I’d like to thank Matt Parker for introducing me to diameter tapes (or D-tapes). These are measuring tapes used by foresters to measure the diameters of trees. The forester wraps the measuring tape around a tree as if measuring the circumference, but the scale on the tape is adjusted so that the measurement gives the diameter…

# Tag: circle

## Irrational rotations of the circle and Benford’s law

Take a collection of real-world data such as the lengths of all rivers in the world, the populations of counties in the United States, the net worths of American corporations, or the street addresses of all residents of Detroit. Strip away all the information except the leading digits. What percentage of these digits do you…

## An Euler line geogebra applet

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…

## 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…

## Three cool facts about rotations of the circle

I was playing around with GeoGebra and made this applet about one of the simplest, but most intersting dynamical systems: the rigid rotation of a circle. Let me tell you a little about this fascinating subject. Let denote a circle. For simplicity, let’s think of it as a circle with circumference 1. Let be any…

## 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….

## The area versus the circumference of a circle

I just found this stop motion animation that I made last year when I was playing around with the iStopMotion software. So I uploaded it to YouTube and posted it here for you all to see. It is not the highest quality, but it was fun to make. It shows the Greek method of relating…

## Flashlights and conic sections

Recently, Ξ over at the 360 blog wrote about hyperbolic light (which was inspired by the article, “The Shape of Lamp Shade Shadows” by Kenneth E. Horst, The Physics Teacher, Volume 39, March 2001). They were looking at the pattern of light on the wall emitted by a desk lamp with a cylindrical lampshade. They observed that the…