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: triangle

## 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….

## Top 8 most popular polygons

Web surfers love lists—best Twitter apps, best albums, greatest films, world’s richest, best colleges (no, wait, we’re not supposed to like this list). So, I thought I’d serve up a list for my audience. The top 8 most popular polygons. My inspiration The idea for this list came to me while my kids were watching…