Question

proof that $\pi$ is irrational

Answer 1

Answer:

In the 1760s, Johann Heinrich Lambert proved that the number π (pi) 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 the 19th century, Charles Hermite found a proof that requires no prerequisite knowledge beyond basic calculus.

MARK ME BRAINLIEST

Answer 2

Symbol -

$\pi$

Introduction on $\pi$

• Pi (π) is a mathematical constant that is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.14159.
• It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes written as pi.

Pi is an irrational number

• Which means that it is a real number that cannot be expressed by a simple fraction.
• That's because pi is what mathematicians call an "infinite decimal" — after the decimal point, the digits go on forever and ever.
• (These rational expressions are only accurate to a couple of decimal places.)

Now ,

We have to prove that pi is an irrational number

Let's see

• We will prove that pi is, in fact, a rational number, by induction on the number of decimal places, N, to which it is approximated.
• For small values of N, say 0, 1, 2, 3, and 4, this is the case as 3, 3.1, 3.14, 3.142, and 3.1416 are, in fact, rational numbers.

More information Regarding $\pi$

Let's see Information about $\pi$

Is negative pi irrational?

• The number, pi, cannot be written exactly equal to a fraction. Since pi is irrational, negative pi is also irrational.

How do you know a number is irrational?

• An irrational number is a number that cannot be written as the ratio of two integers.
• Its decimal form does not stop and does not repeat.

Is Pi a integer?

• π is an irrational number, meaning that it cannot be written as the ratio of two integers.
• Fractions such as 227 and 355113 are commonly used to approximate π, but no common fraction (ratio of whole numbers) can be its exact value.