Crop Circles

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Crop Circles

• Be able to use a pair of compasses to make an
  accurate construction

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What is a crop circle?

• Crop circles are patterns created by the
  flattening of crops such as wheat, barley, rye,
  or corn. The term crop circle entered the Oxford
  Dictionary in 1990.
• Self-described pranksters Doug Bower and Dave
  Chorley claimed to have started the crop circle
  phenomenon in 1978. Their work is continued by
  other groups of crop circle makers such as the
  circle-makers arts collective founded by John
  Lundberg in the early 1990s.
• Source Wikki

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What is a crop circle?

• It has been claimed that evidence suggesting
  these formations are caused by some force other
  than humans is found in hundreds of photographs
  of bent or warped growth nodes. While it has been
  suggested that ball lightning and vortices in the
  wind might rarely produce isolated indentations
  in crops, neither is capable of the complex and
  often delicate patterns seen in more elaborate
  crop circles.

Source Wikki
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• How Do You Make a Crop Circle?
• Crop circles appear to be very intricate
  formations, with many geometric shapes linked in
  sophisticated patterns. But the basics of
  crop-circle creation and the tools involved are
  actually fairly simple.
• In general, circlemakers follow the following
  steps
• Choose a location.
• Create a diagram of the design (although some
  circlemakers decide to come up with an idea
  spontaneously when they arrive at their intended
  site).
• Once they arrive at the field, they use ropes and
  poles to measure out the circle.
• One circlemaker stands in the middle of the
  proposed circle and turns on one foot while
  pushing the crop down with the other foot to make
  a center.
• The team makes the radius of the circle using a
  long piece of rope tied at both ends to an
  approximately 4-foot-long (1.2-meter) board
  called a stalk stomper (a garden roller can also
  be used). One member of the team stands at the
  center of the circle while the other walks around
  the edge of the circle, putting one foot in the
  middle of the board to stomp down the circle's
  outline.

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A Math Forum Web UnitSuzanne Alejandre's
Designs With Circles
In the Islamic culture the circle is a unit of
measure. The circle is the basis for the
organization of space. It is a starting point in
architecture, poetry, music and even calligraphy.
From a circle it is possible to construct many
regular polygons. The decimal system we use did
not appear as a standard until the eighth century
A.D. Before exact units of measurement were used,
the scale from one building's plan was used to
create another building by referring to the
geometric patterns. Egyptian rope-stretchers and
temple surveyors developed a reproducible method
by using pegs and cords to trace circles and
straight lines on sand. They established
geometric procedures for generating precise and
accurate constructions. Perfect
interrelationships between the parts and the
whole of the composition were attained
irrespective of mode, form, or scale of
expression. A universality was achieved in the
Islamic world, consistent with the Islamic belief
that all creations are harmoniously interrelated.

• Draw a circle with a compass.

• Without changing the opening (radius) on the
  compass, draw another circle whose center is on
  the rim of the first circle.

• If you connect the centers and one of the points
  where the circles cross, you get an equilateral
  triangle.
• Why do all the sides have the same length?

• Again without changing the radius, draw another
  circle whose center is one of the intersection
  points.

• Keep drawing new circles at the new intersection
  points.

• Does this design have rotation symmetry? By what
  angles? Does this design have reflection
  symmetry? Across what lines?
• Keep drawing more circles at the intersection
  points until you have a pattern that covers most
  of the page.

• What kinds of symmetry does this pattern have,
  assuming it goes on forever?
• Can you find the pattern of triangles in the
  circle pattern? You will have to imagine or draw
  in the lines.

• How Do You Make a Crop Circle?
• Crop circles appear to be very intricate
  formations, with many geometric shapes linked in
  sophisticated patterns. But the basics of
  crop-circle creation and the tools involved are
  actually fairly simple.
• In general, circlemakers follow the following
  steps
• Choose a location.
• Create a diagram of the design (although some
  circlemakers decide to come up with an idea
  spontaneously when they arrive at their intended
  site).
• Once they arrive at the field, they use ropes and
  poles to measure out the circle.
• One circlemaker stands in the middle of the
  proposed circle and turns on one foot while
  pushing the crop down with the other foot to make
  a center.
• The team makes the radius of the circle using a
  long piece of rope tied at both ends to an
  approximately 4-foot-long (1.2-meter) board
  called a stalk stomper (a garden roller can also
  be used). One member of the team stands at the
  center of the circle while the other walks around
  the edge of the circle, putting one foot in the
  middle of the board to stomp down the circle's
  outline.

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A Math Forum Web UnitSuzanne Alejandre's
Designs With Circles
In the Islamic culture the circle is a unit of
measure. The circle is the basis for the
organization of space. It is a starting point in
architecture, poetry, music and even calligraphy.
From a circle it is possible to construct many
regular polygons. The decimal system we use did
not appear as a standard until the eighth century
A.D. Before exact units of measurement were used,
the scale from one building's plan was used to
create another building by referring to the
geometric patterns. Egyptian rope-stretchers and
temple surveyors developed a reproducible method
by using pegs and cords to trace circles and
straight lines on sand. They established
geometric procedures for generating precise and
accurate constructions. Perfect
interrelationships between the parts and the
whole of the composition were attained
irrespective of mode, form, or scale of
expression. A universality was achieved in the
Islamic world, consistent with the Islamic belief
that all creations are harmoniously interrelated.

• Draw a circle with a compass.

• Without changing the opening (radius) on the
  compass, draw another circle whose center is on
  the rim of the first circle.

• If you connect the centers and one of the points
  where the circles cross, you get an equilateral
  triangle.
• Why do all the sides have the same length?

• Again without changing the radius, draw another
  circle whose center is one of the intersection
  points.

• Keep drawing new circles at the new intersection
  points.

• Does this design have rotation symmetry? By what
  angles? Does this design have reflection
  symmetry? Across what lines?
• Keep drawing more circles at the intersection
  points until you have a pattern that covers most
  of the page.

• What kinds of symmetry does this pattern have,
  assuming it goes on forever?
• Can you find the pattern of triangles in the
  circle pattern? You will have to imagine or draw
  in the lines.

• How Do You Make a Crop Circle?
• Crop circles appear to be very intricate
  formations, with many geometric shapes linked in
  sophisticated patterns. But the basics of
  crop-circle creation and the tools involved are
  actually fairly simple.
• In general, circlemakers follow the following
  steps
• Choose a location.
• Create a diagram of the design (although some
  circlemakers decide to come up with an idea
  spontaneously when they arrive at their intended
  site).
• Once they arrive at the field, they use ropes and
  poles to measure out the circle.
• One circlemaker stands in the middle of the
  proposed circle and turns on one foot while
  pushing the crop down with the other foot to make
  a center.
• The team makes the radius of the circle using a
  long piece of rope tied at both ends to an
  approximately 4-foot-long (1.2-meter) board
  called a stalk stomper (a garden roller can also
  be used). One member of the team stands at the
  center of the circle while the other walks around
  the edge of the circle, putting one foot in the
  middle of the board to stomp down the circle's
  outline.

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Your challenge

• Top Teacher Tips for great constructions
• 1. Keep the pencil sharp.
• 2. Use a short pencil
• 3. Once you have set the radius, only handle the
  plastic parts of the compass
• If you are struggling, hold the compass still and
  turn the paper.

Assuming that the circles are man-made, the
artists only use rope to make the circles and
planks to flatten the grain. You can use a pair
of compasses to create a crop circle on
paper. Im looking to excellent circles and
arcs, accuracy and display quality work.
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Plenary you decide!