Geometry Puzzle

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mklotz
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Re: Geometry Puzzle

Post by mklotz » Wed Nov 22, 2017 2:33 pm

If you start with the large triangle as a single piece, you'll never reproduce the puzzle since smaller triangles sliced from the large one will have the same slope. The puzzle depends on the fact that the angles of the two smaller triangles are different. Given that fact, with their bases parallel, their hypotenuses can never form a continuous straight line.

I had hoped that when I pointed out the different slopes, folks would detect what was going on. I was wrong.
Regards, Marv

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SteveHGraham
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Re: Geometry Puzzle

Post by SteveHGraham » Wed Nov 22, 2017 7:42 pm

The real question is why ctwo is torturing us with this when we are clearly too stupid to figure it out.
Every hard-fried egg began life sunny-side up.

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ctwo
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Re: Geometry Puzzle

Post by ctwo » Thu Nov 23, 2017 12:38 pm

I am sure you are familiar with misery loves company...
Standards are so important that everyone must have their own...
To measure is to know - Lord Kelvin
Disclaimer: I'm just a guy with a few machines...

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mklotz
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Re: Geometry Puzzle

Post by mklotz » Fri Nov 24, 2017 10:21 am

Here's one that's a bit simpler - no geometry, just simple algebra. It's a 'proof' that all the integers are equal to zero !

a = b
a² = ab
a² + a² = a² + ab
2a² = a² + ab
2a² - 2ab = a² + ab - 2ab
2a² - 2ab = a² - ab
2(a² - ab) = 1(a² - ab)
2 = 1

Now, if we subtract '1' from both sides, we have:

2 - 1 = 1 - 1
1 = 0

So, 0 = 1 = 2

Adding '1' we have:

1 + 1 = 2 + 1
2 = 3

We can continue adding '1' to both sides to prove that all the integers are equal to zero.

So, what's wrong here?
Regards, Marv

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SteveHGraham
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Re: Geometry Puzzle

Post by SteveHGraham » Fri Nov 24, 2017 2:10 pm

In the top series of equations, you multiplied by zero!

Let's see.

4(0) = 10(0)
4=10
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mklotz
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Re: Geometry Puzzle

Post by mklotz » Fri Nov 24, 2017 2:32 pm

Well done, Steve.

Technically, the problem is not MULTIPLYING by zero, which is legal.

4(0) = 10(0)

simply reduces to:

0 = 0

which is a tautology. It's when you DIVIDE by zero, an illegal operation, that you open up the possibility of "proving" almost anything.
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SteveHGraham
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Re: Geometry Puzzle

Post by SteveHGraham » Fri Nov 24, 2017 2:37 pm

This bit here is equivalent to my "proof," which I plan to submit for consideration for a Fields Medal.
2(a² - ab) = 1(a² - ab)
2 = 1
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tornitore45
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Re: Geometry Puzzle

Post by tornitore45 » Fri Nov 24, 2017 3:23 pm

This is as old as the hills. It appears to be triangle but one side is ever so slightly concave to rob one unit square.
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TimOldman
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Re: Geometry Puzzle

Post by TimOldman » Thu Feb 22, 2018 9:08 am

tornitore45 wrote:
Fri Nov 24, 2017 3:23 pm
This is as old as the hills. It appears to be triangle but one side is ever so slightly concave to rob one unit square.

Probably that is old but I previously have never met it. We often solve short quizzes on the breaks at the college. Some of those in the thread are interesting to me. I gonna share with my friends, wanna make them confused

John Hasler
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Re: Geometry Puzzle

Post by John Hasler » Thu Feb 22, 2018 2:46 pm

> I wanted to machine it out of aluminum, but I think I will not be able to pull off a good enough illusion.

I think it depends on the edges being a little ragged. Machine it carefully out of metal and the lines will almost disappear in the assembly on the left while there will be glaring gaps in the assembly on the right. Maybe if you mill it with one of those DIY drill-press conversions?

Now let's see a Banach-Tarski sphere dissection done in Delrin. Or maybe with a piece of fruit.

https://en.wikipedia.org/wiki/Banach%E2 ... ki_paradox

TomB
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Re: Geometry Puzzle

Post by TomB » Sat Feb 24, 2018 4:41 pm

The pieces are not in the same arrangement Note that the two step pieces in the first image make a solid rectangle. Then the height of that rectangle is less that what is being perceived in the second arrangement. To make the triangles line up switch them. This makes the smaller triangle's height match the height of the two step pieces. The base of the larger triangle will match the width of the two adjacent step pieces.

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