# Magic triangle (How does it work?) **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [August 20, 2007, 9:48pm UTC](https://boards.straightdope.com/t/magic-triangle-how-does-it-work/416300 "2007-08-20T21:48:29Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![Lobsang](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lobsang/32/4067_2.png) [@Lobsang](https://boards.straightdope.com/u/Lobsang)\ **Post date:** [August 20, 2007, 9:48pm UTC](https://boards.straightdope.com/t/magic-triangle-how-does-it-work/416300/1 "2007-08-20T21:48:29Z")
[http://img.photobucket.com/albums/v98/lobley/magictriangle.gif](http://img.photobucket.com/albums/v98/lobley/magictriangle.gif) ---
**Author:** ![Zeldar](https://avatars.discourse-cdn.com/v4/letter/z/b77776/32.png) [@Zeldar](https://boards.straightdope.com/u/Zeldar)\ **Post date:** [August 20, 2007, 9:57pm UTC](https://boards.straightdope.com/t/magic-triangle-how-does-it-work/416300/2 "2007-08-20T21:57:47Z")
[QUOTE=Lobsang] [![](https://img.photobucket.com/albums/v98/lobley/magictriangle.gif) ](https://img.photobucket.com/albums/v98/lobley/magictriangle.gif) [/QUOTE] It appears to work because the component pieces are close enough to the dimensions needed to disguise that the hypotenuse in the second (bottom) example is not quite a straight line. Using the Pythagorean theorem you can determine that the missing square is just the result of a fool-the-eye trick. ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [August 20, 2007, 10:10pm UTC](https://boards.straightdope.com/t/magic-triangle-how-does-it-work/416300/3 "2007-08-20T22:10:09Z")
Just look at the little slivers of space where the hypotenuse slices through a square. They don’t match up on the top and bottom diagrams. ---
**Author:** ![Gary\_Robson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gary_robson/32/3448_2.png) [@Gary\_Robson](https://boards.straightdope.com/u/Gary_Robson)\ **Post date:** [August 20, 2007, 10:26pm UTC](https://boards.straightdope.com/t/magic-triangle-how-does-it-work/416300/4 "2007-08-20T22:26:08Z")
Look at the dimensions of the dark green triangle: 2 high x 5 wide. The red triangle is 3 high. If the slopes match, then it would be 7-1/2 wide, but it isn’t. It’s 8 wide. In the top picture, the hypotenuse is concave (bowed inward). In the bottom picture, the hypotenuse is convex (bowed outward). That’s where the extra square comes from. ---
**Author:** ![Yeticus\_Rex](https://avatars.discourse-cdn.com/v4/letter/y/a698b9/32.png) [@Yeticus\_Rex](https://boards.straightdope.com/u/Yeticus_Rex)\ **Post date:** [August 20, 2007, 11:47pm UTC](https://boards.straightdope.com/t/magic-triangle-how-does-it-work/416300/5 "2007-08-20T23:47:36Z")
To back it up mathematically, the slopes of the two component triangles aren’t equal, therefore, the hypotenuse of the whole triangle itself is not a straight line. Red triangle slope is 3/8 = .375 Dark green triangle slope is 2/5 = .400 The slope of the whole triangle is 5/13 = .384615… Also, the area of the large triangle is 32.5, although the sum of the components only add up to 32. A little eye trickery…shorting the top triangle of 1/2 and adding 1/2 of empty space to the missing half to get one whole empty square.