

Six Visual Proofs - cruise02
http://www.billthelizard.com/2009/07/six-visual-proofs_25.html

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notaddicted
(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

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cruise02
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

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nazgulnarsil
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).

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screwperman
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...](http://www.amazon.com/Proofs-without-Words-Exercises-
Classroom/dp/0883857006/ref=sr_1_1?ie=UTF8&s=books&qid=1248540566&sr=8-1)

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anatoly
Wow. Thanks!

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cruise02
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.

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cruise02
I also _saw_ it here...and I need to learn how to proof read.

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

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

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kingkawn
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.

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cruise02
I'm pretty sure "1/4 + 1/16 + 1/256... = 1/3" was in the title of the post.

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

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alanthonyc
Awesome post. I think I upvoted every comment too.

