Challenges from Ancient Greece

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Challenges from Ancient Greece
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Geometry

• Born in Ancient Greece
• Mathematics was thought to be embedded
• in everything from music to art to the governing
  of the universe.

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Plato

• Let no man ignorant of geometry enter here.
• The study of shapes and logic.

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Euclid

• Greek mathematician
• The Father of Geometry
• His work Elements is the most successful textbook
  in the history of mathematics.

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Unit EQ

• Does the construction of accurate geometric
  shapes require the use of measurement?
• Can accurate geometric constructions be performed
  using simple tools without any reference to
  measurement?
• Think-Pair-Share

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Challenge

• Construct geometric objects using two simple
  tools (Euclidean tools)
• A straight edge without any markings (lines)
• A compass (circles)

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Can you construct a target?

• Construct 3 circles.
• The largest circle should have a radius 3 times
  the length of the radius of the smallest circle.
• The middle circle should have a radius 2 times
  the length of the radius of the smallest circle.

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Teach it

• Now that you have constructed a target with a
  straight edge and a compass, write a set of
  instructions that another student could use to
  create your target.

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Can you

• construct a square?
• construct a regular pentagon?
• bisect an angle?

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What am I going to learn?

• Guiding EQs
• How do I use basic tools to create geometric
  shapes?
• Why is the definition of a circle a foundation
  for geometric constructions?
• In what ways can I use congruent triangles to
  justify many geometric constructions?
• What steps do I use to copy a line segment?
• What steps do I use to copy an angle?
• What steps do I use to bisect a line segment?
• What steps do I use to bisect an angle?
• What steps do I use to construct perpendicular
  lines, including the perpendicular bisector of a
  line segment?
• What steps do I use to construct a line parallel
  to a given line through a point not on the line?

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Constructions for Dummies

• You will be creating
• a handy resource
• for performing basic
• constructions.

CONSTRUCTIONS
Hi
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Where in the world is Carman Sandiego?

• You will perform
• basic constructions
• to find the elusive
• jewelry thief
• Carman Sandiego.