Not Electrical related, but can you explain this?

[K8MHZ]

I noticed an error in today's drawing. I wrote '13x5' when it should be 13 x 8.

Sorry.....but I don't think the error detracts from the point I was trying to make....hopefully....:ashamed1:

 

[ronaldrc]

I noticed an error in today's drawing. I wrote '13x5' when it should be 13 x 8.

Sorry.....but I don't think the error detracts from the point I was trying to make....hopefully....:ashamed1:

Sorry Mark
I reworked your picture to explain, I don't know any thing I can add to this to explain it any better.

 

[K8MHZ]

Sorry Mark
I reworked your picture to explain, I don't know any thing I can add to this to explain it any better.

It really makes more sense if you try to make the puzzle starting with the 13 x 8 triangle and scaling the pieces to fit.

They won't. When you re-arrange the pieces scaled from a real triangle you can easily see where the space comes from.

Let's look at the square blocks. In the first arrangement, there are 15 (3x5). That fits into the big (real) triangle with room to spare. Now look at the second arrangement. The blocks occupy 16 (2x8). That won't fit into a real 13 x 8 triangle, the upper left corner juts out past the big triangle's hypotenuse just a bit.

OK, so back to the first arrangement. If we adjust the two small triangles to exactly fit the sides of the square block, that creates a small angle pushing toward the center of the shape with the vertex of that angle being located at the upper left corner of the square blocks. (Now the 2 x 8 is really too big to fit in the overall shape)

Now, reversing the small triangles also reverses the angle, just enough to be able to now fit the 2 x8 section in (Now the 3 x 5 is really too small to fit in the overall shape).

The extra space is not created at all. It's just that with the tiny angle bowed in, it leaves a space of 15 units, while bowed out it leaves a space of 16 units. Bowed in, the 3 x 5 fits exactly, bowed out the 2 x 8 fits exactly.

Make sense?

 

[ronaldrc]

Like the single phase thingie I've said all I know to say.

But I am trying to understand.:slaphead:

 

[david luchini]

Like the single phase thingie I've said all I know to say.

But I am trying to understand.:slaphead:

Try thinking of it this way. The before and after are both supposed to show a 13x5 unit triangle. The area of a 13x5 unit triangle would be 32.5 square units.

Now break it into components. You have a green triangle of 5x2 units with an area of 5 square units, and a red triangle of 8x3 units with an area of 12 square units. You also have 7 orange squares and 8 light green squares. The total area of these components is 5+12+7+8= 32 square units. As you can see, the components are one half of a square unit smaller than a 13x15 triangle.

Adding in the black dot square, the total area is 33 square units. This is one half of a square unit larger than a 13x5 triangle. As Mark showed in his diagram, the components are either "bowed in" or "bowed out". The space covered by the "bowing out" is 1 square unit larger than the space covered by the "bowing in." That is why the block dot square fits into the puzzle when the arrangement is "bowed out."

 

[K8MHZ]

Like the single phase thingie I've said all I know to say.

But I am trying to understand.:slaphead:

Well, I messed up the explanation......I really don't want to write it again, so here is what is incorrect.

The first version has the 16 squares filling the room under the small triangles, not 15 as I said. The small triangles are adjusted so the hypotenuse of the overall shape touches the corner of the squares, making up the smallest angle of the quadrilateral.

Reversing the triangles reverses the angle and now points the small angle in, and the change takes up a space and makes it so the 15 squares fits without slop.

The rest of the other post should be OK. I just had the first and second arrangements reversed, but the application is the same.

 

[ronaldrc]

Well, I messed up the explanation......I really don't want to write it again, so here is what is incorrect.

The first version has the 16 squares filling the room under the small triangles, not 15 as I said. The small triangles are adjusted so the hypotenuse of the overall shape touches the corner of the squares, making up the smallest angle of the quadrilateral.

Reversing the triangles reverses the angle and now points the small angle in, and the change takes up a space and makes it so the 15 squares fits without slop.

The rest of the other post should be OK. I just had the first and second arrangements reversed, but the application is the same.

I think Mivey had it right everybody over thinks this thing.


Can't you see when the orange and light green section are seperated it makes a space?

 

[K8MHZ]

I think Mivey had it right everybody over thinks this thing.


Can't you see when the orange and light green section are seperated it makes a space?

That has little to do with the real puzzle. Seeing it on the computer makes it hard to understand. Drawing the puzzle out and cutting it precisely makes it much easier to understand. The real phenomena has nothing to do with overlapping or separation of the pieces and everything to do with geometry and the fact that the eye can't really see a 1.24 degree angle.

You WILL see it when you try to lay out the puzzle on paper or cardboard.

I just made one out of cardboard. I cut out the single unit so when I make the first arrangement, there is a one unit space (hole) in the middle. I also drew, on another piece of cardboard, a 13 x 5 unit triangle. First I place the pieces in the outline of the triangle like the first arrangement. Of course, it looks like a perfect fit, and there is a one unit hole in the middle. Then, I switch the small triangles and the L shapes and place them back in the outline (still looks like a perfect fit) and the hole vanishes.

It really adds to the effect if you can re-arrange the pieces rapidly and with as little movement as possible. It really looks like the hole just vaporizes into thin air.

It all revolves around that 1.24 degree angle and the fact that it is too small for the eye to see that you are looking at a quadrilateral, not a triangle. The illusion is even more distinct if you place the pieces over a real triangle.

This is more than a geometry trick, it's also a great magic trick once you get fast with it.

 

[ronaldrc]

Are you really saying that seperating the orange and light green sections by one space would not
make a space? :slaphead: :slaphead:

 

[K8MHZ]

Are you really saying that seperating the orange and light green sections by one space would not
make a space? :slaphead: :slaphead:

Of course not, but that is not why the trick works.

If you still don't see it, draw it out and cut out the shapes. You need no separation for it to work.

I'll try to post some pics of the cardboard puzzle so you can see that separation has nothing to do with the trick.

 

[ronaldrc]

Thanks, that was cool. So here is one in return.

This one has always been one of my favorites.

http://www.milaadesign.com/wizardy.html

It freaked my sister right out!!!

Me to I don't understand that

 

[K8MHZ]

Me to I don't understand that

Ain't that cool!!

It took me about 3 or 4 tries to figure that one out. Do it over a few times and see if you can figure it out. I'll post the solution later.

But....as promised, here are the pics.

First, the shape drawn on the cardboard.

View attachment 6565

Now, the pieces set on the outline with the space showing

View attachment 6566

And now the pieces set in so the space has vanished.

View attachment 6567

You can't see it, but the 1.24 degree angle is there, I know it is, I put it there.

:thumbsup:

Click for a closer look. There are no separations, no overlaps. Just enough angle to make the trick work, but not enough to even take up the width of the outline drawn with the silver marker.

 

[K8MHZ]

Me to I don't understand that

That can be made into a close trick, too.

Once you know how it works, print out the page with all the numbers and symbols on it. Then, on an index card, draw the symbol that the person will pick. (You will know once you figure out the trick)

Stash the card somewhere. Have someone (girls work best, they get freaked right out), choose their number...in their head so no one can hear it, have them do the math diddy silently then have them look at the at the chart and notice which symbol their number is over, but they are not to say anything. Then tell them where the index card is stashed and have them go get it. Remember, only they know what number they picked and only they know which number the math resulted in. Watch the look on their face when they see that the symbol on the card is the one over their number.

FWIW, I love dissecting magic tricks. I know how some of the very best are done. To me, it doesn't take away the enjoyment by knowing how the trick is done, just the opposite. The creativity, imagination, dexterity and knowledge of geometry that it takes to do the tricks is what I really appreciate.

I think I was a magician in a former life.

Chris Angel shows how he does some of his tricks and I have done them up close. He does one where he 'forces' lipstick through a girl's hand. I have done it and it really freaks the girls right out.

Guys don't usually get freaked out. They just get funny looks on their faces while they try to figure out the tricks.

 

[ronaldrc]

Ain't that cool!!

It took me about 3 or 4 tries to figure that one out. Do it over a few times and see if you can figure it out. I'll post the solution later.

But....as promised, here are the pics.

First, the shape drawn on the cardboard.

View attachment 6565

Now, the pieces set on the outline with the space showing

View attachment 6566

And now the pieces set in so the space has vanished.

View attachment 6567

You can't see it, but the 1.24 degree angle is there, I know it is, I put it there.

:thumbsup:

Click for a closer look. There are no separations, no overlaps. Just enough angle to make the trick work, but not enough to even take up the width of the outline drawn with the silver marker.

Mark

Nice illustration but that just proves my point.

On that numbers guessing game I did notice it misses about ever fifth time thats
probably the odds on it being wrong. Is that it?

 

[K8MHZ]

Mark

Nice illustration but that just proves my point.

If it does, it's not because of overlaps, I assure you. If the puzzle was machined to a strict tolerance, the result would still be the same. Forgive me if my arts and craft skills are lacking, but there are no separations, trust me. Why don't you construct one with a perfectly straight hypotenuse and try to make the trick work with whatever separation you think makes it work? Short answer, it won't . If the pieces are constructed precisely, they will line up just as I showed with no spaces or separations where you say you see them. All the change in area is done by reversing the 1.24 degree angle by swapping the two triangles.

On that numbers guessing game I did notice it misses about ever fifth time thats
probably the odds on it being wrong. Is that it?

It's never wrong, you did the math wrong.

Notice that the resultant number is always divisible by 9. For instance, taking 55, adding the two fives for ten and subtracting the 10 gives you 45. Do the trick again, this time notice that your answer will be divisible by nine and all the numbers divisible by nine have the same symbol.

 

[ronaldrc]

[.




It's never wrong, you did the math wrong.

Notice that the resultant number is always divisible by 9. For instance, taking 55, adding the two fives for ten and subtracting the 10 gives you 45. Do the trick again, this time notice that your answer will be divisible by nine and all the numbers divisible by nine have the same symbol.[/QUOTE]


Now thats just not possible I have never been wrong.:roll:

But thanks for explaining it to me.

 

[ronaldrc]

Mark, Thanks again now I can quit looking for that hidden camera.

 

[K8MHZ]

[.




It's never wrong, you did the math wrong.

Notice that the resultant number is always divisible by 9. For instance, taking 55, adding the two fives for ten and subtracting the 10 gives you 45. Do the trick again, this time notice that your answer will be divisible by nine and all the numbers divisible by nine have the same symbol.

Now thats just not possible I have never been wrong.:roll:

But thanks for explaining it to me.[/QUOTE]

:happyyes:

I was in the process of taking pictures from real low angles of the cardboard puzzle where you can see the angle. When you look down the 'hypotenuse' like aiming a rifle, the angle really shows up.

Then my batteries went dead. They are on the charger now....

 

[K8MHZ]

Mark, Thanks again now I can quit looking for that hidden camera.

You would have never found it anyway:lol:. I hide them good!

 

[ronaldrc]

Now thats just not possible I have never been wrong.:roll:

But thanks for explaining it to me.

:happyyes:

I was in the process of taking pictures from real low angles of the cardboard puzzle where you can see the angle. When you look down the 'hypotenuse' like aiming a rifle, the angle really shows up.

Then my batteries went dead. They are on the charger now....[/QUOTE]

Are you sure one of your batteries is not 180 degrees out of phase?:rotflmao: