Three corner puzzle.

[3_M]

Cut the top puzzle and than arrange the A and B as you see on the bottom one and you will find that there is an opening. Why?
If you cut the outside of both and lay it on top of each other you will see that they are ecaxtly the same size. Why is there an opening when you change A and B like on the bottom one? I don't know.
Mike M

[GrayBeard Phil]

Your eyes are playing tricks on your brain.

This puzzle, I think, makes you think that the the two smaller triangles are similar geometric triangles. They are not AS THE PUZZLE IS DRAWN!!

The original triange, as you have drawn it, is 26 squares, by 10 sq high.

Triangle 'A' is a 16 by 6 (angles of 20.6, 90, 69.4)
Triangle 'B' is a 10 by 4 (angles of 21.8, 90, 68.2)

Now recheck the original triangle - the hyponenuse is a stright line, therefore we must conclude the graphical construction of the smaller shapes must be fooling our eyes.

If we take the original triangle of 26 by 10, that gives angles of 21.04, 90.0 and 68.96 degrees.

The height of 'A' at the the 16 square point is not 10 units, as shown, but is
(tan (21.04)*16 = 6.156 squares high.

Now figure D can be presummed drawn correctly, but figure 'C' is drawn 0.156 squares too low.

Left side is 4.156 squares high, then 10 squares across, 2.156 squares down, 6 squares to the right and then two squares down, and four more to the right.

The missing area is the difference between the graphical drawing of 'C' and the calculated value of 'C'

BTW, the reconstruction of the 4 shapes to form the 2nd triangle does not show the corrected shape of 'C'. when re-arranged there should be a wisker gap between the bottom of 'A' and the top of 'D' due the increased height of 'C'

Does any of this make any sense to Anyone????

Phil

[SharonW0111]

Gee I wish I knew what you just said..

[CanadianScroller]

???.

Now Phil, I know you know what you are talking about. But did you cut the puzzle out?

This is similar in concept to the dissapearing man illusion . I still havent figured either one out even with explanations.

Somethings are best left for us to awe. But perhaps I just have a simple mind.

[3_M]

Hi Phil,

That explanation was way over my head, sorry about that, Phil. Like Carl was saying, did you cut both pieces and lay it on top of each other? The bottom of B is shorter than the bottom of A. Why are both triangles the same size but one leaves an opening?

Mike M

[3_M]

Phil,

Check this site: http://www.pops-shop.net/phpBB/viewt...hp?p=9094#9094
John Siers agrees with you. Nice to have people with more knowledge about geometry on this board than I have,.
Thank you Phil, with what you explained and what John explained it is now getting more clear to me.
Would be a nice conversation piece at craftshows.

Mike M

[Woodbutcher68]

Compare the intersections of "A", "B", and "C" and you'll see part of the reason. If "C" was cut correctly, the difference would be even greater. I didn't know Phil's answer to it, but I did see the difference at the intersection.

[GrayBeard Phil]

Using Corel Draw!



Phil

[Forester21]

A picture is worth a thousand words!! Now I see.
T

[SharonW0111]

Thanks Phil --- now I see it is the way they were stacked ( c on top of D ) works.. I knew it looked like that is where the diff was but with all the little squares my eyes couldnt see it ...