Transcript Eratosthenes

1. How Did Eratosthenes
Determine the Circumference of
the Earth?
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Eratosthenes was a Greek
mathematician from 276 BC - 194 BC
and is credited for being the first
person in history to determine the
circumference of the Earth. His
calculations were made during a time
when the spherical model of the Earth
was not widely accepted. Quite a
feat.
From what you have already learned
about angle relationships of two lines
cut by a transversal and what you
know about circles, try and determine
how Erastothenes was able to
determine the circumference of the
Earth.
http://www.malaspina.com/jpg/eratosthenes.jpg
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2. Information Sources
Biographical Sites
1)
Eratostenes #1
2) Ertosthenes
#2
Eratosthenes and the story of Cyrene
1) Cyrene #1
2) Cyrene #2
The sites listed here tell about Eratosthenes
and how he determined the circumference of
the Earth from a historical perspective, but
not a geometric perspective. Your job is to
explain the historical event from a geometric
perspective.
http://www.mlahanas.de/Greeks/images/eratosthenes3.gif
http://www.mlahanas.de/Greeks/images/eratosthenes3.gif
These materials are © 2005 NAME, SCHOOL, all rights reserved.
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3. The Activity
You are to write a narrative description that
explains how Eratosthenes was able to determine
the circumference of the Earth and include all the
elements listed.
1. What angle relationships are mandatory to know?
Angle
Relationships
Required
Angle Relationships
2. What circle characteristics are mandatory to
know?
Circle
Characteristics
Required
Other
Thoughts
Circle Characteristics
Eratosthenes
3. Historical Background
Who was Eratosthenes and what other disciplines
(other than math) was he know for?
4. What type of labor would be required? Is
precision important and why? How could you get
the most precise measurements?
5. From the perspective of geometric concepts,
explain how Eratosthenes was able to determine
the circumference of the Earth.
Labor
Required
Historical
Background
How Did He
Do It?
6. What are your thoughts? Do you find his
epiphany impressive and/or relevant? Why or
why not?
These materials are © 2005 NAME, SCHOOL, all rights reserved.
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4. The Assessment Activity
The writing activity will largely be assessed based on the accuracy
of the geometric explanation of the events of Cyrene around 240
BC. Of course, a recap of the event that have been read about is an
important element as well. Because geometry and indeed math in
general is a visual discipline, a visual representation will also be
required. Students must cite specific theorems and/or postulates
that apply.
In addition, students must explain why this
event was relevant and such an amazing
feat.
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5. Enrichment Activity
The following site is an
excellent source from one of
the great storytellers of all
time. Watch the video clip
depicting Carl Sagan’s
rendition of the story of
Eratosthenes. The visual
modeling in this clip should be
useful and can be used as a
source for your paper.
•
Carl Sagan Video Clip From the Series
Cosmos on Eratosthenes (Crazy Brilliant!!!)
http://upload.wikimedia.org/wikipedia/commons/thumb/5/50/Eratosthenes.bjb.svg/400px-Eratosthenes.bjb.svg.png
These materials are © 2005 NAME, SCHOOL, all rights reserved.
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6. Teacher Support Materials
California Geometry Standards
7.0 Students prove and use theorems involving
the properties of parallel lines cut by a
transversal, the properties of quadrilaterals, and
the properties of circles.
8.0 Students know, derive, and solve problems
involving the perimeter, circumference, area,
volume, lateral area, and surface area of
common geometric figures.
The goal of the lesson is for
students to see a real life example
from an historical perspective of
how having a knowledge of angle
relationships can be profound.
The ubiquitous question in math is
“Why do we have to know this?”
Real world examples that make
the curriculum relevant often
create bridges for student
comprehension.
These materials are © 2005 NAME, SCHOOL, all rights reserved.