Marky the Sparky
If its the answer on Ebausworld or other places on the web about the top border line being crooked thats not the answer.
Not Electrical related, but can you explain this?
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Marky the Sparky
If its the answer on Ebausworld or other places on the web about the top border line being crooked thats not the answer.
mivey
Senior Member
Well you can say screen graphics have nothing to do with it but the fact remains that the pieces can't be lining up. The background grid does not represent the same area covered by the pieces. There are gaps and overhangs. There is no other way it can be or else we can create a perpetual motion machine by creating something from nothing.
Here is a simple confirmation for you: Cut out a one unit square section of paper and weigh it on a high-resolution scale (like you have in a chem lab). Next, weigh the pieces. The ratio of the weight of the pieces vs the unit square reference gives you the ratio of actual area. Now cut out the paper grid areas that are supposed to represent the area of the pieces in the different configurations. The weights will not match.
It is the weight of the gaps and overhangs that is making the difference. In other words, the pieces do not exactly align with the base grid although they might look like it on the screen.
Mivey I think Marky the Sparky might be on to it, although I couldn't make heads or tails out of the graphic he posted. There is nothing magical about it, there is nothing being gained or lost in the graphic. It is an illusion
which becomes apparent when you really know what it does. Has nothing to do with the line spaces between the blocks or the top line being crooked. I worked it so many times when I made the parts it finally donged on me what was happening. I showed it to my better half and she said it makes you feel stupid don't it. It goes againsted everything you thought you know.
Sparky What is card stock, I have never heard of it. I googled it never come up as a browser?
Ronald
K8MHZ
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Marky the Sparky
If its the answer on Ebausworld or other places on the web about the top border line being crooked thats not the answer.
I'm not saying. But, if you lay out the bottom triangle on card stock and re-arrange it like the top one, there will be a square missing.
K8MHZ
Senior Member
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- Electrician
Mivey I think Marky the Sparky might be on to it, although I couldn't make heads or tails out of the graphic he posted. There is nothing magical about it, there is nothing being gained or lost in the graphic. It is an illusion
which becomes apparent when you really know what it does. Has nothing to do with the line spaces between the blocks or the top line being crooked. I worked it so many times when I made the parts it finally donged on me what was happening. I showed it to my better half and she said it makes you feel stupid don't it. It goes againsted everything you thought you know.
Sparky What is card stock, I have never heard of it. I googled it never come up as a browser?
Ronald
Card stock is what post cards are made of. A manilla folder works fine.
mivey
Senior Member
Well, I'll keep thinking about it but I haven't heard anything that would convince me otherwise yet. Maybe I'm over-thinking or under-thinking it. It may be simpler than what I'm thinking but I'm not ready for the spoiler yet. Either way, I do appreciate you posting the thinking exercise.Mivey I think Marky the Sparky might be on to it, although I couldn't make heads or tails out of the graphic he posted. There is nothing magical about it, there is nothing being gained or lost in the graphic. It is an illusion
which becomes apparent when you really know what it does. Has nothing to do with the line spaces between the blocks or the top line being crooked. I worked it so many times when I made the parts it finally donged on me what was happening. I showed it to my better half and she said it makes you feel stupid don't it. It goes againsted everything you thought you know.
Sparky What is card stock, I have never heard of it. I googled it never come up as a browser?
Ronald
mivey
Senior Member
I probably will jump into AutoCAD after lunch to see if anything jumps out at me. I don't trust my scissor skills and bi-focals that much.
Oh, OK when you said you didn't use Ie I thought you meant you used another browser name Card stock.
I did it with card board a while back could you see what is happening?
Don't really need to use math.
Mivey don't let it bug you to much. It just happen to dong on me when I physically moved the orange section and the lite green sections apart from each other.Thats too much information.
K8MHZ
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- Electrician
Oh, OK when you said you didn't use Ie I thought you meant you used another browser name Card stock.
I did it with card board a while back could you see what is happening?
Don't really need to use math.
Once you start laying out the trick, you will probably notice the reason. If you want to make it even harder for someone to figure out, leave out the grid lines. But when you lay out the trick, you MUST use the grid lines and line up EVERY point the graph crosses the perimeter exactly. If I told why, that would be a spoiler.
If you want to amaze yourself even further, lay out each individual piece. The solution is not so obvious if you do it that way.
Or, lay it out like the top, half of a 5 x 13, and the trick won't work.
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I understand exactly what is going on once it dongs on you you are no longer amazed, you
just wonder why you didn't figure it out sooner.
K8MHZ
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I understand exactly what is going on once it dongs on you you are no longer amazed, you
just wonder why you didn't figure it out sooner.
To be honest with you, my eyes aren't that good, bad enough to overlook the solution. Once I zoomed in and started looking at the grid lines, it dawned on me.
K8MHZ
Senior Member
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- Electrician
I saw a documentary on the brain, Discovery Channel I think. Penn and Teller were showing how they used their knowledge of how the brain worked to do magic. Even after they showed people how a trick worked, most of them still were tricked as they had mastered the art of distraction to the point that people didn't even know they had looked away for a fraction of a second. Just enough time to do some slight of hand work. It was great.
There are two graphics that are about that Trigrid maybe you are looking at the wrong one
#2 is Jim Browns unbelievable story. It has a trigrid outline which does not line up exactly with the trigrid.
#3 is the Trigrid Illusion which is the best example with no trigrid outline.
Ronald
Mark and Mivey
Good morning
Last night I was making a graphic presentation to show how I thought
this worked by stretching the length of the orange and light green blocks
to make that extra space.
When I rearranged my parts both ways and drew a line for the resulting
hypotenuse, the hypotenuse rises more in one than it does the other one.
That is where the area for the extra block comes from.
Ronald
Good morning
Last night I was making a graphic presentation to show how I thought
this worked by stretching the length of the orange and light green blocks
to make that extra space.
When I rearranged my parts both ways and drew a line for the resulting
hypotenuse, the hypotenuse rises more in one than it does the other one.
That is where the area for the extra block comes from.
Ronald
K8MHZ
Senior Member
- Occupation
- Electrician
Mark and Mivey
Good morning
Last night I was making a graphic presentation to show how I thought
this worked by stretching the length of the orange and light green blocks
to make that extra space.
When I rearranged my parts both ways and drew a line for the resulting
hypotenuse, the hypotenuse rises more in one than it does the other one.
That is where the area for the extra block comes from.
Ronald
If you draw the puzzle (I just did this) on graph paper with a true straight hypotenuse, there isn't enough room for the two L shaped blocks drawn exactly 2 units by 5 units. The corner juts across the hypotenuse just a little bit. So I re-scaled the L shaped blocks to fit in the room available and cut out the puzzle. Re-arranging the now to scale pieces, they won't fit, BUT where the overlay in the original puzzle was the extra square, there is now only about half a block of overly, and there is also the same area of spaces left out, so if I cut out the overlay and cut that in half, the two pieces would fit in the spaces and we would, once again, have a full 5 x 13 triangle.
K8MHZ
Senior Member
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- Electrician
The gist of the trick is that the 'triangle' is not a triangle. It is a quadrilateral. The hypotenuses of the inner triangles are the two top sides that look like a single hypotenuse. In the first arrangement, the angle 'bows out' only about 1 1/2 degrees, but adds 1/2 a square to the quad as opposed to a straight hypotenuse. Switching the two inner triangles causes the angle to 'bow in', which subtracts a 1/2 square from the area of the quad as opposed to a straight hypotenuse.
K8MHZ
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- Electrician
Here is an exaggerated example of how the puzzle works:
View attachment 6562
The solid lines show the first arrangement. The rectangle below the triangle on the right is the area that would be occupied by the two L shape sections.
The dotted lines show the triangles reversed, like the second arrangement. Note the difference in the area of the dotted lined rectangle vs. the solid lined one.
Sorry about the hand drawing, but if you look close you can see where the real hypotenuse should be and the deviation caused by the difference in slopes of the two inner triangles. Now imagine bringing the original shape closer and closer to a real triangle but stop just shy of the real hypotenuse so that there is only 1/2 a unit of area over where the real hypotenuse should be.
View attachment 6562
The solid lines show the first arrangement. The rectangle below the triangle on the right is the area that would be occupied by the two L shape sections.
The dotted lines show the triangles reversed, like the second arrangement. Note the difference in the area of the dotted lined rectangle vs. the solid lined one.
Sorry about the hand drawing, but if you look close you can see where the real hypotenuse should be and the deviation caused by the difference in slopes of the two inner triangles. Now imagine bringing the original shape closer and closer to a real triangle but stop just shy of the real hypotenuse so that there is only 1/2 a unit of area over where the real hypotenuse should be.
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K8MHZ
Senior Member
- Occupation
- Electrician
I made the out of a manilla folder.
When I drew it out, instead of having the two triangles slope differently, I drew a subtle arc instead. That makes the imperfection even harder to see.
I made a small one, about 6 inches across the bottom. To make the trick work you have to first lay out the L blocks. Then lay out the legs of the outside triangle. You will now see that the blocks extend beyond where the hypotenuse would be.
Set a ruler on the corner of the blocks and even up the spaces on the ends. Tilting the pen as you draw is enough to make the needed arc.
Care must be taken while cutting the shapes out, of course.
When I drew it out, instead of having the two triangles slope differently, I drew a subtle arc instead. That makes the imperfection even harder to see.
I made a small one, about 6 inches across the bottom. To make the trick work you have to first lay out the L blocks. Then lay out the legs of the outside triangle. You will now see that the blocks extend beyond where the hypotenuse would be.
Set a ruler on the corner of the blocks and even up the spaces on the ends. Tilting the pen as you draw is enough to make the needed arc.
Care must be taken while cutting the shapes out, of course.
K8MHZ
Senior Member
- Occupation
- Electrician
I also noticed that the puzzle that OP linked to has a straight hypotenuse but the blocks cross it, so the puzzle is still not a triangle. Actually, if you look close, it has 6 sides.
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