Pi - NumberDB

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Number

$\pi$

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141274

Definition

$\pi$ is the area of the unit disk.

Formulas

(1)

$C = 2\pi$, where $C$ is the circumference of the unit circle.

(2)

$\pi = 4\arctan 1$.

(3)

$\sum_{n\geq 1} n^{-2} = \pi^2/6$.

Programs

(P1)

Sage

from sage.rings.real_arb import RealBallField

numbers = [RealBallField(1024).pi()]

Links

[1]

Wikipedia: Pi

[2]

OEIS: A000796

Similar tables

rational multiples of $\pi$ — stores the scaled values $a\pi$; its entry at $a=1$ equals $\pi$

Data properties

Entries are of type: real number

Table is complete: yes (it holds the single number named by the definition; the scaled values $a\pi$ are held by rational multiples of $\pi$)

How well the digits are known: proven

How they were obtained:

Computed by Sage's RealBallField(1024).pi() in ball arithmetic and checked against $\pi$ recomputed at 4000 bits: the stored value is within one unit in the last place of the 301 digits held.