cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A019810 Decimal expansion of sine of 1 degree.

Original entry on oeis.org

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

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Author

N. J. A. Sloane

Keywords

Comments

An algebraic number of degree 48. - Charles R Greathouse IV, Apr 14 2014
This algebraic number has denominator 2, the least integer k > 0 such that k times the number is an algebraic integer. - Charles R Greathouse IV, Nov 12 2014
The Fifteenth Century Persian mathematician Jamshid Al-Kashi was the first to calculate the value of sine of one degree correct to ten sexagesimal places (17 decimal digits) in his Risala al-Watar wa'l Jaib. - Mohammad K. Azarian, Jan 14 2017
The minimal polynomial is 281474976710656 *x^48 - 3377699720527872 *x^46 + 18999560927969280 *x^44 - 66568831992070144 *x^42 + 162828875980603392 *x^40 - 295364007592722432 *x^38 + 411985976135516160 *x^36 - 452180272956309504 *x^34 + 396366279591591936 *x^32 - 280058255978266624 *x^30 + 160303703377575936 *x^28 - 74448984852135936 *x^26 + 28011510450094080 *x^24 - 8500299631165440 *x^22 + 2064791072931840 *x^20 - 397107008634880 *x^18 + 59570604933120 *x^16 - 6832518856704 *x^14 + 583456329728 *x^12 - 35782471680 *x^10 + 1497954816 *x^8 - 39625728 *x^6 + 579456 *x^4 - 3456 *x^2 + 1 (WolframAlpha). - Rick L. Shepherd, Apr 12 2017

Examples

			0.01745240643728351281941897851631...

References

  • Mohammad K. Azarian, Forty-Five Nested Equilateral Triangles and cosecant of 1 degree, Problem 813, College Mathematics Journal, Vol. 36, No. 5, November 2005, pp. 413-414. Solution published in Vol. 37, No. 5, November 2006, pp. 394-395.

Links

Crossrefs

Cf. A110937, A280188.

Programs

  • Mathematica
    Join[{0},RealDigits[N[Sin[Pi/180],200]][[1]]] (* and/or *)
Join[{0},RealDigits[N[Sin[1 Degree],200]][[1]]] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2011 *)
  • PARI
    sin(Pi/180)
  • PARI
    real((I^(89/90) - I^(91/90))/2) \\ (imaginary part is not exactly zero only because of finite precision) Rick L. Shepherd, Apr 12 2017

Formula

Equals sin(Pi/180) = cos(89*Pi/180) = (i^(89/90) - i^(91/90))/2 (the last from WolframAlpha, rearranged). - Rick L. Shepherd, Apr 12 2017

Extensions

More terms from James Sellers, Jan 19 2000

A280189 Version of sexagesimal expansion of sine of one degree given by the Persian mathematician Al-Kashi in the 15th Century.

Original entry on oeis.org

1, 2, 49, 43, 11, 14, 44, 16, 26, 17
Offset: 1

Views

Author

Mohammad K. Azarian, Dec 28 2016

Keywords

Comments

The fifteenth century Persian mathematician Jamshid Al-Kashi was the first to calculate the value of sine of one degree correct to ten sexagesimal places (17 decimal digits) in his Risala al-Watar wa'l Jaib.

Links

Crossrefs

Cf. A019810, A019812, A049469, A110937, A280188.

A280190 Base-60 (Babylonian or sexagesimal) expansion of sine of 3 degrees.

Original entry on oeis.org

3, 8, 24, 33, 59, 34, 28, 14, 50, 5, 28, 29, 38, 47, 51, 57, 24, 25, 56, 50, 24, 30, 4, 12, 1, 50, 22, 37, 14, 19, 57, 37, 6, 18, 54, 32, 55, 20, 41, 45, 16, 27, 55, 52, 52, 7, 9, 20, 25, 8, 58, 18, 22, 58, 32, 34, 3, 2, 15, 27, 36, 33, 23, 19, 12, 48, 0, 33, 42, 3, 6, 1, 37, 1, 19, 21, 55, 46, 56
Offset: 1

Views

Author

Mohammad K. Azarian, Jan 14 2017

Keywords

Comments

The Fifteenth Century Persian mathematician Jamshid Al-Kashi was the first to calculate the value of sine of one degree correct to ten sexagesimal places (17 decimal digits) from sine of 3 degrees in his Risala al-Watar wa'l Jaib.

Links

Crossrefs

Cf. A019810, A019812, A049469, A110937, A280188, A280189.

Programs

  • Mathematica
    RealDigits[Sin[3 Degrees], 60, 200][[1]]
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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