A134974 -id:A134974 - cp's OEIS frontend

A344212 Decimal expansion of 1 + 1/sqrt(5).

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

Offset: 1

Wesley Ivan Hurt, May 11 2021

Decimal expansion of the midradius of a rhombic triacontahedron with unit edge length.

Essentially the same sequence of digits as A176453, A134974, A020762 and A010476. - R. J. Mathar, May 16 2021

			1.447213595499957939281834733746255247088123671922305...

Wikipedia, Rhombic triacontahedron.
Index entries for algebraic numbers, degree 2.

Cf. A019952 (rhombic triacontahedron inscribed sphere radius).
Cf. A344171 (rhombic triacontahedron surface area).
Cf. A344172 (rhombic triacontahedron volume).
Cf. A010476, A020762, A081005, A134974, A176453, A187798, A242671.

RealDigits[1 + 1/Sqrt[5], 10, 100][[1]] // Flatten

5^-.5+1 \\ Charles R Greathouse IV, Feb 04 2025

polrootsreal(5*x^2-10*x+4)[2] \\ Charles R Greathouse IV, Feb 04 2025

From Amiram Eldar, Nov 28 2024: (Start)
Equals 2*A242671 = 1/A187798.
Equals Product_{k>=0} (1 + 1/A081005(k)). (End)

A176453 Decimal expansion of 4+2*sqrt(5).

Original entry on oeis.org

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

Offset: 1

Klaus Brockhaus, Apr 20 2010

Continued fraction expansion of 4+2*sqrt(5) is A010698 preceded by 8.
a(n) = A010476(n) = A020762(n-1) = A134974(n) for n > 1.
Rajan (2010) claims the variance of a discrete distribution generated by the linear convolution of Fibonacci sequence with itself, saturates to a constant of value 8.4721359. [From Jonathan Vos Post, May 10 2010]

			4+2*sqrt(5) = 8.47213595499957939281...

Arulalan Rajan, Jamadagni, Vittal Rao, Ashok Rao, Convolutions Induced Discrete Probability Distributions and a New Fibonacci Constant, May 6, 2010. [From _Jonathan Vos Post_, May 10 2010]

Cf. A002163 (decimal expansion of sqrt(5)), A010476 (decimal expansion of sqrt(20)), A020762 (decimal expansion of 1/sqrt(5)), A134974 (decimal expansion of 8/(1+sqrt(5))), A010698 (repeat 2, 8).

RealDigits[4+2Sqrt[5],10,120][[1]] (* Harvey P. Dale, Sep 08 2018 *)

A380982 Decimal expansion of the long/short edge length ratio of a disdyakis triacontahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Feb 10 2025

			1.8472135954999579392818347337462552470881236719223...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.
Wikipedia, Disdyakis triacontahedron.

Cf. A380981 (medium/short edge length ratio).
Cf. A020762, A379388, A379708, A379709, A379710, A379711, A380940, A380941, A380942.
Apart from leading digits the same as A176453, A134974 and A010476.

First[RealDigits[7/5 + 1/Sqrt[5], 10, 100]] (* Paolo Xausa, Feb 10 2025 *)

Equals 1/sqrt(5) + 7/5 = A020762 + 7/5.

A348757 Decimal expansion of the area of a regular pentagram inscribed in a unit-radius circle.

Original entry on oeis.org

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

Offset: 1

Amiram Eldar, Nov 12 2021

An algebraic number of degree 4. The smaller of the two positive roots of the equation 16*x^4 - 2500*x^2 + 3125 = 0.

			1.12256994144896343110486287949381696894803120580270...

Robert B. Banks, Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics, Princeton University Press, 2012, p. 15.

Herta T. Freitag, Problem 3855, School Science and Mathematics, Vol. 81, No. 4 (1981), p. 352; Solution to Problem 3855 by David A. Blaeuer, ibid., Vol. 82, No. 3 (1982), pp. 265-266.
Mathematics Stack Exchange, Area of a five pointed star, 2014.
Wikipedia, Pentagram.
Index entries for algebraic numbers, degree 4

Cf. A001622, A019845, A019916, A019952, A019970, A094874, A104955, A134974, A179050, A188593, A344172.

RealDigits[5*Sin[Pi/5]/GoldenRatio^2, 10, 100][[1]]

Equals 5*sin(Pi/5)/phi^2, where phi is the golden ratio (A001622).
Equals 5/(cot(Pi/5) + cot(Pi/10)).
Equals 10*tan(Pi/10)/(3 - tan(Pi/10)^2).
Equals (5/2)*sqrt((25 -11*sqrt(5))/2).
Equals 5*(5 - sqrt(5))/(4*sqrt(5 + 2*sqrt(5))) = A094874 * A179050 = 10 * A094874 / A344172.

cp's OEIS Frontend

A344212 Decimal expansion of 1 + 1/sqrt(5).

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A176453 Decimal expansion of 4+2*sqrt(5).

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A380982 Decimal expansion of the long/short edge length ratio of a disdyakis triacontahedron.

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A348757 Decimal expansion of the area of a regular pentagram inscribed in a unit-radius circle.

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