Surveying and GeometryYolli Luna/Geometry TeacherTom Williams/Construction Technology

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”

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?

Rope-Stretchers and Pythagoras

• Pythagoras travelled to Egypt• Provided a formal proof of this method• Method became known as the Pythagorean

Theorem

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         

Indirect Measurement and Surveying

h

wf

d

A

C E

D

B

observer

Ground level

Eye level

• Measure tall objects• Use right triangles• Use simple tools

Mirror

Project #1 - Making a Clinometer

• Surveying tool• Measures angles• Materials: protractor, straw, string, paper

clips

Project #2 - Using Small Mirrors

• Angle of Incidence = Angle of Reflection• Similar Right Triangles• Proportions

h

wf

d

A

C E

D

B

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)