Exploring the Pythagorean Theorem

Sal Khan from Khan Academy goes through several proofs of the Pythagorean theorem. What I particularly love about all of these is how geometric and visual they are. It might even be possible to do Bhaskara’s proof with a couple of squares of paper and some scissors, making it accessible to little kids with no concept of algebra.

President James Garfield’s proof using trapezoids

Bhaskara’s proof

Proof using similarity

Visual proof using parallelograms

Curiosity Mission

I watched the landing of the newest Mars rover Curiosity last night. It was fun being a part—if just an observer—of this event, and I was moved not only by the accomplishment (amazing!), but by the emotion in the room. It will be exciting to see how this mission unfolds over the next 2+ years.

And how about this? I had said to my family that there would be no pictures of the landing vehicle, since there are no cameras in this area of Mars. But I was wrong! The HiRISE camera on the Mars Reconnaissance orbiter snapped a picture of it with chute deployed. Incredible.


Solar Dynamics Observatory

I’d heard of the Solar Dynamics Observatory (SDO), but it wasn’t until the Transit of Venus in June that I realized just how amazing were the publicly available resources NASA has provided. Amazing photos and video, the ability to construct time lapses from data, as well as all that they provide to researchers. It is truly gratifying that a small part of my income tax goes to support this amazing project. I wish that more of my tax dollars went to support this kind of research and access.


Interesting Educational Sites

The first, which is quickly becoming famous is Salman Khan’s http://khanacademy.org, which extensively uses YouTube to provide what he calls “asynchronous learning”. Over two thousand videos covering a wide array of subjects, with particular strength in math, economics, and science. He also has over 60 videos on astronomy and cosmology. At about ten minutes each, the offerings are fairly near 400 hours of educational material. The site also is beginning to add assessment tools and there are some schools in the Peninsula that are trying it out as a complement to their standard materials.

The second, which I only heard about today, is http://quizlet.com, a flash card creation tool, that actually does several things I’d wanted to do in Flash, namely games and tests with packages of material. But perhaps the coolest aspect of this site is that the community is building these flash card sets, and thus there are literally  thousands of sets. Also, your progress can by measured against the community: speed tests are ranked, items with the most errors are shown, and so on.

Both are currently free. Let’s hope they stay that way!

Sloop v. Xebec

It’s been many years since I read Master and Commander, but I distinctly remember the battle between Lucky Jack Aubrey, newly made Commander of a sloop (was it called Sophie yet?) and an Ottoman xebec far larger and more capable. I need to read those books again!
But I never knew upon whom this story was based, and today, pretty much randomly, I stumbled across the Wiki entry for Thomas Cochrane, clearly one of the inspirations for Aubrey.