Books about the history of physics.
Watching Cosmos (2014) has rekindled my interest in physics and the history of physics.
Understanding Physics by Isaac Asimov
The Evolution of Physics by Einstein & Infeld
Six Easy Pieces and Six Not So Easy Pieces by Richard Feynman, also the complete Feynman Lectures on Physics are available online, as are his messenger lectures.
A blog about the things I find interesting including, but not limited to, mathematics, education policy, data visualization, and juggling.
Monday, June 23, 2014
Visual Proofs
Sometimes, a visual proof is more helpful than pages of computations. Here are two interesting math concepts which you might find interesting.
1. "Dual" of polyhedra -- basically take a solid like a cube, find the midpoint of each edge, and rotate each edge about the midpoint until it connects with the other sides. Those two shapes are "dual". http://hyrodium.tumblr.com/post/76098308148/dual-polyhedrons
2. The "Sum of squares" 1 + 2 + 4 + 9 + 16 + ... has an elegant representation. Just think about stacking blocks and count up how many blocks are in the solid rectangle when you're done:
Proof 1 - fantastic animation! (source) Here is a Non animated 2d proof.
Sometimes, a visual proof is more helpful than pages of computations. Here are two interesting math concepts which you might find interesting.
1. "Dual" of polyhedra -- basically take a solid like a cube, find the midpoint of each edge, and rotate each edge about the midpoint until it connects with the other sides. Those two shapes are "dual". http://hyrodium.tumblr.com/post/76098308148/dual-polyhedrons
2. The "Sum of squares" 1 + 2 + 4 + 9 + 16 + ... has an elegant representation. Just think about stacking blocks and count up how many blocks are in the solid rectangle when you're done:
Proof 1 - fantastic animation! (source) Here is a Non animated 2d proof.
Linkdump from today's explorations
Investement simulator
http://www.cfiresim.com/input.php?id=89449
From this thread
Investement simulator
http://www.cfiresim.com/input.php?id=89449
From this thread
187 million taxi rides
2013 taxi data from NYC yields some interesting insights.
https://www.mapbox.com/blog/nyc-taxi/
The discussion on hackernews was interesting. https://news.ycombinator.com/item?id=7926358 and revealed some fascinating insights. The current top comment offers some insights into how this data could be manipulated to find out, say, who is attending what bars and when... https://news.ycombinator.com/item?id=7927034
Reddit also picked up some interesting bits of info from the data including what percentage of people tip, and how much: http://www.reddit.com/r/bigquery/comments/28ialf/173_million_2013_nyc_taxi_rides_shared_on_bigquery/
From the reddit thread, someone linked a detailed yet approachable article about how the data may not be very anonymous: https://medium.com/@vijayp/of-taxis-and-rainbows-f6bc289679a1
> It took a while longer to de-anonymize the entire dataset, but thanks to Yelp’s MRJob, I ran a map-reduce over about 10 computers on EMR and had it done within an hour.
Interesting stuff!
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