• Java plugin?
• Flash plugin?
• HTML 5?

Which technology to use?

• Vector graphics
• JavaScript

- All major browsers come with JavaScript

- JavaScript is fast

Open source library for interactive Geometry / Mathematics in the web browser

B = A + (0,1)

Space filling Hilbert curve:

Who said JavaScript is slow...?

t = brd.createElement('turtle');
function koch(x,level) {
    if (level<1) t.fd(x);
    else {
        koch(x/3,level-1);
        t.lt(60);
        koch(x/3,level-1);
        t.rt(120);
        koch(x/3,level-1);
        t.lt(60);
        koch(x/3,level-1);
    }
}
t.setPos(-250,0);
t.rt(90);
koch(400,7);
            

16385 data points

Point
Line
Ray
Segment
Circle
Perpendicular
Intersection
Angle
...

Scripting with JavaScript enables recursive constructions

Interaction

t.forward(100);
t.right(90);
t.left(90);
t.back(30);
...

Lindenmayer systems

Axioms + Rewriting rules + Turtle:

• Space filling curves,
• Plants,
• Penrose tilings,
• ...

Simulate differential equations

y₀ = s

Δy = α⋅ y⋅ Δt

dy = alpha.Value()*t.Y()*dt;
t.moveTo([dt+t.X(),dy+t.Y()]);
            

Numerical on-the-fly-evaluation of ordinary differential equations (explicit Runge-Kutta).

Archimedes' approximation of π

Power series

• Lagrange interpolation
• Cubic spline interpolation
• Polynomial curve interpolation

Controlling JSXGraph from the "outside".

There is no "inside" or "outside" of the construction anymore.

Not only controlling JSXGraph from the "outside" is possible.

Hooks are functions called by JSXGraph on every update.

With this it is possible to access and display information from "inside" the construction anywhere on the HTML page.

With JSXGraph elements like points can leave a trace.

This is useful to determine geometric loci.

Example for how to extend JSXGraph server side using AJAX:

Determination of geometric loci with CoCoA and matplotlib.

GEONE_xT:

JXG.JSXGraph.loadBoardFromFile(
    'box', 
    'cube.gxt', 
    'Geonext'
    );            

→ GEONE_xT²

Intergeo:

JXG.JSXGraph.loadBoardFromFile(
    'box', 
    'intergeo2.i2g', 
    'Intergeo'
    );            

JSXGraph has (the first?) JavaScript implementations of gunzip and unzip

GeoGebra