Introduction

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Words and concepts relating to circles: Centre, radius, diameter, circumference, Pi, area, semi-circle, concentric circles, sphere, cylinder, ellipse, hyperbola, parabola

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  • Real Life Examples of Circles
How many circles can you see? external image Supermarket%20-%20by%20Flickr%20user%20fazen.jpg
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This is the Moon. During its full moon phase, it appears as a circle in the sky. If a dot is placed in the center of this circle, the edge of the moon at any point is equidistant from the center point.
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This picture of gears is a good example of the circle conic. The equation for a conic circle is (x-h)+(y-k)=r2. What more is there to say? The gears intersect in order to keep spinning.
external image slinky.jpgThe slinky is a perfect example of one of the conic sections; the parabola, and a good example of another; the circle. Since it can be picked up and moved, the slinky can represent all the directions that the parabola can take. This means that the slinky represents the equations (x-h)2=4p(y-k), (x-h)2=-4p(y-k), (y-k)2=4p(x-h), and (y-k)2=-4p(x-h). In addition, the slinky can somewhat represent the fact that parabolas can go on forever on a grid by being stretched out. Meanwhile, the slinky’s rings can somewhat represent the circle. Although the rings never connect, the fact that the rings repeat make it look like it’s made out of a bunch of circles. All I can really say now is that the circle formula is (x-h)+(y-k)=r2.

external image mickeymouse.jpgHmm…. wonder who this is. Yes, it’s Mickey Mouse! Mickey’s ears are circles which are conic sections. The equation is (x-h)+(y-k)=r2 for a circle. What’s interesting is that Mickey’s ears are always circles no matter where the camera is. Weird huh?
external image smile.jpgexternal image satellite-dish_web.jpgexternal image conic.jpgAny cylinder sliced on an angle will reveal an ellipse in cross-section
1. This is a picture of Tycho Brahe Planetarium in Copenhagen. This cylindrical building was designed bye the Danish architect Knud Munk. This Planetarium is on of the largest of its kind in Europe. It was opened in 1989. The theater screen in 75 ft and the theater seasts 275 people. There is even a gift shop and restaurant inside of it.
The equation for this ellipse would be (x-h)2/a2+ (y-k)2/b2=1
external image image.pngObviously, the movement of the planets has to do with the fact that the orbit is elliptical. This relates to the concept of eccentricity (measure of the ovalness), which can be used to measure how skewed the orbit is from being circular.
external image atom.jpgIn Chemistry, circles are everywhere, from the shapes of the electons and protons and nukleus, to the paths the electrons follow around the nukeus.
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  • Concentric circles: Circles with the same centre but different radiiexternal image ConcentricCircle.jpg external image img_08491.jpgexternal image 2764378654_24d8d91411.jpgexternal image cd.gifexternal image getimage.asp?table=inv&field=image2&keyname=invky&keyvalue=7112389external image 16217524_e6752b7e52_m.jpgexternal image circles-citiesxl.jpg external image 800px-US_38_Star_Flag_concentric_circles.svg.pngexternal image concentricCircles.jpgexternal image 828522-001.jpg?v=1&c=IWSAsset&k=2&d=F5B5107058D53DF53A745FC6524146EB176CAFC3C2860A7717048042DA450F05E30A760B0D811297external image spider-web.jpgexternal image patchwork_circles_08.jpgexternal image dartboard.jpegexternal image q-photo-road-sign-no-cycling.jpg

  • Crop Circlesexternal image google-logo-Pacific.jpg
Google, UFO's and Crop Circles:




On the 15th of September 2009, Google put a graphic of a crop circle out on their main page. This has led to speculation on Googles twitter account regarding certain coordinates and other UFO information which happens in different places on the planet.



Some other interesting crop circles: external image cc001-1.jpgexternal image cc001-4.jpgexternal image cc001-5.jpgexternal image cc001-6.jpgexternal image cc001-7.jpgexternal image cc001-8.jpgexternal image cc001-9.jpgexternal image cc001-10.jpgexternal image cc001-11.jpgexternal image cc001-12.jpgexternal image cc001-13.jpgexternal image cc001-14.jpgexternal image cc001-15.jpgexternal image cc001-16.jpgexternal image cc001-17.jpgexternal image cc001-18.jpgexternal image cc001-19.jpgexternal image cc001-20.jpgexternal image cc001-0.jpgexternal image cc001-2.jpgexternal image cc001-3.jpgexternal image cc001-4.jpgexternal image julia.jpg
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Crop Circles and Infinity, Crop Circles and the Mobius Strip: external image 2008-d.jpgexternal image 2008-d.gifexternal image 2008-e.jpgexternal image 2008-f.jpgexternal image 2008-g.gif



Question: Do these last few crop circles look like the Mobius Strip? Here is the Mobius strip:external image mieren.jpg
If you follow the ants in their tracks, you will see that they can continue walking endlessly without crossing over one of the strip's edges; yet they walk over the strip's entire surface. Even though the strip exists of only one dimension (with only one side and one edge), it can only exist in 3 dimensions. The Möbius Strip not only symbolises endless movement (you recognise the infinity symbol), it also represents the transcending of dimensions and - thereby - the exposure of the Illusion in which we (think we) live.


The theme of infinity (of energy? of the soul?) reappeared on August 8 (8-8-8) in the gigantic formation at the foot of Milk Hill, Alton Barnes:



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[[@http://www.cropcirclesandmore.com/geometries/geometries.html ]]
  • Mayan Calendar: external image bertjanssen-maya0.jpg
  • Earth external image earthsolstice.jpg

  • Create your own Mandala

http://www.princetonol.com/groups/iad/lessons/middle/Larry-radial.htm
  • Create your own Dart Board: Working with degrees in circles
  • Create your own circle designs: Try and create some of these designs (on the worksheet). You may want to cut out some of the white bits, and cover them with see through celophane to create a stained glass (or lead light) effect. Worksheet:
  • Radius, Diameter, Circumference, Pi

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  • Area of a circle