Six Visual Proofs

#1

Post by cruise02 » Sat, Jul 25, 2009, 12:51 PM UTC

Re: Six Visual Proofs

#2

Post by cruise02 » Sat, Jul 25, 2009, 12:53 PM UTC

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.

Re: Six Visual Proofs

#3

Post by [deleted] » Sat, Jul 25, 2009, 1:40 PM UTC

cruise02 wrote: post #2

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]

Re: Six Visual Proofs

#4

Post by nazgulnarsil » Sat, Jul 25, 2009, 2:27 PM UTC

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).

Re: Six Visual Proofs

#5

Post by kingkawn » Sat, Jul 25, 2009, 3:21 PM UTC

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.

Re: Six Visual Proofs

#6

Post by cruise02 » Sat, Jul 25, 2009, 3:34 PM UTC

kingkawn wrote: post #5

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.

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

Re: Six Visual Proofs

#7

Post by notaddicted » Sat, Jul 25, 2009, 4:02 PM UTC

(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

Re: Six Visual Proofs

#8

Post by ianbishop » Sat, Jul 25, 2009, 4:39 PM UTC

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

Re: Six Visual Proofs

#9

Post by screwperman » Sat, Jul 25, 2009, 4:49 PM UTC

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...

Re: Six Visual Proofs

#10

Post by omail » Sat, Jul 25, 2009, 5:24 PM UTC

ianbishop wrote: post #8

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

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