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Mathematics of this optical illusion

  1. Oct 26, 2005 #1
    Hello everbody, long time no see!!!
    I hope this is the right forum for this, I'm not ready to post it in the topology forum:cry:
    Okay, so I saw this neat optical illusion. It really started to bug me as I was playing around with it in paint trying to figure it out.
    http://www.ebaumsworld.com/images/illusioncount.gif" [Broken]

    So as I'm playing with it, and trying to figure out how it occurs, I notice the people are almost the same size, as if they have "slices" taken out. Then I start thinking the illusion must work something like the "extra square illusion"

    I remember one like this one, were 2 triangls made 2 different size squares, ( or maybe its just 2 of these together).
    Anyhow, my latest reasoning I had is that this people illusion must work similar to the square, where the people are almost the same and are missing "slices" of a person that add to to a half person, either adding or subtracting the half to make a difference of one person. That was my latest logic, and it was bothering me too since it still didn't click for me.
    Finally, I decided to bring it to the experts to have it disected. I thought we could have an interesting discussion on the mathematics of this an other optical illusions - such as how they are generated or created, and possibly we could think of some new possibilities of ilussions not yet done ( styles or methods".
    On another note, what ever happened to lethe? Does he come around here still, or is he too busy at IAS?
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Oct 26, 2005 #2


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    These are so obviously not the same triangles I can't see how anyone could miss that.
  4. Oct 26, 2005 #3

    yah, there was i a much better example i remember, but maybe i'm just imagining that? Maybe it was just a long time ago and it was impressive back then.

    I'm still stumped by this people illusion as of now.
  5. Oct 26, 2005 #4


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    I am having trouble understanding your post. Could you explain the phrase "people illusion"?

    As for the posted link, neither of those shapes are triangles. They are quadrilaterals with a very large interior angle on the side which seems to be the hypotenuse. The large Red triangle is not similar to the small Green triangle. Similar, used in this context has a well defined meaning.
  6. Oct 26, 2005 #5
    I solved that years ago.

    The answer is simple: They are the same parts, but that is not a triangle. it is a quadrilateral. The point the Sloped long line intersects the point from the 5sided figures creates a tiny angle.

    Basically if you analize the slope of the line in one triangle it would be 2/5 but in the other one is 3/8 and while that is damn close, it's not the same. Basically one figure has a 1/2 square exageration one direction, the other a 1/2 exageration the other way. DIfferent arrangements make it appear in differnt spots. The top puts the 1/2 square in a very very obtuze tirngle that has an angle of almoust 180, that's why it's apparently inexistent, the second half combines with the exageration with the triangle going the other way and forms 1 square that goes to the bottom.

    Considering the right hand end of the triangle as point (0,0) , the point (8,3) DOES NOT belong to both the line uniting the (0,0) and (13,5) and the point

    The ponit (8,3) does not belong to the line formed by (0,0) and (13,5) is the most mathematical way in which I can explain.
  7. Oct 26, 2005 #6


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    Look very carefully at the two top triangles. Their slopes are not he same. It should be obvious where the missing square went.
  8. Oct 26, 2005 #7
    my bad!!!!!

    my original post had this link, but the site was having problems and i scuffed my post up upon redsoig it.

    I understand the triangle problem. the illusion that was bother me was this one:
    http://www.ebaumsworld.com/images/illusioncount.gif" [Broken]
    I was thinking it might work similar to the triangle one.....

    Sorry about the confusion, I hope this clears things up.
    Last edited by a moderator: May 2, 2017
  9. Oct 26, 2005 #8


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    It's clever, basically it's the body parts change between the two sets of people. For example keep your eye on the third guy on the left in the black T-Shirt to see where the extra head comes from.
  10. Oct 26, 2005 #9
    what the hell are you talking about? if the parts are the same then why couldn't it contain a space of nothing. It doesn't make its volume of substance(color) change, just the volume of its form. it is the form that expands not what's in it. same thing with everything. it's not an illusion, well, perhaps the substance(color) is ;p
    Last edited: Oct 26, 2005
  11. Oct 27, 2005 #10
    Maybe I will get it eventually, but I"M STILL TRIPPIN!! on this one. It is very clever. I'm just still having a difficult time visualising the appearance / dissapearence ot the extra person!:grumpy: :yuck: :cry: :uhh:
  12. Oct 27, 2005 #11
    I figured out what happened on the first post... when I made it a hyper link, I thought I had screwed because the url was there twice. It was actually there for the hyperlink text.

    So I still had the hyperlink there (as I found out when I edited my post) , but there was no hyperlink text so I essentially I created an illusion with that one. It was there but it wasn't. The irony is killin me.:surprised

    is it just me that makes that illusion so baffling? :rolleyes:
  13. Oct 27, 2005 #12


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    I don't know what this has to do with math, it's just a clever trick. The guy who starts out on the right side with the black shirt moves without lining him up with any extra pair of feet on the left, and then they shift the images over without giving the guy on the far left a new set of hair (he looks a little "cropped" after the move). That's all. There's really nothing mathematical about an optical illusion, or else we'd probably call them mathematical illusions. Some like this one aren't really even illusions, just tricks, others rely more on the way the eye and brain process images relative to one another...that's the illusion part.
  14. Oct 27, 2005 #13


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    Add up the heights of the 12 people. Add up the heights of the 13 people. It should be the same. I'm trying here :tongue:

    This is a cute puzzle though. Long before I saw it I wanted to create money this way. Cut up 10 one dollar bills and make 11 one dollar bills. People might notice the scotch tape though.
  15. Oct 27, 2005 #14
    okay so the people who swap have a similar slice missing?

    Yes, I failed to see what this has to do with math also. Hence my question.

    What it does have to do with math, I was having a difficult time comprehending. So I wanted to get a quantitative analysis as to what was actuaclly occuring.

    Maybe we could build upon the method used here, and by using some special sort of fractal we could create something much more clever and interesting.
  16. Nov 2, 2005 #15
    This was posted on another forum of mine, they tore it apart very easily.
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