Geometry Problems and Theory

Much Ado About Ellipses This page takes you to a number of articles about the ellipse (just standard stuff so far).
Topics include: ellipses in standard form and in polar form. Kepler's Three Laws,
and their theoretical proof by use of Newton's laws of motion and his universal law of gravitation.
(Flat-earthers don't bother.)

Here are presented two papers on how to do geometry problems using vectors.

Paper 1 This paper was first published in the AJNP in January 1991.

Paper 2 This paper was first published in the AJNP in April 1991.

Angle Bisectors Are Concurrent The Angle Bisectors of a Triangle Are Concurrent (uses trigonometry).

Determining a Circle from Three Distinct, Noncollinear Points in a Plane The algebraic solution. This proof uses some linear algebra techniques.

The Wedge Geometry Page Here are presented a number of papers on using Wedge Technology to do high school geometry and to establish the real numbers to some degree by geometrical means.

The Triangles Page Here are presented a number of papers on trigomonetry using techniques other than geometric algebra. For proof using geomnetric algebra, consult the appropriate page, please.

The Projective Geometry Page Here are presented a number of papers on projective (incidence) geometry following the presentation of the book The Geometry of Incidence by Harold L. Dorwart, Prentice-Hall (1966). At some point, I hope to present a proof of the harmonic ratio and a discussion of the finite projective plane.

Here are presented a 'fun' geometry problem I used analytical geometry to solve:

Distance between Centers of Two Circles.

It's easy to visualize that two distinct non-parallel planes in R3 intersect in a line. We'll prove this by parametarizing the intersection of these planes by a single variable, proving that the intersection space is one-dimensional. Intersection is a line. Knowledge of Cramer's Rule is assumed here.