Circles Definition and 307 Threads

Crop Circles We all know that many to most circles are hoaxed. It is my understanding that beyond any doubt, this phenomenon predates modern reports by at least decades. Some years ago I watched a Nova or similar that discussed this subject purely in meteorological terms. It was shown that...

http://www.newsnet5.com/news/2524748/detail.html

I'm thinking Hall of Fame? http://www.paratexas.com/Vacantlotcircles.htm

Why does a circles angles equal up to 2pi? Wouldn't it be 1pi? Please help. My geometry teacher (last year - and now he's gone) drew a circle for me and defined all the points in terms of pi (is there an ASCII character for pi, by-the-way, on the keyboard?). Where the 90 degree point would be...

"HOWELL TOWNSHIP -- They've come late at night, holding flashlights, their beams cutting the dark in the middle of 1,000 acres of wheat fields. They've come in the afternoon under blue sky to lift their arms and pray." http://www.freep.com/news/mich/signs5_20030805.htm

""The holes appeared and there it was but you couldn't see what made it, but I seen it right when it happened," farm owner Arthur Rantala said." http://www.themilwaukeechannel.com/news/2342726/detail.html

In general, |z - zo|=r, where z_o is a fixed point and r is a positive number, represents a circle centered at z_o and with radius r. |z - z1|=k|z - z2|, where z_1 and z_2 are fixed points, also apparently represents a circle, except maybe in the case where k=1. Then we have a line, or a...