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Geometry Expressions Newsletter

January 2012  
From Java Applets to JavaScript/HTML5 apps
causticFirst there were Java Applets.  In the 1990's at Saltire Software, we had an experimental geometry tool which created applets and inserted them in web pages.  The results can be seen in our Geometry Applet Gallery

Two problems with Java applets are:
  1. Users of the applet must have the Java runtime environment on their computer.  This is not a problem for most computers, but smart phones and tablets typically do not have Java enabled.
  2. Creators of the applet must have a Java compiler.   

These problems were sufficient to persuade us not to commercialize our Java Applet generation technology.


The advent of JavaScript removed both of these obstacles.   

  1. JavaScript/HTML5 apps run inside the browser without any additional plug-ins.  They work well on computers, tablets and smart phones.
  2. JavaScript source code is embedded directly in the web page, and no compilation is necessary.

All this means that you can generate a web page with a JavaScript app at the press of a button from within Geometry Expressions.


We re-created our Geometry Applet Gallery so you can compare the Java Applet Version with the JavaScript Version


How to...create an applet with draggable points
We illustrate how to create an app with points which the user can drag.  Our app will display a triangle along with the lengths of its sides and its area.  The user will be able to drag the vertices of the triangle.
  • First draw a triangle.
  • Constrain the coordinates of the vertices of the triangle, leaving the default variable names in place. (To be draggable, a point must have both coordinates constrained to be variables.) 
  • Now Calculate Symbolic measurements for the lengths of its sides and for its area.  (Only symbolic measurements can appear in the app).
  • Do File / Export / HTML5/JavaScript App
  • Fill in the app dialog, being sure to set Auto-scale to False.  


The finished web page may be seen here

Problem of the Month
Steiner Ellipse
Given a triangle ABC, points D,E,F are defined to be proportion t along the sides AB, BC, CA respectively.

Point G is at the intersection of AE and BF.

Point H is at the intersection of BF and CD.

Point I is at the intersection of CD and AE.

Using Geometry Expressions (or otherwise) show that the loci of G,H and I as t varies are portions of ellipses.
Show further that they are portions of the same (translated) ellipse.

An app illustrating this property is here.

Under what circumstances is the ellipse a circle?
Electronic Book Bundle

10 Geometry Expressions eBooks are now available as a bundle for the recession-friendly price of $79.95
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 

Learning Calculus with Geometry Expressions is a unique electronic resource containing lecture-ready slides and lab-ready Geometry Expressions files.
Available for $6.99 per chapter, or $34.95 for the whole book.

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

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