Using GXWeb for Theorem Proving and Mathematical Modelling

Abstract

GXWeb is the free browser based version of the symbolic geometry software Geometry Expressions. We demonstrate its use in an educational setting with examples from theorem proving, mathematical modelling and loci and envelopes.

Figures (4)

• Figure 1: The circumcenter $D$, incenter $J$ and orthocenter $G$ of triangle $ABC$ are constructed on the diagram. The numeric panel, to the right shows values for lengths $a$, $b$, $c$, and for the ratio $|JG|/|GD|$ The symbolic panel, below shows exact values for the distance between $J$ and $GD$, along with $|DG|$, $|JG|$ and their ratio.
• Figure 2: Triangle $ABC$ has side lengths $a, b, c$. The incircle and the three excircles are constructed. Numerical radii are shown for these circles where $a=3$, $b=4$, $c=5$. Symbolic values for two of the radii and for the area of the triangle are shown.
• Figure 3: A geometric model of a box solar cooker with incident ray at angle $\phi$ to the horizontal and box lid open at angle $\theta$.
• Figure 4: The caustic curve due to reflection in a circle of light emanating from point $C$ inside the circle.