Geometry

A Waste of Marshmallows

While working on the geometry of the Platonic Solids, we spent some class time constructing them from chopsticks and marshmallows.

We had a lot of fun putting them together!

Unfortunately, the more complicated structures weren’t really strong enough to stand on their own.  And after the fact, we realized that we probably shouldn’t leave marshmallows sitting around the classroom indefinitely.

But it certainly was lively way to wrap up a unit on geometric solids!  You can see more pictures of the activity on my Facebook page.

By patrick honner, ago

The Saccheri Quadrilateral

We’ve been exploring non-Euclidean geometries lately, and the Saccheri Quadrilateral plays a pivotal role in this particular mathematical history.

The Saccheri quadrilateral is a biperpendicular quadrilateral with two congruent legs.  It’s an object that is “obviously” a rectangle in Euclidean geometry, but proving that without the aid of the parallel postulate turns out to be rather tricky.

In fact, just proving that the measure of the green angle is less than the measure of the orange angle is pretty tough!

By patrick honner, ago

Spherical Geometry Explorer

This is a simple and powerful tool for exploring some basic ideas of spherical geometry.

http://www.math.psu.edu/dlittle/java/geometry/spherical/toolbox.html

In addition to investigating points, lines, and line segments on the surface of sphere, you can construct triangles, antipodes, and even circles in spherical geometry!

A picture may be worth a thousand words, but a good interactive spherical geometry applet is worth a thousand well-drawn diagrams!

By patrick honner, ago
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