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 1-6 of 6 results.

A335928 Decimal expansion of the arclength on y = sin(x) from (0,0) to (Pi/4,sqrt(2)).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jul 01 2020

Keywords

Examples

			arclength = 1.05809550139256305772788939193594688774...

Crossrefs

Cf. A335929, A335930, A335931.

Programs

  • Mathematica
    r = NIntegrate[Sqrt[1 + Cos[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
RealDigits[r][[1]]

A335931 Decimal expansion of (1/Pi)*arclength on y = sin(x) from (0,0) to (Pi,0).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jul 03 2020

Keywords

Examples

			(arclength)/(segment length) = 1.21600672342497978031259272328085470564030...

Crossrefs

Cf. A335928, A335929, A335930, A335932.

Programs

  • Mathematica
    r = NIntegrate[Sqrt[1 + Cos[t]^2]/Pi, {t, 0, Pi}, WorkingPrecision -> 200]
RealDigits[r][[1]]

A335932 Decimal expansion of arclength on y = cos(x) from (0,1) to (Pi/4,sqrt(1/2)).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jul 03 2020

Keywords

Comments

This arclength is also the arclength on y = sin(x) from (Pi/4,sqrt(1/2)) to (Pi/2,1).

Examples

			arclength = 0.85200339312129295122449164914977475820649330754394...

Crossrefs

Cf. A335928, A335929, A335930, A335931.

Programs

  • Mathematica
    r = NIntegrate[Sqrt[1 + Sin[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
RealDigits[r][[1]]

A335957 Decimal expansion of s/c, where s = arclength on y = sin(x) from (0,0) to (Pi/4,sqrt(1/2)), and c = arclength on y = cos(x) from (0,1) to (Pi/4,sqrt(1/2)).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jul 03 2020

Keywords

Examples

			s/c = 1.24189118251777949328029742670369236529...
c/s = 0.80522352849999684548520974994993752239...
c-s = 0.20609210827127010650339774278617212954...

Crossrefs

Cf. A335928, A335929, A335930, A335931, A335932, A335958, A335959.

Programs

  • Mathematica
    r1 = NIntegrate[Sqrt[1 + Cos[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
r2 = NIntegrate[Sqrt[1 + Sin[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
r1/r2
r2/r1
r1 - r2
RealDigits[r1/r2][[1]]      (* A335957 *)
RealDigits[r2/r1][[1]]      (* A335958 *)
RealDigits[r1 - r2][[1]]    (* A335959 *)

A335958 Decimal expansion of c/s, where s = arclength on y = sin(x) from (0,0) to (Pi/4,sqrt(1/2)), and c = arclength on y = cos(x) from (0,1) to (Pi/4,sqrt(1/2)).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jul 03 2020

Keywords

Examples

			s/c = 1.24189118251777949328029742670369236529...
c/s = 0.80522352849999684548520974994993752239...
c-s = 0.20609210827127010650339774278617212954...

Crossrefs

Cf. A335928, A335929, A335930, A335931, A335932, A335957, A335959.

Programs

  • Mathematica
    r1 = NIntegrate[Sqrt[1 + Cos[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
r2 = NIntegrate[Sqrt[1 + Sin[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
r1/r2
r2/r1
r1 - r2
RealDigits[r1/r2][[1]]      (* A335957 *)
RealDigits[r2/r1][[1]]      (* A335958 *)
RealDigits[r1 - r2][[1]]    (* A335959 *)

A335959 Decimal expansion of s - c, where s = arclength on y = sin(x) from (0,0) to (Pi/4,sqrt(1/2)), and c = arclength on y = cos(x) from (0,1) to (Pi/4,sqrt(1/2)).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jul 03 2020

Keywords

Examples

			s/c = 1.24189118251777949328029742670369236529...
c/s = 0.80522352849999684548520974994993752239...
c-s = 0.20609210827127010650339774278617212954...

Crossrefs

Cf. A335928, A335929, A335930, A335931, A335932, A335957, A335958.

Programs

  • Mathematica
    r1 = NIntegrate[Sqrt[1 + Cos[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
r2 = NIntegrate[Sqrt[1 + Sin[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
r1/r2
r2/r1
r1 - r2
RealDigits[r1/r2][[1]]      (* A335957 *)
RealDigits[r2/r1][[1]]      (* A335958 *)
RealDigits[r1 - r2][[1]]    (* A335959 *)
Showing 1-6 of 6 results.

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