Eratosthenes hired a man to pace the distance between the two cities and learned they were 5,000 stadia apart, which is about 800 kilometers. He could then use simple proportions to find the Earth's circumference — 7.2 degrees is 1/50 of 360 degrees, so 800 times 50 equals 40,000 kilometers.

How did they calculate the circumference of the Earth?

Eratosthenes sent a man to Syene from Alexandria on foot to measure the distance between Alexandria and Syene. Thus, Eratosthenes measured the distance between the two cities is 800 km. He multiplied by 800 km to 50 and calculated that the Earth's circumference is 40,000 km.

How is Eratosthenes calculated?

Eratosthenes divided 360° by 7.2° and got 50, which told him that the distance between Alexandria and Syene (500 miles) was 1/50 of the total distance around the Earth. So he multiplied 500 by 50 to arrive at his estimate of the Earth's circumference: 25,000 miles.

How did Eratosthenes estimate the size of the Earth in 240 BC?

How did Eratosthenes estimate the size of the earth in 240 bc? By comparing whether sun light could reach water down in water wells in two cities at different latitudes and using simple trigonometry.

Is Eratosthenes method of determining the circumference of the earth logical and reasonable Why?

Eratosthenes reasoned that the ratio of the angular difference in the shadows to the number of degrees in a circle (360°) must equal the ratio of the distance to the circumference of the Earth. The resulting estimate, about 25,000 miles (40,234 km), is astonishingly accurate.

How Eratosthenes calculated the Earth's circumference

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How did Eratosthenes measure the size of the Earth quizlet?

How did Eratosthenes measure the circumference of the Earth? He used geometry and ratios to determine the size of the Earth, by basing his calculations on observations of the sun.

What is Eratosthenes method?

In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, 2. ... It may be used to find primes in arithmetic progressions.

What did Eratosthenes discover?

What is Eratosthenes famous for? Eratosthenes measured Earth's circumference mathematically using two surface points to make the calculation. He noted that the Sun's rays fell vertically at noon in Syene (now Aswān), Egypt, at the summer solstice.

Did Eratosthenes get married?

Eratosthenes was a Greek scientist who lived from 276 to 194 B.C. He studied astronomy, geography, and math. ... Some people believe that Eratosthenes starved himself to death on purpose after going blind. He never married. Eratosthenes is most famous for making the first good measurement of the size of Earth.

Who is the father of Eratosthenes?

Life. The son of Aglaos, Eratosthenes was born in 276 BC in Cyrene. Now part of modern-day Libya, Cyrene had been founded by Greeks centuries earlier and became the capital of Pentapolis (North Africa), a country of five cities: Cyrene, Arsinoe, Berenice, Ptolemias, and Apollonia.

What is the main ideas of Eratosthenes?

Eratosthenes calculated the tilt of Earth's axis relative to the plane of its equator with good accuracy. He produced the first map of the world featuring meridian lines and parallel lines. These were similar to our modern lines of latitude and longitude.

How do you find a circumference?

To find the circumference of a circle, multiply the circle's diameter by pi (3.14).

How did Eratosthenes measure the angle?

Eratosthenes knew that the Sun was never directly overhead, even on the Summer Solstice, in his home city of Alexandria, which is further north than Syene. He realized that he could determine how far away from directly overhead the Sun was in Alexandria by measuring the angle formed by a shadow from a vertical object.

How is the Sieve of Eratosthenes done?

The Sieve of Eratosthenes is a mathematical algorithm of finding prime numbers between two sets of numbers. Sieve of Eratosthenes models work by sieving or eliminating given numbers that do not meet a certain criterion. For this case, the pattern eliminates multiples of the known prime numbers.

How did Eratosthenes establish prime numbers?

By inventing his “sieve” to eliminate nonprimes—using a number grid and crossing off multiples of 2, 3, 5, and above—Eratosthenes made prime numbers considerably more accessible. Each prime number has exactly 2 factors: 1 and the number itself.

What is the Sieve of Eratosthenes and why does it work?

Sieve of Eratosthenes is a simple and ancient algorithm used to find the prime numbers up to any given limit. It is one of the most efficient ways to find small prime numbers. For a given upper limit n the algorithm works by iteratively marking the multiples of primes as composite, starting from 2.

What is it called when a planet temporarily moves westward in the sky?

Their westward motion is called retrograde motion by astronomers.

How are wavelength frequency and energy related for photons of light?

The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, the higher its energy. Equivalently, the longer the photon's wavelength, the lower its energy.

What is the difference between the umbra and the penumbra of a lunar eclipse?

The umbra is the darkest part of the shadow while the penumbra is the lighter portion on the edges.

What is the circumference of 18?

2 Answers. The answer is 56.57 .

What is the formula for perimeter of circumference?

Learn that the perimeter of a circle has its own special name, called "circumference." The symbol is a capital C. It is calculated using the formula Pi x diameter, or 3.14 x d = C. It can also be calculated by Pi x (2 x radius) = C or 3.14 x (2 x r) = C. Learn about Pi.

How do you find circumference without radius?

Replace π with an estimate such as 3.14, or use the π button on your calculator for a more accurate result. Multiple the values for π and d together, and you get C, the circumference. For example, if the diameter was 6 units long, you'll get (3.14) x (6 units) = 18.84 units.

What is Eratosthenes map?

Reconstruction of Eratosthenes; Map, 1883. ... In his three-volume work Geography, he described and mapped his entire known world, even dividing the Earth into five climate zones: two freezing zones around the poles, two temperate zones, and a zone encompassing the equator and the tropics.

How did Eratosthenes contribute to oceanography?

Besides navigation, Eratosthenes also measured the Earth's circumference fairly well. Research into physical oceanography included Strabo, who observed volcanic activity and concluded that land was not totally static. He also realized that streams eroded continents and deposited sediments into the ocean.