They look the same but...
- Author:
- Rafael Losada Liste
This activity belongs to the GeoGebra book Linkages.
Let's look at another example. While the elementary version, faithful to the construction model of Dynamic Geometry (a point A, a segment of fixed length 1, another segment of fixed length 1), makes the entire construction depend on A (the only completely free point) and behave as follows:
the version with script removes that prominence from point A:
We see that, in this second representation, although it provides a very good mode of interactivity to convey impressions, the visualization really goes beyond the construction model with Dynamic Geometry.
Let us remember that a mechanism is represented by a mathematical model that simply responds to the imposed restrictions (equations). In this case, the length of the two bars AB and BC. We see then that the dynamic geometric model incorporates more information than the algebraic model (guaranteed that length is always equal to 1), since it not only maintains this limitation but also decides how to represent it interactively (this difference does not occur in static images).
As we have seen, the scripts that are activated in this second case when trying to move A, B or C, are in charge of altering the order of hierarchical dependency in the construction, so that the point that we move, whatever it is, appears to have the same freedom of movement.
For this reason, we must be very careful with what is meant by visualizing a mathematical model of a geometric object. The object is chosen, the model is chosen, the way to visualize it is chosen... and it is expected that the visualization accurately captures the mathematical model, not the object.
The scripts used in this second construction are detailed below.
Script that is triggered by moving A:
SetValue(B, Intersect(Ray(A,B), Circle(A,1)))
SetValue(C, Intersect(Ray(B,C), Circle(B,1)))
Script that is triggered by moving B:
SetValue(A, Intersect(Ray(B,A), Circle(B,1)))
SetValue(C, Intersect(Ray(B,C), Circle(B,1)))
Script that is triggered by moving C:
SetValue(B, Intersect(Ray(C,B), Circle(C,1)))
SetValue(A, Intersect(Ray(B,A), Circle(B,1)))
Author of the construction of GeoGebra: Rafael Losada