Geometry puzzle
May 18, 2006 11:35 PM Subscribe
Attention geometry wizards, Explain this picture
http://en.wikipedia.org/wiki/Missing_square_puzzle
The key to the puzzle is the fact that neither of the 13x5 "triangles" has the same area as its component parts.
The four figures (the yellow, red, blue and green shapes) total 32 units of area, but the triangles are 13 wide and 5 tall, which equals 32.5 units. The blue triangle has a ratio of 5:2, while the red triangle has the ratio 8:3, and these are not the same ratio. So the apparent combined hypotenuse in each figure is actually bent.
The amount of bending is around 1/28th of a unit, which is very difficult to see on the diagram of this puzzle, though just about possible.
posted by Khalad at 11:42 PM on May 18, 2006
The key to the puzzle is the fact that neither of the 13x5 "triangles" has the same area as its component parts.
The four figures (the yellow, red, blue and green shapes) total 32 units of area, but the triangles are 13 wide and 5 tall, which equals 32.5 units. The blue triangle has a ratio of 5:2, while the red triangle has the ratio 8:3, and these are not the same ratio. So the apparent combined hypotenuse in each figure is actually bent.
The amount of bending is around 1/28th of a unit, which is very difficult to see on the diagram of this puzzle, though just about possible.
posted by Khalad at 11:42 PM on May 18, 2006
Im not sure but the lines dont appear to be completely accuarate.
The point where the dark green, red and orange shapes meet in the second picture is exactly on the plot point. The triangle edge misses that plot point on the top pic.
Could small rounding errors like this make up a whole square?
posted by phyle at 11:43 PM on May 18, 2006
The point where the dark green, red and orange shapes meet in the second picture is exactly on the plot point. The triangle edge misses that plot point on the top pic.
Could small rounding errors like this make up a whole square?
posted by phyle at 11:43 PM on May 18, 2006
It turns out that the top triangle "bulges" slightly when assembled the way it is, just enough to represent the area of one square distributed around its entire outer perimeter.
Or it would if they were drawing it honestly. This is a variant on P.T. Barnum's "tigers and natives" illusion.
posted by Steven C. Den Beste at 11:43 PM on May 18, 2006
Or it would if they were drawing it honestly. This is a variant on P.T. Barnum's "tigers and natives" illusion.
posted by Steven C. Den Beste at 11:43 PM on May 18, 2006
Take a ruler and put it up against the screen, along the hypotenuse, or longest side of the triangle. You'll find in both cases that this is not really a triangle at all.
The first "triangle" has a "hypotenuse" bent inwards, while the second "triangle" has a "hypotenuse" that bends outwards.
If you calculate the difference in area between the two fake hypotenuses, you'll find that this is where that one missing unit "goes".
posted by Mr. Six at 11:47 PM on May 18, 2006
The first "triangle" has a "hypotenuse" bent inwards, while the second "triangle" has a "hypotenuse" that bends outwards.
If you calculate the difference in area between the two fake hypotenuses, you'll find that this is where that one missing unit "goes".
posted by Mr. Six at 11:47 PM on May 18, 2006
The two small triangles within the shapes aren't similar triangles. (the small one is 2:5, the large one is 5:8) which means that the large shapes aren't really a triangle so the total area covered by each triangle-look alike is different. You can tell this by looking at the top point on the blue triangle on the bottom shape. On the bottom shape this point touches a node on the graph. On the top diagram no line crosses through the same node.
posted by kechi at 11:49 PM on May 18, 2006
posted by kechi at 11:49 PM on May 18, 2006
Beaten but at least I can answer the other question:
You can make a link by typing < a href="http:// insert website here"> the text you want linked goes here< /a>.
And take away the spaces after the <. There should be a button below the comment box with a link shortcut.
posted by kechi at 11:53 PM on May 18, 2006
You can make a link by typing < a href="http:// insert website here"> the text you want linked goes here< /a>.
And take away the spaces after the <. There should be a button below the comment box with a link shortcut.
posted by kechi at 11:53 PM on May 18, 2006
kechi: you can put HTML without creative spacing by using the ampersand symbols (> and < for greater-than and less-than, respectively) instead of the actual symbols. To even write those, I had to use &
<a href="http://...">title</a>
posted by vanoakenfold at 1:11 AM on May 19, 2006
<a href="http://...">title</a>
posted by vanoakenfold at 1:11 AM on May 19, 2006
It works with 1,2,3,5,8,13,21,34,55,89,144,233.....somewhat related to nautalus shells, pinecones and pine needles.strong>fibonacci paradox falacy
posted by hortense at 1:16 AM on May 19, 2006
posted by hortense at 1:16 AM on May 19, 2006
This thread is closed to new comments.
posted by juv3nal at 11:42 PM on May 18, 2006