Geometry Puzzle

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ctwo
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Geometry Puzzle

Post by ctwo »

I cut the shapes in a 13x5 cm triangle out of craft board as shown on the left. I rearranged the same pieces as shown on the right, yet now I have a 1x1 cm square hole. How it's possible?
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earlgo
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Re: Geometry Puzzle

Post by earlgo »

Look around on the floor, you may have dropped the part covering the hole. :shock:
The surface area of the two parts is still the same no matter how they are arranged. This is how all those funny plastic puzzles work wherein they only fit in the box in the proper orientation. Basically you have a 2 piece jigsaw puzzle
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mklotz
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Re: Geometry Puzzle

Post by mklotz »

The two triangles don't have the same slope. The smaller has a slope of 2/5 and the larger has a slope of 3/8.
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SteveHGraham
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Re: Geometry Puzzle

Post by SteveHGraham »

Turn them over and see if a picture of Elvis appears.
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Re: Geometry Puzzle

Post by SteveM »

SteveHGraham wrote:Turn them over and see if a picture of Elvis appears.
That only appears on black velvet.

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spro
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Re: Geometry Puzzle

Post by spro »

It appears that you are trading triangles and now a wasted hole.
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NP317
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Re: Geometry Puzzle

Post by NP317 »

"Look around on the floor..."
That's my vote.
:lol:
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mklotz
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Re: Geometry Puzzle

Post by mklotz »

A lot of feeble attempts at humor but nothing resembling an explanation.

As I said in an earlier post, the two triangles do not have the same slope. The hypotenuse in the left hand picture is a straight line. In the right hand picture it isn't and your mind is tricked into thinking it is. The slight difference in area afforded by this deception allows the rectangular pieces to be rearranged to display the missing square.

A visual explanation of the effect is shown in the gif on this page...

https://www.google.com/search?q=triangl ... n3XimF3-MM:
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Re: Geometry Puzzle

Post by spro »

Whoa. I gotta check this Marv. I was about to attempt humor but this is more.
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Re: Geometry Puzzle

Post by spro »

I just don't see that now. I put a straight edge against the screen and it is very deceptive, if it is. These appear to be the same pieces arriving to the same right angle. The arrangement creates the hole ( so far)but I need read further into this. I can only imagine how terrible it would be, working to deceptive SD's CD's etc. Yeh. Blueprints. Man. Then we wonder about necessary modifications when it all worked out on paper.
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Re: Geometry Puzzle

Post by mklotz »

spro wrote:I just don't see that now. I put a straight edge against the screen and it is very deceptive, if it is. These appear to be the same pieces arriving to the same right angle. The arrangement creates the hole ( so far)but I need read further into this. I can only imagine how terrible it would be, working to deceptive SD's CD's etc. Yeh. Blueprints. Man. Then we wonder about necessary modifications when it all worked out on paper.
Spro, I don't have a clue what you're on about but, if you're confused, the best advice is to make one of the puzzles for yourself and play with it. There are many variants of these appearing/disappearing area puzzles. One of the simpler to make is the 64 = 65 puzzle, pictured and explained here...

http://mathematicscentre.com/taskcentre/155_6465.htm
Regards, Marv

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ctwo
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Re: Geometry Puzzle

Post by ctwo »

First, I cut out the large triangle at dimensions 13x5.

Then I sliced off the medium triangle at a right angle to the base, as best I could.

Then I sliced off the small triangle, again trying to make a right angle triangle.

So, aside from my cutting tolerances, the triangles should have the same angles, but that is just the way I made it and Marv's gif shows explains the classic puzzle, which is made from an 8x3, 5x2, and 5x3 cm shapes.

The area of the large triangle is 32.5cm^2

The area of the medium triangle is 12cm^2

The area of the small triangle is 5cm^2

The area of the other two shapes is 15cm^2

Doing some math, I am only seeing a 0.5cm difference in area, not a full square.

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