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...
Wow. Thanks!
Six Visual Proofs
11–18 of 18 posts
Re: Six Visual Proofs
#12Awesome post. I think I upvoted every comment too.
Re: Six Visual Proofs
#13What 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.
true enough, buts its quite different if it is wedded to the image.
Re: Six Visual Proofs
#14(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
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
Re: Six Visual Proofs
#15What 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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Re: Six Visual Proofs
#16I 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.
I also saw it here...and I need to learn how to proof read.
Re: Six Visual Proofs
#17Oh my god. The Pythagorean one just blew my mind. I am so embarrassed.
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").
Re: Six Visual Proofs
#18[deleted]