Posted on 05/01/2005 10:21:25 AM PDT by yankeedame
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.
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.
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.
I still don't get it. You're saying it shouldn't be a straight line, but it ~IS~.
Hmmm, well I'm puzzled. Maybe my brother will be able to explain it when he responds to my email.
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.
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.)
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.
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.
Anyone know the answer? This is driving me crazy!
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.
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."
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.
THE Answers... check posts 33 and 34
http://www.freerepublic.com/focus/chat/1394751/posts?page=32#33
Correct.
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