Link to

A Simple Proof of the

Classification of Conics by the


Martin Flashman
Humboldt State University
Arcata, CA
send comments to:
flashman at
"My Favorite Geometry Proof"
MathFest August, 2013

html/knowls version of MathFest presentation.
This version contains some materials not actually presented at Mathfest.

Notes for using this presentation.


    "knowls" are files that open and close in the window from which they are linked.

    The knowls are indicated by an underdot feature which highlights the text when covered by a mouse action. The knowls are activated and deactivated by clicking on the mouse over the highlighted region.

Specific features of the "knowls" and some unresolved issues:

Sage: When a knowl uses Sage for further display of information the button labeled "evaluate" needs to be pushed to activate the features further.

    In the knowl Points and Lines in the Real Projective Plane with 3D Calc Plotter "evaluate" will activate the 3D Calc Plotter in the knowl. To see the point, line, and plane objects visualized in the plotter i) download the file Objects in RP2.txt, then ii) open this file under the File menu in the plotter with "Load an Exploration Script" and iii) click on the "step" button to see the objects in a 3D viewing screen.

    In the knowl Conics in 3D with SAGE "evaluate" will activate a SAGE driven 3 D java figure controlled by i) a menu to choose a conic type, a parameter, ii) "a" in the equation of the conic, and iii) the selection of a "plane" to see show or hide the "XY" plane.  
The figure can be manipulated with various mouse actions in the virtual space of the figure.


    The title and end knowl A Simple Proof...  and The End include on a split screen the same animated view of the projective plane in perspective using Geogebra with conics varied through a cycle of ellipse, parabola, hyperbola. This can be stopped by clicking on the corner of the corner of the Geogebra window.

    In the knowl Planar Views of Conic Curves: Euclidean and Real Projective (in Perspective) Geogebra has two linked pages for viewing conics in both Euclidean and projective (perspective) planes. Use the check boxes to show/hide the curves. Comparable views are linked for the fixed examples. The dynamic examples are not linked.

Geogebra and SAGE Java Issue: While in use Geogebra and SAGE sometimes interfere with the mouse wheel scrolling feature. At this time the only way I know to ensure return of the full scrolling mouse features is a page reload.

Coming perhaps in the future: A YouTube video of the presentations showing the 3-D printed model of a cone with two planes illustrating an hyperbola built using a file created by the 3D Calc Plotter.