When Alexander the Great died, his vast empire fell into the hands of three generals. The responsibility of Egypt fell on Ptolemy. Only the virtuous appreciate knowledge. Ptolemy gradually built a vast repository of knowledge, the famous Library of Alexandria. He brought great scholars from home and abroad.Cyrene is a town in Egypt. Eratosthenes of Cyrene was born there in 26 BC. He was a fan of knowledge. Run far and wide in search of knowledge. Meanwhile, Ptolemy needed people to look after that huge library. He finds Eratosthenes. Eratosthenes was then thirty years old. Ptolemy summoned him to look after the famous Library of Alexandria. Eratosthenes did not miss this opportunity to learn.
He later became the chief librarian of the Alexandrian Library. He was simultaneously a mathematician, geographer, poet, astronomer and music theorist. But the two most famous reasons for this are, for the first time, the discovery of a fancy method of determining the circumference of the earth almost accurately and of determining prime numbers.
This article will summarize the great works of Eratosthenes. Broadly speaking, the content of this article is roughly divided into three parts:
- 'Save of Eratosthenes' in determining prime numbers;
- Eratosthenes's method of determining the circumference of the earth; And
- Eratosthenes in geography and astronomy.
Let's go to the main discussion without further ado.
*Eratosthenes filter’ method in determining prime numbers
In English this method is called 'Sieve of Eratosthenes', in Bengali it is called 'Sieve of Eratosthenes'. What is the function of this filter? This filter separates the prime numbers from the many numbers.
The prime numbers are those numbers which cannot be divided by any number other than 1 and 7. It is very easy to know whether a number is basic or not, we will find out all the producers whether it is basic or not.
Well, if the number is too large, for example, to find out whether 1933 is fundamental or not, we have to divide it by 1932 numbers! It also has a simple intellect, you don't need to divide by all the numbers to know whether a number is prime or not, you just have to look at the square root of that number. Why?Suppose, N is a number and N = a × b. Now we have to prove that one of a, b must be smaller than the square root of N, the other is bigger than the square root of N. Assuming at the beginning, both are larger than the square root of N. But multiplying a, b will be greater than N. Therefore, if a number is not prime, it must have a product, which is smaller than the square root of N. From this it is easily understood that another product will be larger than the square root of N.
We found a way to find the prime number and it was a pretty good method. But if we are asked to separate the prime and non-prime numbers from many numbers, then it is not at all a good idea to find out the product separately for each number. This is why the filter of Eratosthenes is needed. This method is still an effective algorithm for finding prime numbers in large ranges, and is widely used in the computer world.
Let’s think very generally. A number that is a multiple of a prime number is no longer a prime. Let's make use of this. I think I want to find all the prime numbers between 1-20. At the beginning we will have all the numbers in the list, gradually the non-prime numbers will be filtered, the prime numbers will remain.