kindergarten…

## Carnot’s Theorem

Here’s a neat theorem from geometry. Begin with any triangle. Let R be the radius of its circumscribed circle and r be the radius of its inscribed circle. Let a, b, and c be the signed distances from the center of the circumscribed circle to the three sides. The sign of a, b, and c…

## The Japanese Theorem

[Update: I’ve written quite a bit more about this theorem since 2009. See this page for more details.] I’ve been playing with GeoGebra for the last few days. As an exercise I decided to create applets to demonstrate the extremely beautiful Japanese Theorem. The first appearance of the Japanese theorem was as a Sangaku problem….

## Folding a golden rectangle

Recently I wrote about the mathematics of cutting and folding paper and about the golden ratio, . Here’s a video that brings these two ideas together. We see how to create a golden rectangle (a rectangle for which the ratio of the sides is ) by folding a piece of paper. [via Anthony Brand’s maths…

## Measuring an angle with a ruler

In the September 2008 issue of the College Mathematics Journal Travis Kowalski presents an neat way to measure an angle using a ruler. He attributes the discovery to a student of his, Tor Bertin. Given an acute angle (the technique can be modified for obtuse angles), measure off a distance on each ray. Then measure…

## The eyeballing game

A friend of mine sent me a link to the Eyeballing Game, presumably because it looks mathematical. At a glance it does look like geometry, but really it is a test to see how well you can recognize when geometric images are correctly aligned. Here’s what the creator of the website (a woodworker) wrote: Some…

## Flatland and other videos about dimension

Not long ago I watched the DVD of Flatland staring Martin Sheen as the voice of Arthur Square. The movie is based on Edwin Abbott Abbott’s 1884 book of the same title. Flatland is a story of polygons living in a two dimensional world and A. Square’s discovery of the third dimension. It is also…