Date started: September 2019

Leads: Glen Whitney

### Abstract

There are several excellent “dynamic geometry” software packages – graphical systems that allow the user to construct points, lines, planes, spheres, circles, and so on, and then watch how the geometric configuration so defined changes as a result of changing the positions of the initial points (and sometimes other entities and attributes as well). Notable examples include Geometer’s Sketchpad, Cinderella, and GeoGebra, but there are many

others.

However, to the best of my knowledge there is no major dynamic geometry program which focused on three-dimensional geometry from its inception. As a result, even those programs which do an excellent job of modeling 3D, such as GeoGebra, suffer from certain limitations: for example, when taking a 2D cross section of a 3D construction, the user cannot control the orientation of the axes of the resulting planar configuration.

Moreover, a construction process is not the natural form in which to specify a geometric configuration. When one is interested in a certain geometric problem or situation, normally one knows the properties, which one can think of as constraints, satisfied by the situation: this point lies on that line, this line and that plane are perpendicular, these two spheres are tangent, etc.

Hence, the motivation for Dyna3: a constraint-based dynamic geometry package developed in 3D from the very beginning. Note that the project is still primarily in conception as of 2019 December: the nascent code base merely produces a set of rotatable axes; it’s not yet possible to even define a point.

### Media

### References

- Geometer’s Sketchpad (https://www.dynamicgeometry.com/)
- Cinderella (https://cinderella.de/)
- GeoGebra (http://geogebra.org)
- Jurgen Richter-Gebert, Realization Spaces of Polytopes, Lecture Notes in Mathematics vol. 1643, Springer-Verlag: Berlin Heidelberg, 1996. (ISBN 978-3-540-62084-6)
- Dyna3 code repository (https://code.studioinfinity.org/glen/dyna3)
- Dyna3 on-line current demo (http://studioinfinity.org/dyna3)