Comments on: Geometry puzzle

Question: Geometry puzzle

Crotalus — Thu, 18 May 2006 23:35:32 -0800

Attention geometry wizards, Explain this picture

By: juv3nal

juv3nal — Thu, 18 May 2006 23:42:05 -0800

the big triangle (composed of all the other bits) isn't actually actually a triangle. The point at which each of the 2 little triangles meet dips inwards or juts out. You can tell because the slopes of the hypoteni (?) of the two smaller triangles differ. That's where the unaccounted space comes from. It's just the size of the image and the relatively small difference in slopes that makes it not obvious.

By: Khalad

Khalad — Thu, 18 May 2006 23:42:18 -0800

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.

By: phyle

phyle — Thu, 18 May 2006 23:43:35 -0800

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?

By: Steven C. Den Beste

Steven C. Den Beste — Thu, 18 May 2006 23:43:50 -0800

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.

By: phyle

phyle — Thu, 18 May 2006 23:45:02 -0800

And beaten by two other people.. :)

By: Mr. Six

Mr. Six — Thu, 18 May 2006 23:47:24 -0800

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".

By: kechi

kechi — Thu, 18 May 2006 23:49:38 -0800

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.

By: juv3nal

juv3nal — Thu, 18 May 2006 23:52:18 -0800

you lot are slow typers.

By: kechi

kechi — Thu, 18 May 2006 23:53:16 -0800

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.

By: kechi

kechi — Thu, 18 May 2006 23:54:42 -0800

I'm not so much a slow typer as a slow geometrician.

By: vanoakenfold

vanoakenfold — Fri, 19 May 2006 01:11:02 -0800

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>

By: hortense

hortense — Fri, 19 May 2006 01:16:31 -0800

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

By: jessamyn

jessamyn — Fri, 19 May 2006 06:22:09 -0800

[linked the image directly]

By: kechi

kechi — Fri, 19 May 2006 12:51:24 -0800

vanoakenfold: <Thanks!>