A list of short documents

Not all of which are finished
Most in Word format, but some are in PDF so you will need Acrobat reader

I'm putting together a collection of theorem's that remind me of the Pythagorean Theorem. I'm calling it Almost Pythagorean

Playing around recently with repeated iteration of square roots led to some interesting stuff.

I'm trying to complete a list of the EXACT Diagonal lengths of a regular polygon with unit sides

There must be 50 ways to leave your lover according to the old Neil Simon song, but I only found 18 (maybe 20) ways to solve a quadratic equation, with some notes about their history.

An article on Paradoxes, including several types

And this one is about some ideas about Concurrency points in a triangle, including some non-typical ones.

This is a document on Fair Division of chores or expenses.

Here is a simple proof of Euler's Theorem on Planer Graphs [V + F = E + 2}

So Why is it Impossible to Solve the problem of the Three Utilities and three houses? Here is a short article with two proofs. I hope my students will understand at least one of them.

A colleague brought one of his students by my room a while back to ask if I could remember, and explain, the OLD BC (before calculators) way we used to do square roots. I managed to rediscover the method by thinking hard about the geometry of it, and wondered that no text I had ever seen included the reasoning. Afterward I wrote the following short article on two (I hope to add a third soon) ancient methods of finding square roots. A more current version is on the web page, it has some additional material on cube roots etc. .

How many distinct five letter combinations can be formed from the letters in Mississippi? This is a short paper I gave my students on counting permutations and combinations when repeats are included. I call it "The Mississippi Alphabet".


Here is the Math Analysis Handout for Products of Vectors

and another about Equations of lines in 3-space with some applications

A document on "Hot hands, Streaks and Run Length" that I wrote based on the studies prompted by the next item(s)

This is a copy of several posts on finding the probability of a run of lenth n in ten flips of a coin.It includes links to some Fathom simulations and a variation of the problem in which the probability is not 1/2.

This article on the Greedy Pig game contains some discussion and links to some programs about the game. It is an interesting exploration.

An article on replacing the Quadratic Formula and completing the square with a vertex approach to solving quadratic equations.

This document is related to the previous one and contains some comments on Quadratics and the complex plane and some worksheets I developed for introducing this topic to students.

Having Some Fun with Medians of a triangle.

And you can find the area of the triangle from the length of the medians.

And after Medians, explore the similar idea of nedians"

Exploring Ceva’s Thm, and Centers of Gravity

More on Centers of gravity,

And this is a Word handout I give my students about the Algebra of the Concurrency theorems of basic geometry. It provides guidance in approaches to writing the equations and finding the intersections of medians, altitudes, and perpendicular bisectors.

Some notes on Applications of the Determinant for Alg II class

Using Reduced Row Echelon Form Matrices to work with intersections of equations of planes in 3-space

Some notes on Using GSP to illustrate the geometry behind the solution of systems of equations by the method of elimination. This is the GSP 4.0 Sketch that it addresses.

Short notes on a relationship between distance from circumcenter of sides of a triangle and the Cosine of the opposite angle

I didn't have anything to do with this, but I thought it was such a great story, that it deserved to be where it could be found. The story is from George Gamow's autobiography and is about the Nobel Laureate, Igor Tamm.