How did Eratosthenes calculate circumference?
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.
What is Eratosthenes formula?
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.
What did Eratosthenes calculate?
In the third century BCE , Eratosthenes, a Greek librarian in Alexandria , Egypt , determined the earth’s circumference to be 40,250 to 45,900 kilometers (25,000 to 28,500 miles) by comparing the Sun’s relative position at two different locations on the earth’s surface.
How did Eratosthenes measure the circumference 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 method was very simple; he measured the length of a shadow from a vertical stick of a known height in two cities on the same day. The ratio between the north-south distance between the two cities and the angles measured gave a ratio which allowed Eratosthenes to calculate the size of the Earth.
What is the circumference of the Earth using Eratosthenes method quizlet?
Eratosthenes concluded that the circumference was 250,000 stades, and this can be used to calculate the diameter of the earth.
How do you measure a circumference?
To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π=3.14).
What is the rules of Eratosthenes?
Each positive integer has at least two divisors, one and itself. A positive integer is a prime number if it is bigger than 1, and its only divisors are itself and 1. For example, 2, 3, 5, 7, 11, 13, 17, and 19 are prime numbers.
How did Eratosthenes measure the size of the Earth in 240 BC?
He correctly assumed the sun’s distance from the Earth to be very great, and therefore rays of light falling towards the Earth to be parallel. If he could determine the distance from Syene to Alexandria, all he would have to do to determine the circumference of the Earth was multiply this distance by 50.
How 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.
What is the circumference of Nearth hint apply the technique used by Eratosthenes to measure Earth’s circumference?
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.
What is Sieve of Eratosthenes algorithm?
Definition. The sieve of Eratosthenes algorithm is an ancient algorithm that is used to find all the prime numbers less than given number T. It can be done using O(n*log(log(n))) operations. Using this algorithm we can eliminate all the numbers which are not prime and those that are less than given T.
What is Sieve of Eratosthenes?
: a procedure for finding prime numbers that involves writing down the odd numbers from 2 up in succession and crossing out every third number after 3, every fifth after 5 including those already crossed out, every seventh after 7, and so on with the numbers that are never crossed out being prime.
What are the actual direct measurements that Eratosthenes used to calculate the size of the Earth?
Is prime Sieve of Eratosthenes?
The sieve of Eratosthenes algorithm is an ancient algorithm that is used to find all the prime numbers less than given number T. It can be done using O(n*log(log(n))) operations. Using this algorithm we can eliminate all the numbers which are not prime and those that are less than given T.