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Surveying and GeometryYolli Luna/Geometry TeacherTom Williams/Construction Technology
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The First Surveyors
• Every year, the flooding of the Nile destroyed property boundaries
• Boundaries were re-drawn annually by the Egyptian “rope-stretchers”
• Rope-stretchers were surveyors • Geometry means “Earth measure”
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Pretend You’re a Rope-Stretcher
• Rope with 12 equally spaced knots• Lay out a right triangle• How accurate is your work?• Find other combinations that form right
triangles• What are these number combinations called?
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Rope-Stretchers and Pythagoras
• Pythagoras travelled to Egypt• Provided a formal proof of this method• Method became known as the Pythagorean
Theorem
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Classic Pythagorean Problems
The Pythagorean Theorem can be used to determine the distance from
the home plate to first base.
24 ft
32 ft
? ft
How far up a wall will an 11m ladder reach, if the foot of the
ladder must be 4m from the base of the wall?
The ladder will reach 10.2 meters up the wall.
112 = x2 + 42 121 = x2 + 16 121- 6 = x2 105 = x2 10.2 = x
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Indirect Measurement and Surveying
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Ground level
Eye level
• Measure tall objects• Use right triangles• Use simple tools
Mirror
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Project #1 - Making a Clinometer
• Surveying tool• Measures angles• Materials: protractor, straw, string, paper
clips
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Project #2 - Using Small Mirrors
• Angle of Incidence = Angle of Reflection• Similar Right Triangles• Proportions
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What’s Next?
• Surveyors Challenge (students compete with other high school students)
• The Noon Day Project (students around the world gather data to measure the circumference of the Earth)