Math Explorations

TitleMathExplorationsWelcome! This is a bonus section.

I recently retired from teaching at Eleanor Roosevelt Community Learning Center, a charter school working with homeschool families. The most popular course I taught there I called “Math Explorations” (for younger students) and explained it as “Stuff that doesn’t look like math.” More recently I spent a few months as a volunteer in the Schoolhouse Teacher program, doing an online column that looks somewhat like Math Explorations, except it is for high school students. A part of each of my “lessons” was a series of videos on some topic, going beyond what is taught in regular school classes. Hopefully the videos and other material collected here will inspire you to think mathematically about the world we live in.

Schoolhouse Teacher Videos

I have my Schoolhouse Teacher Videos in a playlist on the YouTube Math Without Borders channel called “Lessons of Interest on Assorted Topics”. There are quite a few videos, so rather than embedding them all here, see them on YouTube.

Here are some of my other math videos:

Solving a Maze


The Pi Series

(A playlist of three videos introducing Pi and taking it to different levels)


Introduction to the Pythagorean Theorem


Constructing a Regular Pentagon with Origami


The Joys of RPN

(Make Your Calculator an Extension of your Brain)

[I have since discovered another option for obtaining an RPN calculator.  Free42 is an open source project emulating an HP 42s calculator, even better than an HP 35s!  You can download it as an “ap” for iPhone, Android, and/or your computer, Windows, Mac, or Linux. A manual for it is available here.]

Multiplying Positive and Negative Numbers


How to Subtract Without Ever Having to Borrow


Adding Fractions


Tying Your Shoes: Square Knot Bow

(Yes, tying your shoes is mathematics too!)


Tying Your Shoes: Surgeon’s Knot Bow

(Yes, even you can learn something new!)


Mathematics of the Rainbow

(This is a bonus section from the Calculus course. It involves a little
physics, a tiny bit of calculus, and a lot of algebra and geometry. It is a
great example of how mathematics can help us understand the natural world.)


About The Math Without Borders, Inc., “Golden Logo”


Disney’s Donald in Mathmagic Land

A classic of educational video from 1959 that ties mathematics to music, art, nature, and games. IMHO, the best educational feature Disney ever made! It is frequently available on YouTube for a short time before being removed. Rather than this cat and mouse approach, I recommend the DVD, which is typically available very inexpensively.

The Ultimate Area Formula

Have you ever wondered how surveyors measure the “acreage” of parcels of land? Some years ago I found a method in a surveyor’s handbook for finding the area of any polygon that I had not seen in math textbooks. It is very simple and it is completely rigorous (i.e. it is not an approximation). I included this method in the supplementary materials for my HSC Geometry program. (I also did a series of videos for the Schoolhouse Teacher site on area, culminating in the Surveyor’s Formula.)