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Geometry Expressions Newsletter
February 2013   
The Farmer and the Mathematician 2
farmer and mathematician 2 cover The farmer is back, and he has a new mathematical friend helping him to make more sophisticated analyses of how best to use his central pivot irrigation equipment.

Packing circular segments into rectangles, triangles and trapezoids uncovers interesting geometry problems with theoretical as well as practical implications.

That and some really bad puns.

Preview the book here.

How to... Use css files in JavaScript export
When you export a JavaScript app from Geometry Expressions, you get a particular default layout of the elements of the app.  You can alter this layout, however, by specifying a css file (Cascading Style Sheet). 

For example, a css which positions every element in the center of the window, rather than left justified would look like this:

#gxInputOutput {
    margin-left: auto;
    margin-right: auto;
}

#gxCanvas {
    padding: 5px;
    text-align: center;
}

#gxHeader {
    text-align: center;
}

#gxFooter {
    text-align: center;
}

The css file is specified in the HTML5 / JavaScript Export dialog.

An app using the above style sheet can be viewed here.


Problem of the Month
heptagon   
ABCDEFG is a regular heptagon.
 
I is the intersection of BD and CE, J is the intersection of CF and BE, K is the intersection of CG and BF, L is the intersection of AC and BG.

Show that B,C,I,J,K,L are vertices of a regular heptagon.

An interactive illustration is here.

Can you generalize this result?


January Problem Solution:
  

CAD is an arc of a parabola with vertex A and focus B.

 

FGHI is the control polygon of a cubic spline.

Can you locate points FGHI so that the spline is exactly the parabolic arc?
If so, where?

An interactive app which lets you play with this problem is here.

Clearly F and I should lie on C and D, and FG and IH should be tangents to the parabola.  Playing with the interactive app suggests that positioning H and G 2/3 of the way to their intersection yields a good approximation to the parabola. 

Is this exact? A Geometry Expressions model confirms that it is:
parabola spline
eBook Bundle

11 Geometry Expressions eBooks are now available as a bundle for the recession-friendly price of $85.95
Bundle includes:
  1. The Tortoise and Achilles
  2. Calculus Explorations  
  3. The Farmer and the Mathematician
  4. Developing Geometry Proofs  
  5. 101 Symbolic Geometry Examples
  6. 101 Conic Sections Examples  
  7. Using Symbolic Geometry to Teach Secondary School Mathematics  
  8. Connecting Algebra and Geometry through Technology
  9. Function Transformations
  10. Exploring with Geometry Expressions
  11. The Farmer and the Mathematician II 


eBooks
Pythagoras proof
Our Euclid's Elements contains over 120 interactive diagrams.
Available on iTunes

Sample chapters of other iPad eBooks are available here

Interactive math Apps which can be viewed on your iPad are available from Euclid's Muse

Videos
See our YouTube channel for videos exploring features in Geometry Expressions.

Watch more videos about creating Apps with Geometry Expressions.

Learn how to Export an Animation with Geometry Expressions.
Quick Links
Euclid's Muse

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Books