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6. In fact, Eratosthenes didn't compute the radius of the Earth but its circumference. He used the following proportion: 5,000 stadia 360 - circumference (Hie cromutiplydivide Compute the circumference, C, in stadia, and convert your result to km. C= km. 7. Compare to the accepted value of the circumference of the Eanth, using Caupiad =2 * Ra with Rea6378.1 km. km. Find the % aror. % error

6. In fact, Eratosthenes didn't compute the radius of the Earth but its circumference. He used the following proportion: 5,000 stadia 360 - circumference (Hie cromutiplydivide Compute the circumference, C, in stadia, and convert your result to km. C= km. 7. Compare to the accepted value of the circumference of the Eanth, using Caupiad =2 * Ra with Rea6378.1 km. km. Find the % aror. % error

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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6. In fact, Eratosthenes didn't compute the radius of the Earth but its cireumference. He used the following proportion: 7° 5,000 stadia 360° circumference (Hint cros-mukiply-divide) Compute the circumference, C, in stadia, and convert your result to km. km. 7. Compare to the accepted value of the circumference of the Earth, using Caoptol =2 n REath with Rath =6378.1 km. km. Find the % error. % eror
Transcribed Image Text:6. In fact, Eratosthenes didn't compute the radius of the Earth but its cireumference. He used the following proportion: 7° 5,000 stadia 360° circumference (Hint cros-mukiply-divide) Compute the circumference, C, in stadia, and convert your result to km. km. 7. Compare to the accepted value of the circumference of the Earth, using Caoptol =2 n REath with Rath =6378.1 km. km. Find the % error. % eror
BACKGROUND An ingenious solution to the Earth's circumference occured in 230 BC. Eratosthenes, a Greek geographer, mathematician, music theorist, poet, astronomer, and philosopher, was reading in the Library of Alexandria when he noticed an account for a deep well near Syene (now Aswan), some distance to the south (800 km) in which at high noon on the longest day of the year the bottom of the well was fully illuminated by the Sun. Eratosthenes exclaimed "Ah-ah!" (or something like that), "I can solve for the circumference of the Earth!". In his mind's eye, Eratosthenes could see that at Syene, at the moment when the bottom of the well was fully lit, the Sun must have been at the Zenith (directly overhead). Yet he knew that at the same moment in Alexandria vertical objects (like a tower, pole) cast shadows. Here is the experiment perfomed by Eratosthenes (see the picture below). • He erected a vertical pole at Alexandria (A) and measured the angle of its shadow at the moment when the well at Syene (S) was fully illuminated; • The angle of the pole equaled the angle formed by the points Alexandria (A), Earth's center (C), and Syene (S). That angle proved to be approximately a = 7°. • The distance between Syene and Alexandria is 5,000 stadia (the units of measure at the time). I stadia = 157.5 m=0.1575 km. Figure 1. The measure of Earth's circumference is based on the assumption that Syene is on the Tropic of Cancer and the same meridian as Alexandria. The image is adapted from a similar image prepared by Gico (Wikimedia).
Transcribed Image Text:BACKGROUND An ingenious solution to the Earth's circumference occured in 230 BC. Eratosthenes, a Greek geographer, mathematician, music theorist, poet, astronomer, and philosopher, was reading in the Library of Alexandria when he noticed an account for a deep well near Syene (now Aswan), some distance to the south (800 km) in which at high noon on the longest day of the year the bottom of the well was fully illuminated by the Sun. Eratosthenes exclaimed "Ah-ah!" (or something like that), "I can solve for the circumference of the Earth!". In his mind's eye, Eratosthenes could see that at Syene, at the moment when the bottom of the well was fully lit, the Sun must have been at the Zenith (directly overhead). Yet he knew that at the same moment in Alexandria vertical objects (like a tower, pole) cast shadows. Here is the experiment perfomed by Eratosthenes (see the picture below). • He erected a vertical pole at Alexandria (A) and measured the angle of its shadow at the moment when the well at Syene (S) was fully illuminated; • The angle of the pole equaled the angle formed by the points Alexandria (A), Earth's center (C), and Syene (S). That angle proved to be approximately a = 7°. • The distance between Syene and Alexandria is 5,000 stadia (the units of measure at the time). I stadia = 157.5 m=0.1575 km. Figure 1. The measure of Earth's circumference is based on the assumption that Syene is on the Tropic of Cancer and the same meridian as Alexandria. The image is adapted from a similar image prepared by Gico (Wikimedia).
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