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Geometry Expressions Newsletter
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Geometry Expressions Newsletter

April 2012  
NCTM
Three of our authors are giving presentations involving Geometry Expressions at this year's NCTM annual convention in Philadelphia. 
  • Crop Circle Algebra: Students Teaching Farmers?  Larry Ottman Friday April 27th, 11:00-12:00, rm 123
  • Teaching Proofs to a Digital Generation   Irina Lyublinskaya Friday April 27th, 2:00-3:00, rm 120C
  • From Pedal Triangles to Savonius Wind Turbines: Students' Mathematical Modeling Projects  Philip Todd  Saturday April 28th, 11:00-12:00, rm 103A

Or come by our booth: Saltire Software ~ Booth 303.   

Area between two curves

 


How to...generate computer code with Geometry Expressions
You can use Geometry Expressions to create computer code in any of the following languages:
  • C / Objective C
  • C++
  • C#
  • Visual Basic (.net)
  • VBA
  • Java
  • JavaScript

Here's a simple example.

 

Let's imagine you want code for the intersection point between two segments.   

  • First draw the segments and create a point E at their intersection.
  • Next constrain the coordinates of the segments end points.
  • Now select point E and Calculate / Coordinates
  • If you want code which re-uses intermediate variables, then select the output and from the right click menu select Output Properties / Use Intermediate Variables / Yes

  • Keeping the output selected, do Edit / Copy As / Source Code / C++  
  • Paste into your editor. 

Here is the code generated for the above example:

 

 void z_0(
     double x_0 ,
     double x_1 ,
     double x_2 ,
     double x_3 ,
     double y_0 ,
     double y_1 ,
     double y_2 ,
     double y_3 ,
     double &z_0_x_ ,
     double &z_0_y_ )
{
    double z_0_x;
    double z_0_y;
    double d_1;
    double d_0;
    double phi_0;
    d_1=((y_2*x_3*(-1.0))+(y_3*x_2));
    d_0=((y_0*x_1*(-1.0))+(y_1*x_0));
    phi_0=(((y_0+(y_1*(-1.0)))*((x_2*(-1.0))+x_3))+((y_2+(y_3*(-1.0)))*((x_0*(-1.0))+x_1)*(-1.0)));
    z_0_x=(((((x_0*(-1.0))+x_1)*d_1)+((x_2+(x_3*(-1.0)))*d_0))*pow(phi_0,(-1.0)));
    z_0_y=((((y_0+(y_1*(-1.0)))*d_1*(-1.0))+((y_2+(y_3*(-1.0)))*d_0))*pow(phi_0,(-1.0)));
    z_0_x_ = z_0_x;
    z_0_y_ = z_0_y;
}  


Problem of the Month
Point A has coordinates (0,1).  A family of circles is defined whose centers lie on the x axis, and whose radii are a factor k times the distance between point A and their center.

Using Geometry Expressions (or otherwise), show that the envelope of this family of circles is a hyperbola if k<1 and an ellipse if k>1

Show that, in either case, A is a focus of the conic.

(See Salmon's "Higher Plane Curves", article 117)

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.


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

Phil Todd's TechIgnite talk connects central pivot irrigation in Texas to Malfatti's Problem
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