# What's the trick to this .gif image? **URL:** \ **Category:** Factual Questions\ **Created:** [July 17, 2012, 8:09pm UTC](https://boards.straightdope.com/t/whats-the-trick-to-this-gif-image/628555 "2012-07-17T20:09:44Z")\ **Posts on this page:** 12\ **Page:** 1
**Author:** ![Blakeyrat](https://avatars.discourse-cdn.com/v4/letter/b/ecd19e/32.png) [@Blakeyrat](https://boards.straightdope.com/u/Blakeyrat)\ **Post date:** [July 17, 2012, 8:09pm UTC](https://boards.straightdope.com/t/whats-the-trick-to-this-gif-image/628555/1 "2012-07-17T20:09:44Z")
I’m sure everybody but me has seen this before, but [here’s an animated gif](http://cheezpictureisunrelated.files.wordpress.com/2012/07/wtf-photos-videos-alright-who-divided-by-zero.gif) that shows 8x8 == 5x13, that is, 64 == 65. Obviously there’s a trick to it, what’s the trick? ---
**Author:** ![srzss05](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@srzss05](https://boards.straightdope.com/u/srzss05)\ **Post date:** [July 17, 2012, 8:14pm UTC](https://boards.straightdope.com/t/whats-the-trick-to-this-gif-image/628555/2 "2012-07-17T20:14:58Z")
It looks to me like some “fudging” is going on when the various portions get moved around (I swear I saw some “blurring”). ---
**Author:** ![Ferret\_Herder](https://avatars.discourse-cdn.com/v4/letter/f/e47774/32.png) [@Ferret\_Herder](https://boards.straightdope.com/u/Ferret_Herder)\ **Post date:** [July 17, 2012, 8:16pm UTC](https://boards.straightdope.com/t/whats-the-trick-to-this-gif-image/628555/3 "2012-07-17T20:16:29Z")
Yup, [it cheats](http://www.cut-the-knot.org/Curriculum/Fallacies/FibonacciCheat.shtml). ---
**Author:** ![ZipperJJ](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zipperjj/32/211_2.png) [@ZipperJJ](https://boards.straightdope.com/u/ZipperJJ)\ **Post date:** [July 17, 2012, 8:17pm UTC](https://boards.straightdope.com/t/whats-the-trick-to-this-gif-image/628555/4 "2012-07-17T20:17:14Z")
Here ya go: [http://www.jimloy.com/puzz/missing.htm](http://www.jimloy.com/puzz/missing.htm) ---
**Author:** ![Sunspace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sunspace/32/1250_2.png) [@Sunspace](https://boards.straightdope.com/u/Sunspace)\ **Post date:** [July 17, 2012, 8:17pm UTC](https://boards.straightdope.com/t/whats-the-trick-to-this-gif-image/628555/5 "2012-07-17T20:17:34Z")
In the second array, there is a long, thin parallelogram between the other pieces, with an area of 1 square. It doesn’t show up well in low-resolution displays. ---
**Author:** ![Blakeyrat](https://avatars.discourse-cdn.com/v4/letter/b/ecd19e/32.png) [@Blakeyrat](https://boards.straightdope.com/u/Blakeyrat)\ **Post date:** [July 17, 2012, 8:18pm UTC](https://boards.straightdope.com/t/whats-the-trick-to-this-gif-image/628555/6 "2012-07-17T20:18:44Z")
> [@Ferret\_Herder](#): > > Yup, [it cheats](http://www.cut-the-knot.org/Curriculum/Fallacies/FibonacciCheat.shtml). Oh feh. I was hoping it was something more cool than “use thick edges on the line so people don’t notice the gap.” ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [July 17, 2012, 8:19pm UTC](https://boards.straightdope.com/t/whats-the-trick-to-this-gif-image/628555/7 "2012-07-17T20:19:00Z")
The slope of the diagonals on the two shapes is different: for the triangles, it’s 3/8, while on the quadrilaterals it’s 2/5. You can see that in the rearrangement, the main diagonal looks a bit “fat” due to these different angles; that’s where the extra square went. ---
**Author:** ![Chessic\_Sense](https://avatars.discourse-cdn.com/v4/letter/c/7c8e57/32.png) [@Chessic\_Sense](https://boards.straightdope.com/u/Chessic_Sense)\ **Post date:** [July 17, 2012, 11:28pm UTC](https://boards.straightdope.com/t/whats-the-trick-to-this-gif-image/628555/8 "2012-07-17T23:28:34Z")
> [@Dr.Strangelove](#): > > that’s where the extra square went. “…comes from.” ---
**Author:** ![dracoi](https://avatars.discourse-cdn.com/v4/letter/d/90db22/32.png) [@dracoi](https://boards.straightdope.com/u/dracoi)\ **Post date:** [July 17, 2012, 11:37pm UTC](https://boards.straightdope.com/t/whats-the-trick-to-this-gif-image/628555/9 "2012-07-17T23:37:45Z")
My way to disprove this would be to add up the angles. You know the angles at the corners have to add up to 90 degrees and the angles in the center have to add up to 180 degrees. I’ll leave the actual calculations to the reader, since this is another way of noticing the slope issue that Dr. Strangelove points out. ---
**Author:** ![yabob](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/yabob/32/2821_2.png) [@yabob](https://boards.straightdope.com/u/yabob)\ **Post date:** [July 18, 2012, 12:23am UTC](https://boards.straightdope.com/t/whats-the-trick-to-this-gif-image/628555/10 "2012-07-18T00:23:20Z")
> [@Blakeyrat](#): > > Oh feh. I was hoping it was something more cool than “use thick edges on the line so people don’t notice the gap.” It’s similar to this one: > **[Missing square puzzle](https://en.wikipedia.org/wiki/Missing_square_puzzle)** > > The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations. Each apparently forms a 13×5 right-angled triangle, but one has a 1×1 hole in it. > The key to the puzzle is the fact that neither of the 13×5 "triangles" is truly a t... Note that that one doesn’t rely on thick lines to cover an obvious gap, since the fudged border is the outer edge of the figure. It points out another factor - the eye just isn’t very good at noticing small differences in slope, and will easily see two adjoining line segments as a straight line when they aren’t. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [July 18, 2012, 2:29am UTC](https://boards.straightdope.com/t/whats-the-trick-to-this-gif-image/628555/11 "2012-07-18T02:29:03Z")
> [@ZipperJJ](#): > > Here ya go: [http://www.jimloy.com/puzz/missing.htm](http://www.jimloy.com/puzz/missing.htm) There are numerous variations on this, some of them artistic, and Sam Loyd had a lot of those. In the link quoted here, see the further link to the “Get Off The Earth” puzzle (near the bottom of the page) for a well-known one. ---
**Author:** ![RadicalPi](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/radicalpi/32/9806_2.png) [@RadicalPi](https://boards.straightdope.com/u/RadicalPi)\ **Post date:** [July 18, 2012, 9:48pm UTC](https://boards.straightdope.com/t/whats-the-trick-to-this-gif-image/628555/12 "2012-07-18T21:48:40Z")
The area of the parallelogram in the middle of the rectangle would have to be 0 for the diagram to be accurate. Which would mean that the magnitude of the cross product of (5, 2, 0) and (8, 3, 0) would be 0. Calculating however, gives us (5, 2, 0) × (8, 3, 0) = (2 ⋅ 0 − 0 ⋅ 3) **i** + (0 ⋅ 8 − 5 ⋅ 0) **j** + (5 ⋅ 3 − 2 ⋅ 8) **k** which works out to (5, 2, 0) × (8, 3, 0) = 0 **i** + 0 **j** − 1 **k** and then to (5, 2, 0) × (8, 3, 0) = − **k**. The magnitude of that, of course, is just 1, which, of course, is also the area of the hidden parallelogram. It would be cool to go the angle route and calculate the sines and arctangents exactly, and then see everything cancel out in the end, but I think that would be a giant mess. I might do it later.