Table of Contents
What is the method of Eratosthenes?
Eratosthenes then measured the angle of a shadow cast by a stick at noon on the summer solstice in Alexandria, and found it made an angle of about 7.2 degrees, or about 1/50 of a complete circle. He realized that if he knew the distance from Alexandria to Syene, he could easily calculate the circumference of Earth.
Did Eratosthenes use trigonometry?
Eratosthenes will always be remembered for the calculation of the Earth’s circumference circa 240 BC, using trigonometry and knowledge of the angle of elevation of the Sun at noon in Alexandria and Syene (now Aswan, Egypt).
How do you get all primes?
To prove whether a number is a prime number, first try dividing it by 2, and see if you get a whole number. If you do, it can’t be a prime number. If you don’t get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 (9 is divisible by 3) and so on, always dividing by a prime number (see table below).
What is the best algorithm for finding a prime number?
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.
What two things is Eratosthenes most famous for?
Of course, Eratosthenes did not only read about great work, he did some great work himself. We know him best for two important achievements: producing an accurate estimate of how big Earth is; and devising a method to find prime numbers.
How is Earth’s area calculated?
To find the surface area of the Earth we have to use the formula of 4*Pi*radius squared. The radius of the Earth is approximately 6,371 kilometers.
What did Eratosthenes observe on June 21st?
On 21 june 2012 : Solstice celebration with Eratosthenes Eratosthenes is a Greek scientist who lived in the third century BC in Egypt. He observed that on the summer solstice at solar noon : the sun was at its zenith in the city of Syene (Southern Egypt, now Aswan), so there was no shadow.
How to do the steps of Eratosthenes using paper?
Figure 3.2 shows how we can carry out the steps using a long strip of paper. Start by listing all the integers, starting with 2 and extending as far as we want. The top row of the figure shows a “paper tape” with numbers from 2 to 21, but the tape can extend arbitrarily far to the right.
The Sieve of Eratosthenes An algorithm for nding prime numbers Mathematicians who work in the field of number theory are interested in how numbers are related to one another. One of the key ideas in this area is how an integer can be expressed as the product of other integers.
What was the circumference of Eratosthenes’s Empire?
Eratosthenes later rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia, likely for reasons of calculation simplicity as the larger number is evenly divisible by 60.
When was Eratosthenes born and when did he die?
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. What were Eratosthenes’ major achievements?