1. How Did Eratosthenes Determine the Circumference of the Earth? 1 2 3 4 5 6 Next 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 These materials are © 2005 NAME, SCHOOL, all rights reserved. 1 2 3 4 5 6 Next 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. 1 2 3 4 5 6 Next 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. 1 2 3 4 5 6 Next 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. These materials are © 2005 NAME, SCHOOL, all rights reserved. 1 2 3 4 5 6 Next 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. 1 2 3 4 5 6 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.