Eratosthenes erected a pole in Alexandria, and on the summer solstice he observed that it cast a shadow, proving that the Sun was not directly overhead but slightly south. Recognizing the curvature of the Earth and knowing the distance between the two cities enabled Eratosthenes to calculate the planet’s circumference.
How did Eratosthenes measure the circumference of the Earth using parallel lines?
Eratosthenes assumed the sun was far enough away from our planet that its rays were effectively parallel when they arrived at Earth. This told him the angle of the shadow he measured in Alexandria was equal to the angle between Alexandria and Syene, measured at Earth’s center.
How do we measure 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 do you use Eratosthenes method?
Thousand thirty kilometers. But over two thousand years earlier in ancient Greece a man arrived at nearly that exact same figure by putting a stick in the ground. That man was Eratosthenes a Greek
How did Eratosthenes measure the size of the earth quizlet?
Eratosthenes measured the circumference of the earth by measuring the distance between two cities. Then he measured the angle of sunlight relative to the vertical on the summer solstice. The sun was overhead in Alexandria but seven degrees away from the vertical in Syene.
What was Eratosthenes experiment?
Eratosthenes analyzed the observations with the assumption that the earth is a sphere and the sun is very far away. The geometry of the situation is sketched at the right. He concluded that the circumference of the earth was about 50 times greater than the distance from Alexandria to Aswan.
What is the circumference of the Earth using Eratosthenes method quizlet?
the math ends up being C= (1*500)/(1/50) = 25,000 mi.
What did Eratosthenes do?
Eratosthenes, in full Eratosthenes of Cyrene, (born c. 276 bce, Cyrene, Libya—died c. 194 bce, Alexandria, Egypt), Greek scientific writer, astronomer, and poet, who made the first measurement of the size of Earth for which any details are known.
How did Eratosthenes measure the size of the Earth in 240 BC quizlet?
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.
Which of the following was Eratosthenes contribution to early astronomy quizlet?
it reduces to one third what it was. Which of the following is a contribution that Eratosthenes made to astronomy? He determined the circumference of the Earth.
When was Copernicus first created quizlet?
When Copernicus first created his Sun-centered model of the universe, it did not lead to substantially better predictions of planetary positions than the Ptolemaic model. Why not? Copernicus used perfect circles for the orbits of the planets. Earth is farthest from the Sun in July and closest to the Sun in January.
Is Eratosthenes method of determining the circumference of the Earth logical and reasonable?
Using elegant mathematical reasoning and limited empirical measurement, in approximately 240 b.c., Eratosthenes of Cyrene (276-194 b.c.) accurately measured the Earth’s circumference. This feat was more than simply a scientific achievement.
What problem did Eratosthenes solve?
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.
Why was Eratosthenes sieve so important?
Eratosthenes made many important contributions to science and mathematics. His prime number sieve provided a simple way for Greek mathematicians (and frustrated modern students!) to find all prime numbers between any two integers.
How do you prove Sieve of Eratosthenes?
- Write a list of numbers from 2 to the largest number n you want to test. …
- Strike off all multiples of 2 greater than 2 from the list . …
- Strike off all multiples of this number from the list.
- Repeat the above steps until no more multiples are found of the prime integers that are less than √n.
How do you sieve Eratosthenes?
1. Any takers well it's because a problem number is any number greater than one and only divisible by itself. And one. So one cannot be a prime number because it is not greater than one. Okay. Now
Why this method called Sieve of Eratosthenes?
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.
Who is Eratosthenes for kids?
Eratosthenes was an ancient Greek mathematician, geographer, and astronomer. He existed from 276 B.C. until 194 B.C. and is most notable for having the first accurate calculation of the Earth’s circumference. He lived and worked in the Egyptian city of Alexandria for much of his life.
What is Eratosthenes math?
In mathematics, the sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), one of a number of prime number sieves, is a simple, ancient algorithm for finding all prime numbers up to any given limit.
When did Eratosthenes calculate the circumference of the Earth?
about 240 B.C.
By around 500 B.C., most ancient Greeks believed that Earth was round, not flat. But they had no idea how big the planet is until about 240 B.C., when Eratosthenes devised a clever method of estimating its circumference.
Who invented math?
Archimedes is known as the Father of Mathematics. Mathematics is one of the ancient sciences developed in time immemorial. A major topic of discussion regarding this particular field of science is about who is the father of mathematics.
How did Eratosthenes contribute to geography?
Eratosthenes made major contributions to geography. He sketched, quite accurately, the route of the Nile to Khartoum, showing the two Ethiopian tributaries. He also suggested that lakes were the source of the river.
How does Eratosthenes define geography?
While serving as the head librarian and scholar at the Library of Alexandria, Eratosthenes wrote a comprehensive treatise about the world, which he called “Geography.” This was the first use of the word, which in Greek means “writing about the world.” Eratosthenes’ work introduced the concepts of torrid, temperate, and …
Who discovered circumference of Earth?
This illustration shows how Eratosthenes actually calculated the circumference of the Earth. At noon on the summer solstice, Eratosthenes measured the length of the shadow cast by a column of known height at Alexandria. With these two lengths, he could solve for the angle between them (θ).
What did Eratosthenes believe in?
Eratosthenes determined the earth’s size by observing known phenomena and applying basic arithmetic and geometry to them. Here’s how he did it. Eratosthenes’ methods were simple but effective. All he needed to know was the distance between two locations and what percentage of a circle this distance constituted.