Visual Encyclopedia of Sorts
Things on the Internet continue to amaze me, as I wonder who has the time and creativity to organize some of the material available. Recently, I discovered the world of VisWiki, formerly named VisualWikipedia. As the name suggests, it is a visual way to represent information.
To illustrate, I was interested in Pythagorean triples. The result on VisWiki provides a great amount of information on Pythagorean triples that is of value to a mathematics teacher, a mathematics researcher, a mathematics historian, and a mathematics student.
For example, the following are accessible visually, or at worst, by the mere click on a link:
Yes, you can get lost in this "web" surrounding Pytjhagorean triples, investigating all of the options and links. Yet, you certainly will would walk away with better and deeper understanding (which seems to be a common goal in professional development).
- A brief definition and examples of the Pythagorean triples
- Procedures for generating Pythagorean triples
- Elementary properties of Pythagorean triples (though missing the neat idea that product of members of triple is always a multiple of 60)
- Some interesting relationships (e.g. triangle's area, incircle, etc.)
- Special cases, such Plato's method of generating triples
- Some interesting geometry underlying some of the methods of generating triples
- Scatterplot of the distribution of Pythagorean triples (as shown above)
- Generalizations, including a connection to Fermat's Last Theorem
- Videos related to Pythagorean triples
- Translations of the words "Pythagorean triples" into ten other languages
- Recommended articles, such the Babylonian's generation of triples in the clay tablet Plimpton-322
- And best of all...a visual display of links, with roll-over summaries
So, suppose before you teach a topic, you consider using VisiWiki to help you understand better what you are teaching. I know one thing...you will walk away feeling that the topic is much bigger than first thought. For example, try "triangle," "prime number," "factorization," or "derivative." The searches become contagious!