A343059 -id:A343059

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A374972

Decimal expansion of the sagitta of a regular heptagon with unit side length.

+0
10

1, 1, 4, 1, 2, 1, 7, 3, 7, 1, 9, 5, 0, 7, 4, 9, 6, 9, 0, 3, 8, 8, 0, 5, 6, 8, 1, 0, 3, 0, 5, 0, 7, 3, 9, 1, 3, 6, 9, 3, 9, 0, 8, 4, 0, 4, 9, 0, 1, 7, 6, 3, 1, 8, 9, 8, 9, 8, 4, 4, 4, 5, 9, 8, 0, 1, 9, 1, 2, 4, 2, 7, 8, 5, 6, 9, 4, 0, 9, 3, 9, 4, 5, 7, 3, 4, 6, 9, 3, 5

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Paolo Xausa, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Regular Polygon.

Eric Weisstein's World of Mathematics, Sagitta.

FORMULA

Equals tan(Pi/14)/2 = A343059/2.

Equals A374957 - A374971.

EXAMPLE

0.114121737195074969038805681030507391369390840490...

MATHEMATICA

First[RealDigits[Tan[Pi/14]/2, 10, 100]]

CROSSREFS

Cf. A374957 (circumradius), A374971 (apothem), A178817 (area).

Cf. sagitta of other polygons with unit side length: A020769 (triangle), A174968 (square), A375068 (pentagon), A375069 (hexagon), A374972 (heptagon), A375070 (octagon), A375153 (9-gon), A375189 (10-gon), A375192 (11-gon), A375194 (12-gon).

Cf. A343059.

KEYWORD

nonn,cons,easy

AUTHOR

Paolo Xausa, Jul 26 2024

STATUS

approved

A343057

Decimal expansion of tan(Pi/32).

+0
2

0, 9, 8, 4, 9, 1, 4, 0, 3, 3, 5, 7, 1, 6, 4, 2, 5, 3, 0, 7, 7, 1, 9, 7, 5, 2, 1, 2, 9, 1, 3, 2, 7, 4, 3, 2, 2, 9, 3, 0, 5, 2, 4, 5, 0, 6, 9, 9, 2, 0, 2, 6, 9, 5, 9, 8, 0, 9, 1, 6, 1, 2, 1, 1, 3, 4, 4, 1, 9, 4, 3, 8, 7, 3, 0, 8, 1, 2, 9, 7, 2, 2, 5, 6, 4, 8, 5, 2, 1, 4, 1, 8, 0, 3, 7, 3, 6, 0, 0, 1, 3, 7, 0, 6, 7, 1, 6, 9, 7, 7, 9, 1, 7, 6, 5

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Wikipedia, Trigonometric constants expressed in real radicals

FORMULA

Equals sqrt( (2-sqrt(2+sqrt(2+sqrt(2))))/(2+sqrt(2+sqrt(2+sqrt(2)))) ).

EXAMPLE

0.098491403357164253077197...

MATHEMATICA

RealDigits[Tan[Pi/32], 10, 120, -1][[1]] (* Amiram Eldar, Apr 27 2021 *)

PROG

(PARI) tan(Pi/32)

(PARI) sqrt((2-sqrt(2+sqrt(2+sqrt(2))))/(2+sqrt(2+sqrt(2+sqrt(2)))))

(Magma) R:= RealField(125); Tan(Pi(R)/32) // G. C. Greubel, Sep 30 2022

(SageMath) numerical_approx(tan(pi/32), digits=125) # G. C. Greubel, Sep 30 2022

CROSSREFS

Cf. A343055 (sin(Pi/32)), A343056 (cos(Pi/32)).

tan(Pi/m): A002194 (m=3), A019934 (m=5), A020760 (m=6), A343058 (m=7), A188582 (m=8), A019918 (m=9), A019916 (m=10), A019913 (m=12), A343059 (m=14), A019910 (m=15), A343060 (m=16), A343061 (m=17), A019908 (m=18), A019907 (m=20), A343062 (m=24), A019904 (m=30), A343057 (m=32), A019903 (m=36).