4 ms·

Six Visual Proofs

49 points by cruise02 17y ago

cruise02 17y 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.
- deleted 17y ago
  [deleted]
- cruise02 17y ago
  I also saw it here...and I need to learn how to proof read.
nazgulnarsil 17y 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).
kingkawn 17y 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.
- cruise02 17y ago
  I'm pretty sure "1/4 + 1/16 + 1/256... = 1/3" was in the title of the post.
  - kingkawn 17y ago
    true enough, buts its quite different if it is wedded to the image.
- deleted 17y ago
  [deleted]
notaddicted 17y 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
- cruise02 17y 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 17y ago
Oh my god. The Pythagorean one just blew my mind. I am so embarrassed.
- omail 17y ago
  IIRC that proof is from India around 900 C.E.
- rudyfink 17y 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.html http://www.sunsite.ubc.ca/DigitalMathArchive/Euclid/byrne.ht... (it's an illustrated version of Euclid's "The Elements").
screwperman 17y 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-Classroom/dp/0883857006/ref=sr_1_1?ie=UTF8&s=books&qid=1248540566&sr=8-1 http://www.amazon.com/Proofs-without-Words-Exercises-Classro...
- anatoly 17y ago
  Wow. Thanks!
alanthonyc 17y ago
Awesome post. I think I upvoted every comment too.
deleted 17y ago
[deleted]

49 points by cruise02 17y 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.

deleted 17y ago
[deleted]
cruise02 17y ago
I also saw it here...and I need to learn how to proof read.

nazgulnarsil 17y 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).

kingkawn 17y 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.

cruise02 17y ago
I'm pretty sure "1/4 + 1/16 + 1/256... = 1/3" was in the title of the post.
- kingkawn 17y ago
  true enough, buts its quite different if it is wedded to the image.
deleted 17y ago
[deleted]

notaddicted 17y 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

cruise02 17y 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 17y ago

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

omail 17y ago
IIRC that proof is from India around 900 C.E.
rudyfink 17y 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.html http://www.sunsite.ubc.ca/DigitalMathArchive/Euclid/byrne.ht... (it's an illustrated version of Euclid's "The Elements").

screwperman 17y 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-Classroom/dp/0883857006/ref=sr_1_1?ie=UTF8&s=books&qid=1248540566&sr=8-1 http://www.amazon.com/Proofs-without-Words-Exercises-Classro...

anatoly 17y ago
Wow. Thanks!

alanthonyc 17y ago

Awesome post. I think I upvoted every comment too.

deleted 17y ago

[deleted]