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Geometry Expressions Newsletter
May 2013   
Geometry Expressions 3.1 Released
Geometry Expressions 3.1 has now been released.  It is a free upgrade for any Geometry Expressions 3.0 user.
New in Geometry Expressions 3.1:
  • Controlled Visibility Object visibility can be made to depend on any expression.
  • App Enhancements Apps can incorporate pictures and use button, media control, random or timer inputs.   
  • SVG output We have added SVG to our long list of supported graphics output formats. 

How to... Create an App with a Picture
owhyee canyonCreating a browser app containing a picture and some mathematical content is easy with Geometry Expressions. 
  1. Use Draw/Picture to insert a picture into Geometry Expressions. 
  2. Add any geometry or graphical elements to the model.
  3. Create measurements as appropriate. 
  4. File / Export / HTML5 / JavaScript App to create your browser app.  


An example is here.

A video showing how to create this model is here.

Note that Lua app generation does not support images.

Problem of the Month
Pythagorean generalization   
Given a triangle ABC, parallelograms ADEB and BFGC are constructed. H is the intersection of DE and GF, I is the intersection between HB and AC.  AJ and CK are parallel to HI. J lies on DH and K lies on GH.


Show that the area of AJKC is the sum of the areas ADEB and BCGF.


Pappus of Alexandria presents this theorem as a generalization of the Pythagorean Theorem.  Show that it is.


An app which lets you explore this problem is here.

April Problem Solution
What is the envelope of the family of circles whose centers lie on an ellipse and whose circumferences pass through one of the foci of the ellipse?

An app which lets you explore this problem is here.

How about a hyperbola?

An app for the hyperbola is here.

general circle envelope
The above Geometry Expressions Model shows the envelope of the circles centered at B on a generic curve and through the origin A.  Point C is at parametric location t on the envelope and point B is at parametric location t on the original curve.  The angle between AC and the tangent at b is shown to be right.  The distance from C to the tangent is shown to be identical to the distance from A to the tangent.  Hence C is the reflection of A in the tangent at B.

For an ellipse the locus of the reflections of one focus in the tangent is a circle centered at the other focus, whose radius is the same as the major axis of the ellipse.

Similarly for the hyperbola.
Watch videos about creating Apps with Geometry Expressions.

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

Learn how to Export an Animation with Geometry Expressions.
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

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