Six Visual Proofs

http://www.billthelizard.com/2009/07/six-visual-proofs_25.html

by cruise02 • 17 years ago

49 14 17 years ago

cruise024• 17 years ago

I got the idea for this post from something I first saw on reddit/r/math earlier this week, but I also so it here on HN (you might recognize the first proof), so I thought I'd submit this here also. Hope you like it.

cruise024• 17 years ago

I also saw it here...and I need to learn how to proof read.

nazgulnarsil• 17 years ago

I discovered that 5th one while doodling in high school. It blew my mind at the time (and it can be extended to dimensions other than 2).

kingkawn2• 17 years ago

What made the 1/4 + 1/16 + 1/256... = 1/3 that was posted earlier this week so good was that it did not use numeric labeling, but purely visual content to make its point. If you could figure out a way to graphically represent what is now labeled, it'd be a complete success.

cruise024• 17 years ago

I'm pretty sure "1/4 + 1/16 + 1/256... = 1/3" was in the title of the post.

kingkawn2• 17 years ago

true enough, buts its quite different if it is wedded to the image.

notaddicted• 17 years ago

(no troll)

  1/2 + 1/4 + 1/8 + 1/16 + ... = 1

is like a binary version of

  9/10 + 9/100 + 9/1000 + ... = 0.999... = 1

cruise024• 17 years ago

Good observation. This is more apparent if you switch to decimal notation, (For want of a better term. I'm sure there's a name for it, I just don't know what to call the decimal point when you're talking about binary. Surely "decimal" point is wrong.)

In binary:

0.1 + 0.01 + 0.001 + 0.0001 + ... = 0.1111... = 1

In decimal:

0.9 + 0.09 + 0.009 = ... = 0.999... = 1

ianbishop• 17 years ago

Oh my god. The Pythagorean one just blew my mind. I am so embarrassed.

omail• 17 years ago

IIRC that proof is from India around 900 C.E.

rudyfink• 17 years ago

I'm not sure if you'll check back on your post, but if you do I think you might really enjoy http://www.sunsite.ubc.ca/DigitalMathArchive/Euclid/byrne.ht... (it's an illustrated version of Euclid's "The Elements").

screwperman• 17 years ago

If you like this, you'll love the book Proofs without Words: Exercises in Visual Thinking: http://www.amazon.com/Proofs-without-Words-Exercises-Classro...

anatoly• 17 years ago

Wow. Thanks!

alanthonyc• 17 years ago

Awesome post. I think I upvoted every comment too.

Six Visual Proofs

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