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The Geometry of Crop Circles

Whether you think crop circles are made by little green men from space or by sneaky earthling geeks, you've got to admit that they are pretty dang cool...  And whoever is making them knows a ton of geometry!

I'd better give a little background in case you don't know what crop circles are...  Suppose you're a farmer and have wheat fields...  You go to bed and the wheat fields are in perfect condition...  The next morning, you wake up and find that someone or something has mashed down huge patches of the wheat in the form of circles!  How weird would that be?  And we're not talking small circles here -- these things are big!  They sometimes cover an area of 200,000 square feet!   

Some think that crop circles date way back to the 1600's or even earlier, way back to when people were doing cave drawings.  But, the modern crop circles we usually see on those cable science channels probably started back in the early 1900's.  They seem to mostly happen in England, but they've popped up all over the world.  No matter how they got started, crop circles are really getting a lot of interest lately.  There are even groups of artists who freely take credit for creating them...  Others are thought to have done them, but will never admit it.  Part of the fun, I think, is the mystery of wondering who made them... and how they made them so fast!  They always happen sometime in the middle of the night...  The next morning, they are there -- completely finished!

You can even make your own crop circles...  All you need is some rope and a short board to press the grain down.  I'll let you figure out exactly how you'd need to go about it, but you better not try it somewhere without asking permission or you're going to get some farmer really mad at you.

Here are some pictures of real crop circles.  All happened in England in the last ten years.  As you can see, crop circle artists (whoever they may be) are getting pretty elaborate...  These aren't just crop CIRCLES:

crop circle photo crop circle photo crop circle photo crop circle photo
crop circle photo crop circle photo crop circle photo crop circle photo
crop circle photo crop circle photo
Crop circle photography by Lucy Pringle

When I saw these, I thought it would be cool to try to draw some with my art program...  The following are all taken from photos of REAL crop circles.

For all of my drawings, the yellow areas are the parts that are mashed down!

Here are some pretty simple crop circles.  Do you see how these could be made if you had two people, some rope and a board to mash the wheat down?

crop circle graphic
One person would stand in the middle (holding the rope) while the other
walked and mashed.  You'd just
change the length of the rope to make
the different circles.
crop circle graphic
You'd need to map out the triangle first...  Say you had three people...
How would you do it?
Would you need four people?
Remember that you can't leave any evidence (like holes in the ground)!
crop circle graphic
This one must have been designed by
girl extraterrestrials! 
crop circle graphic
How many circles do you see on
 this one? 
This crop circle was 300 feet wide!
crop circle graphic crop circle graphic
crop circle graphic

Here are some crop circles that were made out of hexagons and triangles.  They were pretty easy to make on my art program, but I don't know how the heck you'd make them out in a field in the pitch dark of night!  Can you figure it out?

crop circle graphic crop circle graphic

The next group of crop circles are a lot more complicated...  The first two weren't too bad for me to figure out how to make, but the third one...  Man, that thing was a beast!  I was pretty proud of myself for piecing it together!  I'm putting my geometry frame next to each so you can see how I started my drawings:

crop circle graphic crop circle graphic
crop circle graphic crop circle graphic
crop circle graphic crop circle graphic
crop circle graphic crop circle graphic
crop circle graphic crop circle graphic

Wow!  Can you believe "someone" actually made these things in a wheat field?

What crop circle design would you make?

 

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