Question

$\textbf{Theory of Erasthosthenes }$

Write its procedure too.

Answer 1

$\huge{\mathbb\pink{ANSWER}}$

$\textbf{Theory of Eratosthenes }$

==>>Eratosthenes::
> A greek mathematician
>Has been know for his important distribution in the formulation of circumference circle.
>procedure for the proof..

Initially Eratosthenes,, being in city of alexandria find out mystery of shadow,, i.e, another neighbour city,, at 12:00am,, sun was correctly at the middle,, such that there was no shadow formation in that city, while in his hometown he tried it again , sharp at 12:00, he with his stick stood out,, at 12:00, such that his shadow appeared yet,,,he was probably in chaos, of how the shadow is formed here, but why not in another city,,...

He just measured out the angle with which the shadow is formed and it found to be 7.2° and he knew the distance between the cities where Shadow is not formed and where shadow is formed..by this he found that earth is circular shape but not in any other..

Sieve of ert=>It is the ancient and simple logical procedure of algorithm to find the all given prime no's upto the any given limit...

calculation==>>>

degree of deviation= 7.2° to normal..

total angle = 360°

distance between two cities = 800km..

let the circumference of circle be 'x'
.
then he simply taken the ratio of them...

i.e,

$\frac{7.2°}{360}$ = $\frac{800}{x}$

x = $\frac{800\times360}{7.2}$

x =$\frac{288000}{7.2}$

x = 40,000km,,~~=~~ 40,040km....

and his another theory,, is SEIVE OF Eratosthenes..

This theory is usefull in finding out the Prime no from 1 to n,,

Procedure==>>

1.Initiation, or note down all the natural no's from 1 to n

2. The first prime no is 2, leave 2 , and round off all of its multiples like, 4,6,8..etc., then the next consecutive prime no is 3.

3. SIMILARLY round off all the values of multiples of 3 except 3.

4.Untill the largest natural no ,, proceed it upto √n, such that it shouldn't exceed..

####$\huge{\mathbb{Thanks}}$

Answer 2

Sieve of Erasthosthenes :

This method helps us to find out Prime number from 1 to n.

Procedure :

Write all natural numbers from 1 to n.

1. The first Prime number is 2, leave 2 and round off all the multiples of 2. They are 4, 6,8... the next Prime number left is 3.

2. Round off all the multiple sof 3 except 3.

3. We have to continue this process up-to the highest Prime number which don't exceed √n.