Saturday, October 22, 2011

Facts + Sensitivity => Impact

Here's an interesting exchange between Neil deGrasse Tyson and Richard Dawkins. Be sure to watch the entire clip.

Two quotes to think about:
Tyson: Being an educator is not only getting the truth right but there's gotta be an act of persuasion in there as well. Persuasion isn't always here are the facts and you're either an idiot or you're not. It's here are the facts and here's a sensitivity to your state of mind and it's the facts plus the sensitivity when convolved together creates impact.
Dawkins: Just one anecdote to show that I'm not the worst in this thing. A former and highly successful editor of New Scientist magazine, who actually built up New Scientist to great new heights, was asked "what is your philosophy at New Scientist?" and he said "Our philosophy at New Scientist is this: science is interesting and if you don't agree you can f#@k off."

Thursday, October 20, 2011

Mathy "60-second Adventures in Thought" Videos

I came across a set of six "60-second Adventures in Thought" videos by the Open University on thought experiments in philosophy, two of which I think would work well in a math class.

This first mathy video is on Achilles and Tortoise, one of Zeno's Paradoxes. Great for Calculus.

This second video is on Hilbert's Infinite Hotel about infinite sets. At the high school level, it could be a good fit in a math club.

There are more videos linked at Brain Pickings on Grandfather Paradox about time travel, on John Searle's Chinese Room about artificial intelligence, on Twin Paradox about relativity, and on Schrödinger's Cat about quantum mechanics.
(via Vitor Pamplona)

Tuesday, October 18, 2011

Untangle

Untangle is a game where the goal is to untangle a geometric graph. The game starts with several connected vertices and the player tries to move the vertices so that no edges intersect. Sounds simple right?

Here's a video of me playing the first few levels of the game.


The game becomes challenging pretty quickly. It's fun and interesting until you hit the "EVIL" level. It becomes more about tracking and organization. The game could use a fullscreen mode.

I remember playing the game some time ago. I revisited it when I was trying to recreate the game in GeoGebra, but a little digging around and I find this paper by Bose, Dujmovic, Hurtado, Langerman, Morin and Wood linked at The Geomblog. From that post, there seems to be a version for iPhone called Planarity and several versions on the android market when you search untangle.

UPDATE: Here's untangle played physically and collaboratively by a group of people.

Sunday, October 9, 2011

Area vs Perimeter of Polygons

I saw the following question shared on twitter by @ddmeyer. I decided to take a closer look with GeoGebra. Scroll down the page until you see the graph below then drag the large red point on the pop-up.

Be sure to disable the pop-up blocker, at least temporarily, if you don't see it. The pop-up is needed for the applet.

Increase the number of sides n by dragging the slider then drag the large red point around again. Also try out the circle. If you accidentally close the pop-up, click on "View" then on "Graphics 2" and the pop-up should return. If you'd like to save a copy of applet simply click on "File" then "Save" or "Save As" and select a filename and location.


This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Created with GeoGebra

Extension (Pre-Calc): Find the general equation for area A in terms of perimeter P given the number of sides n. Is this function linear, quadratic, cubic, exponential, or does it use some other model?

Extension (Calculus): What do you notice as n increases? Conjecture about what happens to the curve as n increases without bound?