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Brain Teaser of the Day...and, no, I don't know the answer.(Maybe you can help)

Posted on 05/01/2005 10:21:25 AM PDT by yankeedame



TOPICS: Chit/Chat; Miscellaneous; Weird Stuff
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To: dinasour

The primary assumption is that the forms are a right triangle. This is not the fact and the hypoteneuse is not a straight line. Several of the posts, by inspection and mathematics point this out.


21 posted on 05/01/2005 11:12:10 AM PDT by Young Werther
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To: yankeedame
It's a Fibonacci number thing. The lines in the diagrams are not straight. The subtle differences in angle make up for 1 unit of area.
22 posted on 05/01/2005 11:12:29 AM PDT by Doctor Stochastic (Vegetabilisch = chaotisch is der Charakter der Modernen. - Friedrich Schlegel)
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To: dinasour; KC_for_Freedom; Young Werther
The hypotenuse of the top triangle is not a straight line, but instead the red and green triangles make a small angle where they meet.

Incorrect. I opened the graphic in Photoshop and checked with the line tool... the hypotenuse is a straight line. It is an optical illusion that makes it appear to curve.

23 posted on 05/01/2005 11:15:11 AM PDT by ecurbh (All I've ever wanted was an honest week's pay for an honest day's work.)
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To: ecurbh

You must not believe your eyes on this one, look at the rise and run of each triangle. If they have the same slope then when they are joined hypotenuse to hypotenuse they will make a straight line. If the slopes are different, (which they are .4 vs .375) then it is photoshop that is misleading. (Perhaps the drawing is not "true" have photoshop replot the shapes from the vertices and see if the original drawing has been "fudged" to make the puzzle harder to solve.


24 posted on 05/01/2005 11:24:59 AM PDT by KC_for_Freedom (Sailing the highways of America, and loving it.)
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To: KC_for_Freedom

I still don't get it. You're saying it shouldn't be a straight line, but it ~IS~.


25 posted on 05/01/2005 11:29:45 AM PDT by HairOfTheDog (I'd rather be happy than right...)
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To: KC_for_Freedom

Hmmm, well I'm puzzled. Maybe my brother will be able to explain it when he responds to my email.


26 posted on 05/01/2005 11:29:48 AM PDT by ecurbh (All I've ever wanted was an honest week's pay for an honest day's work.)
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To: HairOfTheDog; ecurbh
What I did when I first saw this problem is graphed it very carefully myself. You can easily see that it should not be a straight line. You can do it on a computer if you have a drafting program. But someone who wants to make it a straight line can draw it as a straight line. The fact that the point where the two triangles meet is not on the straight line from the top of the upper triangle to the bottom of the lower triangle should be clear if the graph is correct. What I am saying is that a thick line can hide the fact where a very thin line will show it.

If I was making a drawing to fool people, I would use thick lines and draw it so the two triangles looked like they joined in a straight line. Try graphing the shapes and fitting them together. I think you can convince yourselves.

27 posted on 05/01/2005 11:56:46 AM PDT by KC_for_Freedom (Sailing the highways of America, and loving it.)
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To: ecurbh; HairOfTheDog

One more thing, you know it has to have a flaw somewhere, right. If it is not the two different slopes, then what is the problem? (You don't have to wait for your brother.)


28 posted on 05/01/2005 12:00:28 PM PDT by KC_for_Freedom (Sailing the highways of America, and loving it.)
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To: KC_for_Freedom

I don't see any flaw in the drawing, in fact I drew many different sizes and shapes of right triangles, and you can divide them up a number of ways to get them to have two different size triangles with apparently different rise and run, with lines that are all straight. I still don't see how that accounts for the appearance of a square. You can cut those two triangles out and they are the exact same size and the lines are perfectly straight.


29 posted on 05/01/2005 12:02:50 PM PDT by HairOfTheDog (I'd rather be happy than right...)
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To: HairOfTheDog

How do you explain that a triangle with sides of 3 and 8 (red triangle in the drawing) and a slope of 3/8 = .375 can line up with a triangle with sides of 2 and 5 (green ) with a slope of 2/5 = .4. The first thing I learned about line segments is that if two of them form a line on a graph then each segment must have the same slope as the combined segment.

In this case the slope of the large triangle is 5/13 =.384615.

It should not be surprising that these segments have different slopes and that the overall slope is in between the two smaller segments. It is so close that you need the math to tell it is not a straight line when the shapes are fitted together.


30 posted on 05/01/2005 12:15:58 PM PDT by KC_for_Freedom (Sailing the highways of America, and loving it.)
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To: yankeedame

Anyone know the answer? This is driving me crazy!


31 posted on 05/01/2005 12:40:38 PM PDT by jdm (You only live once, and usually not even then.)
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To: jdm
If the shapes are the same than Pythagoras says that the sum of the squares of the sides equal the square of the hypoteneuse then the movement of the components should not be a problem. When I calclate the some of the two triangles and compare them to the sum of the "larger shape" there is a difference! The lengths are not the same ergo no triangle.

Also the 15 squares in both yellow/green polygons is the same and the Hole appears then we need to ask Stephen Hawkings about holes appearing out of apparant nothingness.

32 posted on 05/01/2005 2:15:45 PM PDT by Young Werther
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To: ecurbh
Incorrect. I opened the graphic in Photoshop and checked with the line tool... the hypotenuse is a straight line. It is an optical illusion that makes it appear to curve.

I don't care what photoshop may show... but a 2x5 right triangle does not have the same opposing angles as a 3x8 right triangle. To maintain the same angles, the larger triangle has to be 7.5 units on the adjacent side if the opposite side is increased from 2 to 3 units.

Given a right triangle, the smaller (2x5) has angles of 90º, 21.8º, and 68.2º. The larger triangle (3x8) has angles of 90º, 20.6º and 69.4º.

The differences make up an area of 1 square unit, hence the appearance of a magically appearing "hole."

33 posted on 05/01/2005 8:18:22 PM PDT by Swordmaker (tagline now open, please ring bell.)
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To: ecurbh
There is a DOUBLE distraction going on here. First the triangles themselves are not identical in proportion or angles... and second the provided "facts". What facts are those? Why the measuring grid! We assume that each square is the same from left to right... they are not. Each square is subtley smaller as you move from left to right. This distorts the measurements of the adjacent sides of the triangles... and then we use this distorted data in our calculations.

Your calculations are correct... but between the fact that the triangles are not the same... and then the fact that they cheat on the measuring ruler, your .5 difference is increased by another .5 to give the appearance of a 1 unit spurious hole.

34 posted on 05/01/2005 8:29:37 PM PDT by Swordmaker (tagline now open, please ring bell.)
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To: jdm; KC_for_Freedom; yankeedame; HairOfTheDog; Young Werther; dinasour; Doctor Stochastic; ...

THE Answers... check posts 33 and 34

http://www.freerepublic.com/focus/chat/1394751/posts?page=32#33


35 posted on 05/01/2005 8:37:35 PM PDT by Swordmaker (tagline now open, please ring bell.)
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To: MikeinIraq

Correct.


36 posted on 05/09/2005 8:00:14 AM PDT by boris (The deadliest weapon of mass destruction in history is a leftist with a word processor.)
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