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Midpoints and Segment Bisectors

Midpoints and bisectors can be used to find the halfway mark between two coordinates.

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Midpoint And Segment Bisectors
Teacher Contributed

RWA Midpoint and Segment Bisectors

Topic

Geometry in Treasure Hunting

Vocabulary

  • midpoint
  • segment bisector

Student Exploration

Can you use Geometry to find a buried treasure?

In 1948, George Gamow wrote a book called One, Two, Three, ... Infinity. In it, he presents a problem suggested by a treasure map found in a grandfather's attic. The map shows a desert island with a gallows, an Elm tree, and an Oak tree. One is to begin at the gallows and walk to the Oak tree, counting paces. Then turn right 90 degrees and walk from the Oak tree the same number of paces. There one drives a spike. Returning to the gallows, the same procedure is followed in walking to the Elm tree, but turn left 90 degrees and after walking the number of paces as from the gallows to the Elm, drive a second spike. The treasure is buried at the midpoint of a string stretched between the two spikes.

Of course, when the treasure hunters go to the island, they found that the gallows was no longer there and not being mathematicians they randomly dug around the island without finding the treasure.

Extension Investigation

  1. Island Treasure Activity - http://jwilson.coe.uga.edu/emt725/Treasure/Treasure.html
  2. Taxicab Geometry - http://www.learner.org/teacherslab/math/geometry/shape/taxicab/
  3. Treasure Hunt Activity – See Attached Go hear for more information http://www.doralacademyprep.org/ourpages/auto/2012/3/28/63702641/Geometry%20Teacher_s%20Implementation%20Guide%20Chapter%209.pdf

Layering (optional)

Further Exploration of Geometry and treasure hinting.

Oak Island Treasure

“The Oak Island Money Pit is the site of the world's longest running hunt for lost treasure, and the hunt is on again!” Read more at http://www.oakislandtreasure.co.uk/component/option,com_frontpage/Itemid,1/

“Here are two of John Coleman's maps showing the strange geometry he has discovered by mapping every location with the word "cross" in the title, with amazing results. You can read more about his discoveries.”

http://www.oakislandtreasure.co.uk/content/view/346/215/

Resources Cited

http://www.doralacademyprep.org/ourpages/auto/2012/3/28/63702641/Geometry%20Teacher_s%20Implementation%20Guide%20Chapter%209.pdf

http://www.oakislandtreasure.co.uk/content/view/346/215/

http://www.oakislandtreasure.co.uk/component/option,com_frontpage/Itemid,1/

http://www.learner.org/teacherslab/math/geometry/shape/taxicab/

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