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Geometry Expressions NewsletterNovember 2012  
Interactive Euclid's Elements for your iPad
Pythagoras proof
We wanted to show off Geometry Expressions capabilities in creating interactive apps which can be inserted into eBooks.  So we took the first four books of Euclid's Elements and added interactive apps for each proposition (over 120 diagrams in all).
 

The eBook is available for $3.99 on iTunes

Sample diagrams can be viewed here.



How to... Use generic functions
Generic functions are a powerful feature of Geometry Expressions. We will explore how to use this feature to create a graphical calculus practice application.  The completed app is here.

The app presents two functions f(x) and g(x).  The user is prompted to set the definitions of the functions so that g(x) is the derivative of f(x).

A slider allows the user to morph f(x) into f'(x) and thus check his answer.

 

Here is how to create the app:

 


Enter a function f(x). In the Variables / Functions tool panel replace the default with your function, e.g. sin(2*x)  

Create a function g(X) and override its definition similarly.

 


Create a third function (1-t)*f(x)+t*f'(x).

Click the Variables tab in the tool panel, select t and set the limits of t to 0 and 1. When t=0 the third function evaluates to f(x), when t=1 the function evaluates to f'(x).

The app user can morph f(x) into f'(x) using the slider.

Problem of the Month
  
A string of length L is pinned at points A and B. Point c is the location of a pen, constrained by the string so that |AC|+|BC| = L
 
The locus of C is, of course, an ellipse with foci A and B and major axis L.

What is the locus of point D, the incenter of the triangle ABC?

An interactive app which lets you play with this problem is  here.
On the Web
A Geometry Expressions app is featured in this caustics article on the Weizmann Institute's website (in Hebrew).

Lua app generation is discussed in this TIPlanet article (in French, or English)

A supertrammel makes a nice electronic toy.

As does this four bar linkage clock.

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.
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