May 2012

Visualization of Curl

This is a great visualization and explanation, of the curl of a vector field:

If you interpret a vector field as the flow of a fluid, then you can interpret the curl as a measure of the tendency to rotate at a given point.

One way to think of this is to imagine a tiny sphere, or paddle-wheel, fixed at a point in space, and then consider how that object would rotate if subjected to the flow of fluid as given by the vector field.

This write-up and series of animations from MathInsight.org are very useful in attaching some intuition to this complex idea.

By patrick honner, 12 years4 years ago

Representation Resources

Combinatorial Bracelets

This is another wonderful visual demonstration from Jason Davies: a combinatorial bracelet generator.

http://www.jasondavies.com/necklaces/

Combinatorics is the mathematics of counting things, and one of the classic “advanced” counting problems is this: given a certain number of beads of various colors, how many different bracelets can you make?

The problem may seem easy enough, but it becomes quite difficult when you start to understand what “different” really means.

For example, if you turn one bracelet into another by rotating it, then those two bracelets aren’t different. Even more complicating is that if you can obtain one bracelet from another by flipping it over, then they are also the same!

This visualization can really help develop a sense of the complicated symmetries at work here.

Click here to see more in Representation.

www.MrHonner.com

By patrick honner, 12 years4 years ago

Teaching

Real School Reform?

Public school teachers seem to be enduring a lot of vocal criticism these days, as politicians and “reformers” call for measures that tie student performance to teacher job security.

While genuine public discourse about educational policy and philosophy should be a good thing for us all, it’s all too easy to lay the “accountability” at the feet of teachers and ignore the many other factors that contribute to student “performance”, some of which may be even more fundamental to student success.

For example, it turns out that if we provide students with healthier, more nutritious meals, they will perform better and miss less school.

http://www.guardian.co.uk/education/2011/apr/10/school-dinners-jamie-oliver

Test scores up. Absenteeism down. Lifetime income substantially raised. All by replacing industrial, highly-processed cafeteria food with the real thing.

I always liked Jamie Oliver.

By patrick honner, 12 years4 years ago