Additional Math Pages & Resources

Tuesday, October 12, 2010

Cross Section to the other side

This post is on the concept of the cross section. If you've forgotten your elementary school geometry, this material is for you!

First - the definition: a cross section is the intersection of a plane surface with that of a three-dimensional geometric shape (or alternatively the intersection of a line with a 2-D object).

When you slice a block of cheese, a loaf of bread or even a hot dog, you create a cross section from a geometric shape. For example, here's a cube.

Here's our cube intersected by a reddish plane. The bright red surface is the cross section. With this diagonal cut we get a triangle.
Here's another way you can do a cross section through a cube. This cut gives us a square shape cross section. If we did a cut at a different angle, could we get a rectangle?
I think we can and we have here, but this is about the limit of my 3-D conceptualization and drawing skills. 
Now let's try cutting a section off of a cylinder that's laying on its side. We get a circular shape if we cut at 90% to the main axis of the cylinder. If we cut at an angle, we'd get an oval (ellipse).
Now let's cut up a sphere. Looks like an olive, doesn't it?
After all this virtual practice, I think it's time to go cut up some real food now - it's time for lunch.  

If you want to play with some online cross-sectioning tools, you can go to the Learner.Org website and chop up some geometric shapes. 

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