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Geometry Expressions Newsletter
Geometry Expressions Newsletter

July2011 
Learning calculus with Geometry Expressions
If you're teaching calculus in the fall, you should take a look at our new Learning calculuselectronic resource: Learning Calculus with Geometry Expressions by L. Van Warren

This breakthrough electronic book consists of a series of pdf slide shows all ready to present in class, along with some of the most beautiful interactive geometry Expressions models ever created.

You can use individual slides from Learning Calculus, or single lectures, course segments or the entire calculus course.  You can use the presentation slides stand-alone, or use the accompanying models with Geometry Expressions for a more dynamic understanding of calculus.

Individual chapters are available for $6.99.  The whole electronic book is priced at $34.95

How to...model a cam
cam 0
We show you how to use the ability of Geometry Expressions to animate with respect to different variables to create a model of a cam.  In the picture on the left, the cam rotates about A, while the follower F moves vertically with a sinusoidal motion. A model of the working cam is on the web here.

Cams are used by mechanical engineers to create specified motion.  The cam synthesis problem is this:  given a desired motion of the follower, what shape should the cam be?

To create the cam shape, we invert the problem, hold the cam fixed and rotate the follower, while making its distance from the center of the cam vary appropriatelycam 1.

The cam profile is the envelope of the circle (obtained by selecting the circle and using Construct/Locus).

So how do we get the cam to move and the follower to stay put?

The trick is to add a parameter t to the argument of the sin function, then hold the angle fixed, while varying t.
cam 2

The end effect of this is a model where the cam rotates, and the follower reciprocates.

Look again at the web model.  This was created with Geometry Expressions 3.0 beta.

Can you work out how the output curve was created?  (Hint: it involved adding another parameter.)
cam 3



Problem of the Month
reflection
A simple solar cooker consists of a box AB and a reflective lid AC (we can assume AC and AB are the same length).

For a given angle of incoming sunlight, what is the best lid angle CAB?  (An applet which lets you play with the problem is here).

If you are allowed to adjust the sun's angle (by tilting the box, for example), what lid angle captures the most sunlight?  (An applet to help you examine this is here.)

Have you encountered this angle before?

GX Books
conics
101 Conic Section Examples contains, as its title suggests, 101 examples of conic sections modeled with Geometry Expressions.

Not a textbook, but it will give you lots of ideas for models which can be created with Geometry Expressions, and introduce you to some arcane knowledge about conic sections

Available in printed, or electronic form 
here

Online PD
Interested in using Geometry Expressions in class?

Free online Professional Development is now available here