Advanced High School Math
Welcome to my math pages. The purpose of this series of pages is to provide high school math teachers and students with detailed, rigorous proofs of elegant and significant mathematical results that require no more than a solid grounding in high school math. The proofs will require no calculus, no group theory (unless I post a stand-alone series on the basics of group theory), limited complex number theory, and limited knowledge of axiomatic set theory. Many of the details that are often left for the reader to fill in will be made explicit, since that filling-in often requires more mathematical ability than high school students have. The notation should be standard and enlightening, not confusing. It is not my goal to address the problem-solving skills and topics that are needed for advanced mathematics competitions, although I'm sure that competition participants will find useful ideas here, too.
I hope to make this a collaborative effort. I already have one friend who has agreed to write pages for this series, and I will accept submissions from readers according to the guidelines posted here. That is also the place to leave a comment if you think you have found an error on one of the pages linked below (that link is also on each of the pages in the sidebar).
If you are interested in my observations on teaching, life, politics, media, etc. please visit the standard blogging section of my site.
Index to pages:
Geometry:
Triangle Centers:
The Classical Centers (circumcenter, centroid, incenter, orthocenter)
The Gergonne and Nagel Centers
The Incenter is also the Nagel Point of the Medial Triangle
Other Proofs:
Advanced Algebra:
The Coolest Math Fact Ever (uses complex numbers)
Trekking Into the Desert (a mathematical modeling problem)
Number Theory:
Divisibility Test for 7, 11, etc.
Group Theory:
No pages yet
Formal Notions:
An Instructive Proof of the Countability of the Rationals
