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In 1761, Joseph Lambert proved that pi was irrational by basically proving that the tangent of some number x could be expressed as a particular continued fraction as a function of x. He then went on to show that if x was rational, the continued fraction must be irrational, and since the tangent of pi/4 was 1 (i.e. rational), then pi/4 and thus pi itself must not be rational.

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Q: Who proved that pi was irrational and when?

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The value of pi has never been proven becauase it is an irrational number which can not be expressed as a fraction

-Pi is irrational, because it does not terminate or repeat. Whenever you multiply an irrational number by a rational number (-1), the result is an irrational number.

Yes. pi - sqrt(2) is irrational.

Sure; for example, 10 + pi is irrational, 10 - pi is irrational. Both are positive. If you add them, you get 20.

Negative pi

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Johann Lambert proved that pi is irrational in 1761.

Johann Lambert proved that pi is irrational in 1761.

Lambert.

The value of pi has never been proven becauase it is an irrational number which can not be expressed as a fraction

He proved that pi is an irrational number.

Pi is an irrational number. Johann Heinrich Lambert proved that in the late 18th Century.

Pi is an irrational number; it can't be represented as a fraction of two integers. It has been proved that the majority of real numbers are irrational. The proof that pi is irrational was found in 1770; it's slightly too complicated to put in this answer, but if you search with google for pi irrational proof then you will find several different proofs.

Pi can't be expressed as a fraction (a ratio of two integers), which makes it irrational. Another way to say it. Pi (π) is an irrational number; it's trancendent. The mathematical proof that pi is irrational can be viewed by using the link to the Wikipedia article on exactly this topic. The challenge is that to understand the proof, one needs some familiarity with integral calculus. Short of that, one would probably have to just accept the fact that pi is transcendent and that it has been proved. (Pi was suspected to be irrational from ancient times, but it was actually proved to be in the 1700's.)

1.Euler 2. Lambert 3.Liouville 4.Hermite 5.Linderman - Euler's infinite Expansion of Pi with primes. - Lamert proved that Pi was irrational - Liouville proves the existence of Transcendental numbers - Hermite proved that the constant was transcendental. - Linderman proved that Pi was trancendental Thanks :)

An irrational number is a real number that cannot be expressed as a ratio of two integers, x and y, where y>0. In 1761, Johann Heinrich Lambert proved that pi is irrational. His proof and alternatives by other mathematicians can be found at the attached link.

It is irrational, just like pi

Pi, is an irrational number (it cannot be written as a fraction) For this reason, 3 times pi is also irrational.

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