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The "trick" functions in the "$\pi$ is transcendental" proofs

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#irrational-numbers #pi #transcendental-numbers
669
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Why does $e^{i\pi}=-1$?

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#intuition #pi #constants
326
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Help me ID this weird $\pi$ formula

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#sequences-and-series #number-theory #pi
277
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Why is it safe to approximate $2\pi r$ with regular polygons?

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#geometry #pi
9.9k
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$\pi^4 + \pi^5 \approx e^6$ is anything special going on here?

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#exponential-function #approximation #pi #constants #diophantine-approximation
91
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Pi for non mathematician

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#coordinate-systems #pi
937
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When the approximation $\pi\simeq 3.14$ is NOT sufficent

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#education #approximation #pi
702
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Which is greater, $e^{\pi}$ or $\pi^e$?

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#calculus #exponential-function #pi
100
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Curious set of $n\sin^2(n)$

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#analysis #number-theory #pi
127
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A formula for $\pi$ and an inequality

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#inequality #definite-integrals #pi
3.7k
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What is the probability of a specific sequence of 11 digits occurring in a random sequence of one billion digits?

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#probability #random #pi
7.1k
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Geometric intuition for $\pi /4 = 1 - 1/3 + 1/5 - \cdots$?

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#real-analysis #sequences-and-series #number-theory #intuition #pi
164
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Trascendence of $e^\pi$ and $\pi^e$

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#abstract-algebra #extension-field #pi #transcendental-numbers
5.2k
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Why is it so difficult to determine whether or not $\Large \pi^{\pi^{\pi^\pi}}$ is an integer?

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#pi
301
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How is PI used to predict weather patterns?

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#probability #pi #pattern-recognition #constants

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