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Problem 1. Suppose you are a two-dimensional being, living on a sphere of radius R. 1. Show that if you draw a circle of radius r, the circle's circumference will be C = 2T Rsin(r/R) (2.1) 2. Idealize the Earth as a perfect sphere of radius R = 6371 km. If you could measure distances with an error of ±1 meter, how large a circle would you have to draw on the Earth's surface to convince yourself that the Earth is spherical rather than flat?

Problem 1. Suppose you are a two-dimensional being, living on a sphere of radius R. 1. Show that if you draw a circle of radius r, the circle's circumference will be C = 2T Rsin(r/R) (2.1) 2. Idealize the Earth as a perfect sphere of radius R = 6371 km. If you could measure distances with an error of ±1 meter, how large a circle would you have to draw on the Earth's surface to convince yourself that the Earth is spherical rather than flat?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 1. Suppose you are a two-dimensional being, living on a sphere of radius R. 1. Show that if you draw a circle of radius r, the circle's circumference will be C = 2T Rsin(r/R) (2.1) 2. Idealize the Earth as a perfect sphere of radius R = 6371 km. If you could measure distances with an error of ±1 meter, how large a circle would you have to draw on the Earth's surface to convince yourself that the Earth is spherical rather than flat?
Transcribed Image Text:Problem 1. Suppose you are a two-dimensional being, living on a sphere of radius R. 1. Show that if you draw a circle of radius r, the circle's circumference will be C = 2T Rsin(r/R) (2.1) 2. Idealize the Earth as a perfect sphere of radius R = 6371 km. If you could measure distances with an error of ±1 meter, how large a circle would you have to draw on the Earth's surface to convince yourself that the Earth is spherical rather than flat?
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