Title of Book: the Librarian Who Measured the Earth

Title of Book: The Librarian Who Measured the Earth

Author: Kathryn Lasky

Publisher: Little, Brown, & Co.

ISBN: 0-316-51526-4

Grade Levels for Recommended Use: 8

New TEKS:

(5)Proportionality. The student applies mathematical process standards to use geometry to describe or solve problems involving proportional relationships. The student is expected to:

(A)generalize the critical attributes of similarity, including ratios within and between similar shapes;

(B)describe π as the ratio of the circumference of a circle to its diameter

9)Expressions, equations, and relationships. The student applies mathematical process standards to solve geometric problems. The student is expected to:

(B)determine the circumference and area of circles

Brief Summary: Beautifully illustrated by Kevin Hawkes, this book by the prolific, award-winning author Kathryn Lasky, tells the story of incredibly bright and inquisitive Eratosthenes. From his birth over two thousand years ago in northern Africa (modern Libya) to his work as the chief librarian at the great library of Alexandria in ancient Egypt, the biography combines history, science and mathematics as Eratosthenes makes discoveries, solves problems, and eventually writes the first geography book. But most important of all, through brilliant math reasoning skill, Eratosthenes measures Earth’s circumference accurately (within 200 miles of today’s measurement)!

Materials needed: worksheet or math journal; pencils; protractors; rulers; tape measures or strips of paper or string; round fruit or foam spheres, a whole and a half (cross-section) for each pair/group of students.

Suggested Activity:

•Read the book to the class prior to beginning geometry activity.

•With Eratosthenes as inspiration, students will measure and calculate circumference, radius, diameter, arcs and angles. Radius can be related to the well at Syrene in the book.

•Discuss and review geometry terms with students, then ask them if they know how to find the radius and diameter of the earth using Eratosthenes’ circumference measurement. Guide them to the correct formula, if needed, and introduce/review pi.

•Work a sample problem with them on the board or overhead using Eratosthenes’ measurement of the earth’s circumference to find radius. Next, have students measure and calculate the spheres at their work stations. Students may work in pairs or small groups.

Students will measure the circumference of the sphere using tape measure or string/paper strip, then perform the necessary calculations to find radii & diameters.
Students will have a half of a sphere, a cross-section with segments, like the grapefruit in the story. Students will sketch a segmented circle diagram based on their cross-section sphere in math journal or on worksheet. Have them shade one segment of the diagram and measure its (a) radius (one side of their segment) and (b) angle.
Ask students how to calculate the circumference based on these measurements. Remind them of Eratosthenes’ solution if they are having trouble. Ask them to write a ratio of their shaded segment to whole (for example, a circle has 360 degrees, and my segment’s angle is 24 degrees; therefore, the ratio is 24:360.)
Next they will solve an equation to find the measurement of the arc for their segment, then calculate circumference of the whole. Give them the formula for finding length of the arc and remind them, if necessary, how they found circumference in part one.
Finish by asking students to review the different ways circumference can be measured, and the relation of radii, diameter, arcs and angles to circumference of circles/spheres. Food for thought: Will they be able to recall and picture the grapefruit and Eratosthenes’ system to help them solve problems like this in the future?

Additional Resources for Teachers:

• (short 2 min. cartoon video about Eratosthenes measuring Earth)

• (Carl Sagan explains how Eratosthenes measured the earth - 6 1/2 min. video)

References:

(Diagrams & geometry help from “Math for Morons Like Us” on ThinkQuest)

Lesson activity by Emily Quant (2005), retrieved from (click on book title under “Trade Books” heading).

Adapted by Brandy Calhoun, 2012