Problem Solving Books

If you are going to teach mathematics, then you must teach problem solving skills.

I have found two excellent texts on problem solving. One old (free!) and one that is relatively new (in it's 3rd edition). I recommend them both.

1. The Canterbury Puzzles by Henry Ernest Dudeney. 1908

• Project Gutenburg - several digital formats (not pdf)
• freepdfdocs.com - download pdf format

2. Crossing the River with Dogs - Problem Solving Strategies. 1st Edition, 1994, Key Press

•  my resource page

For inspiration and insight as to why you must teach problem solving skills, read A Mathematician's Lament by Paul Lockhart. 

Magic Squares

This work of art is by Paul Calter:

It didn't strike me as a magic square at first. That's what so interesting about it.

More art work by Paul Calter: Calter's Web Gallery

More info on magic squares: Wikipedia

How to Make a Monochord

A monochord is a single string device with an adjustable bridge thus allowing two pitches to be heard simultaneously on either side of the bridge. Pythagoras' most important work is his study of the ratio of these string lengths. This study led to the development of traditional harmony and the major scale.

These ratios are referred to as the "musical ratios". Applications of the musical ratios can be found in art and architecture. [more info by Paul Calter]

Doodling in Math Class: Snakes + Graphs

This speaks for itself. Vi Hart has interesting ideas. See more at: http://vihart.com/

Florence, Italy

Photos that I took on my trip to Florence, Italy as part of my REB award.
"Architecture is frozen music." - Johann Wolfgang von Goethe
web album

Mathematics and Music

This has become my "white whale". I have found it to be very difficult to collect material in such a way so that both topics are meaningfully addressed. There are many examples of good mathematics that deal with music in a trivial way and vice-versa and I don't want to add to that sort of academic fluff!

Below is a link to a my current outline for a 3 week course. It is in no way finished as I am still adding and deleting content and ideas. I look forward to any comments and/or suggestions.

Outline: http://geometryonline.pbworks.com/w/page/33060523/Math-and-Music

pediment vs. rectangle

Does the ratio of the pediment relate to that of the rectangle beneath? I think about this everytime I see one. The picture is from Christ Lutheran Church in Fredricksburg, Va.

The Geometry of Nature, Art, and Architecture

Course Description

This three week course will give teachers of mathematics an opportunity to study geometric design and apply this knowledge in creative ways. In doing so, the learner will gain a perspective of the world that reveals the secrets of proportion and how the greatest artists and architects utilized them to create masterpieces. Emphasis will be placed on the use of technology to import graphics from digital cameras or the web and analyze and/or reconstruct them using dynamic geometry software.

Visit: http://geometryonline.pbworks.com