Mind Games

[rickoff]

Who's face do you see in the picture below? Everyone who looks at this may think of a different person. Hint: It may well remind you of someone in government. To find your answer, tilt your head to the right until you see things more clearly.

[Pamela Vicik-Smith]

Hahahaha!!! That last one is pretty funny!

[rickoff]

In the illustration below, the colored objects seen at left are rearranged at right. The same exact sizes and shapes are used in both, but the figure at left has a total of 64 squares, while the figure at right has 65. Since all the pieces fit together perfectly, with no intervening space, how can the figure at right have a larger area?

[rickoff]

Pink, or green?

Now here's a really cool illusion. First, let your eyes follow the moving dot as it moves clockwise, and all you see is pink dots. Then focus directly at the + in the center, and the moving dot will appear green! Continue to focus on the + for a few more seconds, and all the pink dots will fade away, leaving only the moving green dot!

[aljhoa]

In the illustration below, the colored objects seen at left are rearranged at right. The same exact sizes and shapes are used in both, but the figure at left has a total of 64 squares, while the figure at right has 65. Since all the pieces fit together perfectly, with no intervening space, how can the figure at right have a larger area?

The same exact sizes and shapes are used in both
Al

[Nadda]

Rickoff,

I thought that last illusion was pretty cool when the missing one turned green, but when all the pink dots dissappeared...that was just plain freaky!

There is no green dot to even begin with! Yet in the end thats all you can see....Seriously amazing

thanks for sharing!

[rickoff]

The same exact sizes and shapes are used in both
Al

Someone is a layer?? Okay, what did someone lay?

No, the statement is true. I assure you that the colored pieces in both drawings are exactly the same size and shape. Just count the squares on each side of each shape, and you will see. Or print the page, cut out the colored shapes, and lay one on top of the other. They are exactly the same. Each of the triangles, regardless of color, are the same (3x8), and each of the quadrangles are identical (3x5x5). The grid squares are all equal size, and you can see that by measuring any ten horizontally and then vertically. You are right, in that the slope of a 3x8 triangle (.375) is slightly different than the 5x13 slope of the larger triangle formed by the combined green triangle and blue quadrangle (.385) The hypotenuse of the 5x13 triangle, however, forms a perfectly straight line. You could also think of the blue quadrangle being a shape that includes a 3x5 rectangle with a 2x5 triangle on top of that. The slope of the 2x5 triangle is .400, and so now you have 3 varying slopes, although they are all drawn at exactly the same 21 degrees acute angle from horizontal.

[rickoff]

Black and white, or color?

Here's a really interesting illusion. Keep looking directly at the picture. First you see a black and white picture of a castle. Then you watch a blurry color overlay. Then you view the castle again, but see it in color, until it fades back to black and white.

YouTube - Castle Optical Afterimage Illusion

[aljhoa]

Someone is a layer?? Okay, what did someone lay?

No, the statement is true. I assure you that the colored pieces in both drawings are exactly the same size and shape. Just count the squares on each side of each shape, and you will see. Or print the page, cut out the colored shapes, and lay one on top of the other. They are exactly the same. Each of the triangles, regardless of color, are the same (3x8), and each of the quadrangles are identical (3x5x5). The grid squares are all equal size, and you can see that by measuring any ten horizontally and then vertically. You are right, in that the slope of a 3x8 triangle (.375) is slightly different than the 5x13 slope of the larger triangle formed by the combined green triangle and blue quadrangle (.385) The hypotenuse of the 5x13 triangle, however, forms a perfectly straight line. You could also think of the blue quadrangle being a shape that includes a 3x5 rectangle with a 2x5 triangle on top of that. The slope of the 2x5 triangle is .400, and so now you have 3 varying slopes, although they are all drawn at exactly the same 21 degrees acute angle from horizontal. If you were to extend the hypotenuse of the 5x13 triangle out until you reach the next perfect intersection on the graph squares, you would then have a 8x21 triangle, with a slope of .381, so you see the slope is variable. It will only be identical at 3x8, 6x16, 9/24, and so on, in multiples.

Assume the geometric figures of 8x8-square are made of gold plate such that each square weighs 10 ounces.
Rearranging these gold pieces into 5x13- rectangle crates diagonal empty space equal to one square on the same grid scale.
Sound minded person would not pay someone $650,000.00 for geometric figures having only 640 ounces of gold?
Al

[rickoff]

That's right, but where does the extra square come from?

[aljhoa]

The exaggerated rectangle shows the diagonal empty space equal to one square worth $10,000.00.
Al

[rickoff]

That's not it. The hypotenuse is a perfectly straight line. I would agree that there is obviously something going on in this illusion, but I think it is probably associated with the black lines that outline the shapes. Notice that, for example, the shortest side of the blue quadrangle in the left arrangement is situated before (above) the grid square line. When rotated into position in the figure at right, however, it is past the line. And, if you were to take away the black lines and just have color meeting color, the color boundaries would not align properly on the grid. I think it's as simple as that, but a very clever illusion indeed. The black lines create the illusion that all is correctly aligned.

[aljhoa]

That's not it. The hypotenuse is a perfectly straight line. I would agree that there is obviously something going on in this illusion, but I think it is probably associated with the black lines that outline the shapes. Notice that, for example, the shortest side of the blue quadrangle in the left arrangement is situated before (above) the grid square line. When rotated into position in the figure at right, however, it is past the line. And, if you were to take away the black lines and just have color meeting color, the color boundaries would not align properly on the grid. I think it's as simple as that, but a very clever illusion indeed. The black lines create the illusion that all is correctly aligned.

In order for hypotenuse to be a perfectly straight line angles must equal as well as slopes.

5/13 slope must equal to 3/8 otherwise
5/13=X/8
X=3.077
however X must equal to 3.00

Al

[rickoff]

Yes, certainly that is correct and obvious. What isn't obvious, though, is that none of the 3/8, 2/5, and 5/13 triangles are actually those proportions. The artful use of the black lines only makes it appear that way. If the actual proportions are known, the slopes will all be identical. In other words, the slope of the greeen triangle is identical to the slope of the blue quadrangle. The sloping black line that appears as a hypotenuse at the center is in fact perfectly straight, and there is no open space as shown in your thumbnail.

[rickoff]

Who is this?

Move in close and look at this picture. Who is it? Did you guess Albert Einstein?
Now move back away from your monitor screen 10 feet or more, and who do you see?
What's your guess? Let me know.