Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 10

How did Eratosthenes use Sun angles to figure out that the 5000 -stadia distance between Alexandria and Syene was \(1 / 50\) of Earth's circumference? Once he knew this fraction of Earth's circumference, how did he calculate the entirety of Earth's circumference?

Short Answer

Expert verified
Eratosthenes used geometric principles and the angle of the sun at the summer solstice to deduce that the Earth's circumference was 250,000 stadia.

Step by step solution

01

Identify the Method Used

Eratosthenes used geometric principles to deduce the size of the Earth. He knew that at noon on the summer solstice, the sun was directly overhead in the city of Syene (casting no shadow), but at the same time in Alexandria, the sun was at an angle of approximately 7.2 degrees from the zenith, casting a shadow. These places were known to be roughly 5000 stadia apart.
02

Constructing Similar Triangles

Next, two right-angled triangles can be constructed, with one vertex at the center of the Earth, and the long side from the center of the Earth to the respective town (Syene and Alexandria). The angle at the peak of both right triangles is equivalent to the angle that sunlight makes with the vertical direction at the given town. Since one angle of two right-angled triangle is the same, they are similar triangles, meaning that the ratios of their corresponding sides are identical.
03

Determine Earth's Fraction with Respect to Stadia

On the summer solstice, the precise calculation of the sun's angle at noon in Alexandria and Syene would yield an angle of around 7.2 degrees, which is \(1/50\) of a full circle. Therefore, the distance between Syene and Alexandria, 5000 stadia, is \(1 / 50\) of the Earth's circumference.
04

Calculating the entire Circumference of the Earth

After he had calculated this fraction of the Earth's circumference, Eratosthenes could easily compute the entirety of Earth's circumference by multiplying by the reciprocal of the fraction. The total circumference of the Earth is then calculated as the product of 50 and the measured distance in stadia, which comes to 250,000 stadia.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Define systems theory as an organizational strategy. What are open systems, closed systems, and negative feedback? When is a system in a steady-state equilibrium condition? What type of system (open or closed) is the human body? A lake? A wheat plant?

Assess your geographic literacy by examining atlases and maps. What types of maps have you used: Political? Physical? Topographic? Do you know what map projections they employed? Do you know the names and locations of the four oceans, seven continents, and most individual countries? Can you identify the new countries that have emerged since 1990 ?

Define cartography. Explain why it is an integrative discipline.

What are the three abiotic (nonliving) spheres that make up Earth's environment? Relate these to the biotic (living) sphere: the biosphere.

State whether the following ratios are large scale, medium scale, or small scale: \(1: 3,168,000 ; 1: 24,000 ; 1: 250,000\).
See all solutions

Recommended explanations on Geography Textbooks

Coasts Geography

Read Explanation

Water Cycle

Read Explanation

Global Resource Management

Read Explanation

Living With The Physical Environment

Read Explanation

Living World

Read Explanation

Globalisation

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free