Page

**2**

Slide 11

Eratosthenes reasoned that by I.29, the angle produced by the sun’s rays falling on the gnomon at Alexandria is equal to the angle between Syene and Alexandria at the centre of the Earth.

Slide 12

The angle at the gnomon, α, was 7°12’, therefore the angle at the centre of the Earth, β, was is also 7°12’ which is 1/50 of a complete circle.

Therefore the circumference of the Earth had to be stadia = 250,000 stadia.

7°12’ x 50 = 360°

50 x 5000 = 250,000

Slide 13

1. The Sun is very far away, so any light coming from it can be regarded as traveling in parallel lines.

2. The Earth is a perfect sphere.

3. A vertical shaft or a gnomon extended downwards will pass directly through the center of the Earth.

4. Alexandria is directly north of Syene, or close enough for these purposes.

Slide 14

Later Eratosthenes made a somewhat finer observation and calculation and concluded that the circumference was 252,000 stadia.

So, how good was his estimate.

It depends….

Slide 15

What, exactly, are stadia?

Stadia are long measures of length in ancient times.

A stade (singular of stadia) is the length of a stadium.

And that was…?

Slide 16

In Greece the typical stadium was 185 metres.

In Egypt, where Eratosthenes was, the stade unit was 157.5 metres.

Slide 17

Compared to the modern figure for polar circumference of 39,942 km, Eratosthenes was off by at worst 17% and at best by under 1%.

Slide 18

Eratosthenes showed that relatively simple mathematics was sufficient to determine answers to many of the perplexing questions about nature.

Slide 19

Hipparchus of Rhodes

Became a famous astronomer in Alexandria.

Around 150 BCE developed a new tool for measuring relative distances of the stars from each other by the visual angle between them.

Slide 20

- Euclid’s Elements at work
- Eratosthenes of Cyrene
- “Beta”
- Eratosthenes’ Map
- Using Euclid
- His data
- Calculating the size of the Earth
- Eratosthenes’ working assumptions
- A slight correction
- Stadium lengths
- Comparative figures
- An astounding achievement
- Hipparchus of Rhodes
- The Table of Chords
- Precession of the equinoxes
- The Problem of the Planets, again
- Claudius Ptolemy
- Ptolemy’s Geography
- The Almagest
- Euclid-like assumptions
- Plato versus Aristotle
- Ptolemy’s Universe
- The Ptolemaic system
- Epicycles and Deferents
- Accounting for Retrograde Motion
- Saving the Appearances
- How did it fit the facts?
- Third Solution: The Equant Point
- Ptolemy’s system worked

- Upcoming Classes
- Soil and Plant Nutrition
- Newton’s Law of Gravity
- Friction
- Gravitation
- Practical Applications of Solar Energy
- Newton’s law of universal gravitation

© 2010-2020 powerpoint presentations