Cut The Knot
December 1, 2007 11:52 PM Subscribe
Interactive mathematics miscellany and puzzles, including 75 proofs of the Pythagorean Theorem, an interactive column using Java applets, and eye-opening demonstrations. (Actually, much more.)
This is excellent. Thank you.
posted by Upton O'Good at 12:28 AM on December 2, 2007
posted by Upton O'Good at 12:28 AM on December 2, 2007
Great site that I hadn't know about, from someone who wants to enthusiastically share his deep love of math with others. I liked the dynamic versions of optical illusions (which have more to do with psychology than math) and the section on math and language (where he compares how mathematical laws were stated before and after the invention of relevant notation).
I don't think he gets very far toward understanding why people find math more formidable and less accessible than music and reading, though. It's an interesting question. The author emphasizes the beauty and elegance of math and clearly wants other people to be able to share in it. Yet few do (in the general population; maybe not among MeFites). Why?
One obvious point is that a person can engage reading and music at different levels that are enjoyable for a variety of reasons. Most people who listen to music don't know musical theory. You can read Us magazine or a technical article or Borges novels.
Getting to the point where you really appreciate the beauty, elegance, connectedness etc. of math seems to require a high level of expertise. The examples on that web site are not trivial math from what I've seen.
There's also the possibility that expertise in math takes a special kind of intelligence. Reading builds on basic capacities to see, hear, and use language. Not much special expertise there. At the simplest level, music enjoyment arises out of basic properties of hearing and motor control. nothing too specialized there. Math, however, seems to require specialized knowledge that only some people may be able to acquire because the underlying capacities vary greatly among individuals.
I don't pretend these are the answers but the web site brought them to mind.
posted by cogneuro at 2:12 AM on December 2, 2007
I don't think he gets very far toward understanding why people find math more formidable and less accessible than music and reading, though. It's an interesting question. The author emphasizes the beauty and elegance of math and clearly wants other people to be able to share in it. Yet few do (in the general population; maybe not among MeFites). Why?
One obvious point is that a person can engage reading and music at different levels that are enjoyable for a variety of reasons. Most people who listen to music don't know musical theory. You can read Us magazine or a technical article or Borges novels.
Getting to the point where you really appreciate the beauty, elegance, connectedness etc. of math seems to require a high level of expertise. The examples on that web site are not trivial math from what I've seen.
There's also the possibility that expertise in math takes a special kind of intelligence. Reading builds on basic capacities to see, hear, and use language. Not much special expertise there. At the simplest level, music enjoyment arises out of basic properties of hearing and motor control. nothing too specialized there. Math, however, seems to require specialized knowledge that only some people may be able to acquire because the underlying capacities vary greatly among individuals.
I don't pretend these are the answers but the web site brought them to mind.
posted by cogneuro at 2:12 AM on December 2, 2007
Ahhh sweet post, thanks !
posted by elpapacito at 6:27 AM on December 2, 2007
posted by elpapacito at 6:27 AM on December 2, 2007
Who knew that President James Garfield is credited with a proof for the Pythagorean theorem? (See also proof 5 in the 75 proofs link.)
posted by Brian B. at 8:10 AM on December 2, 2007
posted by Brian B. at 8:10 AM on December 2, 2007
The first thing I checked when I saw the 75 proofs link was whether Pres. Garfield's proof made it (yay!) Had a prof show it to me years ago -- had to get independent confirmation that it really was Garfield's and not some elaborate hoax.
He came up with his proof while serving in the House of Representatives. Probably born in an inspired doodling session triggered by a boring committee meeting, if God has a sense of humor.
posted by Opposite George at 5:02 PM on December 2, 2007
He came up with his proof while serving in the House of Representatives. Probably born in an inspired doodling session triggered by a boring committee meeting, if God has a sense of humor.
posted by Opposite George at 5:02 PM on December 2, 2007
Can you imagine if our president now was able to do ANY proofs, much less a 75-step one? :)
I just hope that Pres. Garfield was working on that proof during non-vital issues! Yeep! Can you imagine mis-voting on a spending bill or something cuz you were finally getting close to a^2+b^2=c^2 ?!
posted by fracturing at 9:31 AM on December 3, 2007
I just hope that Pres. Garfield was working on that proof during non-vital issues! Yeep! Can you imagine mis-voting on a spending bill or something cuz you were finally getting close to a^2+b^2=c^2 ?!
posted by fracturing at 9:31 AM on December 3, 2007
Garfield's proof is by no means 75 steps — it's short and quite elegant, actually. (P.S. The links above are for clicking.)
posted by parudox at 10:56 AM on December 3, 2007
posted by parudox at 10:56 AM on December 3, 2007
Cogneuro: Keith Devlin makes a compelling argument in The Math Gene that the quality in our brain that lets us do math is the same as that which lets us use and create language. Math ability is universal; "math phobia" is an attribute of this society.
It's an excellent book, I can't recommend it too highly.
posted by phliar at 8:45 PM on December 3, 2007
It's an excellent book, I can't recommend it too highly.
posted by phliar at 8:45 PM on December 3, 2007
D'oh! Apparently I shouldn't make fun of Bush when my reading comprehension skills were questionable. :)
posted by fracturing at 8:13 AM on December 6, 2007
posted by fracturing at 8:13 AM on December 6, 2007
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posted by parudox at 11:52 PM on December 1, 2007