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U MAD MATH?! (imgur.com)

submitted ago by Qrko

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[–]Rottendog 81 points82 points ago

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The slopes of the trapezoids and triangles do not match

the slope of the trapezoids have a Rise/Run of 2/5

the triangles have a rise/run of 3/8

2/5= 0.4

3/8=0.375

this means that there is a tiny gap between shapes, resulting in about 1 unit

x = 2 - (3x5)/8 = 0.125

the area of triangles are = 2x (5 x 0.125)/2 = 0.625

the area of trapezoid is = 3 x 0.125 = 0.375

the total missing space is = 0.625+ 0.325 = 1

and thats 64 + 1(which is missing area) = 65

Basically because the slopes are different between the triangles and the trapezoids, when you shift them around and pair them up in a different configuration - the line is no longer straight, only NEARLY straight to the naked eye. In reality it is just enough difference that across the entireity of it, it creates a small enough gap to make up 1 square if combined.

[–]leviathan709 9 points10 points ago

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Smart.

[–]Rottendog 2 points3 points ago

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I can't really take the credit. Someone else originally did the math, I only read up on it and re-did it for myself just to prove it out.

It originally perplexed me the 1st time I saw it too, especially because If there's one thing I know, unless you're woman talking about your age or weight, numbers never lie and 64 definitely does not = 65! (Which is why I had to go find out why)

[–]endline80 1 point2 points ago

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i learned a proof in number theory that .99999 repeating = 1 i'll try to dig it up.

[–]dagit 2 points3 points ago

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Let s = 0.999999...

Then, 10s - s = 9.99999... - 0.9999... = 9

So we have 9s = 9. Now divide both sides by 9 to get s = 1.

Here is another way to think of it, but this one is less of a proof and more of just fun with patterns:

1/9 = 0.1111... 2/9 = 0.2222... 3/9 = 0.3333... ... 7/9 = 0.7777... 8/9 = 0.8888... 9/9 = 1 (by the pattern, it should be 0.9999...)

[–]skycake10 0 points1 point ago

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A different (admittedly less rigorous) way to think about it is that two real numbers are distinct if there exists another real number between them. There is no real number that exists between .9999... and 1, therefore they are equal.

[–][deleted] 0 points1 point ago

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A way to express this logically would be that that there is no measurable difference between the objects being compared.

[–]AnderBerger 0 points1 point ago

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.9 repeating technically cannot exist because it cannot be represented as a fraction. Though that theory is what your proof above confirms.

[–]dagit 0 points1 point ago

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Does that mean pi cannot exist? I agree that Reals are a weird bunch, but saying they cannot exist seems a bit strong. I suspect I'm misunderstanding what you mean.

[–]AnderBerger 0 points1 point ago

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Pi can be represented as a fraction. Pi=C/d, where C is the circumference of a circle and d is it's diameter. It is just that the resultant (Pi) is irrational, but that does not mean it cannot be represented by a fraction.

[–]gallais -1 points0 points ago

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1/1 looks like a fraction to me

[–]endline80 0 points1 point ago

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you are awesome!

[–]saxet 2 points3 points ago

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if i remember correctly, the illusion is that the pieces don't actually line up. its just poorly drawn

[–][deleted] 6 points7 points ago

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Draw it on paper, cut it out and re-arrange it like in the gif. You'll have your answer.

[–]Rottendog 2 points3 points ago

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Draw it on paper, cut it out and re-arrange it like in the gif. You'll have your answer.

This guy actually gives you the easiest and probably the smartest (common sensewise) way to tell why it's not actually true.

[–]imnoscar 4 points5 points ago

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The top diagonal is a 3/8 slope while the bottom is 5/2, by flipping the shapes on the bottom you get a slope of 2/5 or 3.2/8 which is close, but won't line up in reality. They mess with the image to make it look like the shapes line up.

[–]so_sassy 6 points7 points ago

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wat

[–]DieEierVonTool 1 point2 points ago

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No fucking clue what this means

[–]VinceWithSLAPCHOP 1 point2 points ago

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I'm going to refresh this comments page until someone smarter than me explains this.

[–]kthxl8r -1 points0 points ago

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Same deal as this, but with squares instead of people.

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