Question

prove that π is irrational no
pls ans fast☺️​

Answer 1

Answer:

Step-by-step explanation:

1. Assume π is rational, π = a/b for a and b relatively prime.

2. Create a function f(x) that depends on constants a and b

3. After much work, prove that integral of f(x) sin(x) evaluated from 0 to π must be an integer, if π is rational.

4. Simultaneously show that integral of f(x) sin(x) evaluated from 0 to π will be positive but tend to 0 as the value of n gets arbitrarily large. This is the required contradiction: if the integral evaluates to an integer, it cannot also be equal to a value between 0 and 1.

5. Conclude π is irrational.

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Answer 2

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$\huge\star\underline\mathbb\orange{π(pi)}$

In the 1760s, Johann Heinrich Lambert proved that the number (π) is irrational : that is,it cannot be expressed as a fraction a/b,where a is an integer and b is a non-zero integer.

In 1882.Ferdinand Von Lindemann proved that π is not just irrational,but transcendental as well.