Eratosthenes calculated the circumference of the Earth using measurements from two cities in Egypt - Syene and Alexandria. He knew that on the summer solstice, the sun was directly overhead at Syene at noon. In Alexandria, 500 miles north, he measured the sun's shadow to be 7.5 degrees. Using this angle and the distance between the cities, he calculated the circumference of the Earth to be approximately 25,000 miles, with an error of only 4%.

2. The Greek World around 450 BC This is the Golden Age of Athens , the time of Pericles and Socrates. Very few ordinary citizens would have travelled outside this area. Athens Alexandria Troy

3. The Decline of Athens, the Rise of Alexandria. By 300 BC Alexandria had eclipsed Athens, both as a merchant power and a centre of culture.

4. The Lighthouse (Pharos) of Alexandria , built under Ptolemy after the death of Alexander. This is one of the 7 ancient wonders of the world. It stood at 117m (384 feet in height). It was finally destroyed by the earth quakes of 1303 and 1323. The library of Alexandria was the foremost seat of learning in the world and functioned like a university. The library contained 600 000 manuscripts.

5. Earth Measure The idea of a spherical Earth was well established in Greek culture. 500 BC: Pythagoras proposes a spherical Earth on purely aesthetic grounds. The Pythagorean’s believed the sphere to be the most perfect shape. 400 BC: Plato espouses the same idea in his dialogue (Phaedo) which receives wider circulation. Aristotle (384 - 322 BC): Aristotle proposes a spherical Earth on geometric and symmetrical grounds but backed up by observational evidence. Eratosthenes (275 – 194 BC): Decides to calculate the Earth’s circumference based on his knowledge of Geography coupled with a mathematical Theorem from Euclid’s work “ The Elements”. His method was based on first hand knowledge of a town, (Syene) that lay approximately 500 miles south of Alexandria.

6. Lunar Eclipse Observational evidence for a Spherical Earth Projection of Earth’s shadow onto the surface of the moon shows curvature.

7. The “sinking” appearance of a departing ship relative to the observer’s horizon. Observational evidence for a Spherical Earth Bottom of ship disappears.

8. All of the ship would remain visible as apparent size diminishes. Whereas on a flat Earth

9. Positioning on the Earth’s Surface To appreciate his method more fully, an understanding of latitude and longitude is useful. It is important to remember that this is a relatively modern day method of positioning and was not known about in ancient times.

10. Positioning on the Earth’s Surface Latitude and Longitude together enable the fixing of position on the Earth’s surface. Equator Latitude 0 o Latitude: ( 90 o N to 90 o S) Latitude 23½ o North Tropic of Cancer Latitude 23½ o South Tropic of Capricorn Longitude 30 o East Longitude 60 o East Longitude 30 o West Longitude 60 o West East is the direction of rotation of the Earth North Pole South Pole 23½ o Grimsby : Latitude 53½ o North 23½ o 53½ o 90 o 90 0 21 st June 22 nd December 22 nd Sept 20 th March Syene Alexandria 30 o E 60 o E 90 o E 90 o W 30 o W 60 o W Longitude 90 o East Longitude 90 o West Greenwich Meridian 0 o Longitude (Cleethorpes) Longitude: (180 o E to 180 o W)

11. 1 Eratosthenes knew that Syene marked the Northern most point of the migration of the Sun and that this occurred each year at noon on the 21 st of June . In today’s terms, it is located on the Tropic of Cancer (23½ o N of the equator). He knew this because the water at the bottom of a local well only became visible at noon on this day. A local vertical placed at Syene at this time would cast no shadow , as the sun is directly overhead. He made the important assumption that rays of light arriving from a distant sun would be parallel to each other. 2 No shadows at noon. Shadows at noon. stick well Alexandria Syene (Aswan) The Method of Eratosthenes 500 miles North 21 st June Alexandria Syene Sun overhead at Syene. on midsummer's day. 3 He calculated that Alexandria was approximately 500 miles north of Syene , which puts it roughly on the same line of longitude. (30 o E of Greenwich). Places on the same line of longitude experience time at the same time . In particular, noon at both places occurs at the same instant . A local vertical placed at Alexandria would cast a shadow at noon.

12. Can you figure out what he did and arrive at an estimate for the circumference of the Earth? Eratosthenes measured angle  as approximately 7½ o Taking the true value as 25,000 miles, find his percentage error. 4% Alternate angles are equal. The Method of Eratosthenes 21 st June Alexandria Syene Sun overhead Syene. at noon on midsummer's day. Shadow line of stick on ground is of minimum length at noon. Not to scale (would you believe) Measurements are approximate. stick 500 miles Syene Alexandria North well Local vertical Local vertical Parallel rays of light at noon no shadows water visible !  7½ o 500 miles Angle Distance 15 o 1000 miles 30 o 2000 miles 60 o 4000 miles 360 o 24000 miles  ? 7½ o