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.

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A195397 Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(sqrt(3),sqrt(5),sqrt(8)).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 17 2011

Keywords

Comments

See A195284 for definitions and a general discussion.

Examples

			(C)=1.6117674029515574301961776191386099256...

Crossrefs

Cf. A195284.

Programs

  • Mathematica
    a = Sqrt[3]; b = Sqrt[5]; c = Sqrt[8];
f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%]    (* (A) A195395 *)
N[x2, 100]
RealDigits[%]    (* (B) A195396 *)
N[x3, 100]
RealDigits[%]    (* (C) A195397 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195398 *)

A195398 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(3),sqrt(5),sqrt(8) right triangle ABC.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 17 2011

Keywords

Comments

See A195284 for definitions and a general discussion.

Examples

			Philo(ABC,I)=0.6011263969176532516541263787772610806686403999...

Crossrefs

Cf. A195284.

Programs

  • Mathematica
    a = Sqrt[3]; b = Sqrt[5]; c = Sqrt[8];
f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%]    (* (A) A195395 *)
N[x2, 100]
RealDigits[%]    (* (B) A195396 *)
N[x3, 100]
RealDigits[%]    (* (C) A195397 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195398 *)

Extensions

a(99) corrected by Georg Fischer, Jul 18 2021

A195399 Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(sqrt(7),3,4).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 17 2011

Keywords

Comments

See A195284 for definitions and a general discussion.

Examples

			(A)=1.75938215709649255886516352490038207092333...

Links

Crossrefs

Cf. A195284, A195400, A195401, A195402.

Programs

  • Mathematica
    a = Sqrt[7]; b = 3; c = 4;
f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%]    (* (A) A195399 *)
N[x2, 100]
RealDigits[%]    (* (B) A195400 *)
N[x3, 100]
RealDigits[%]    (* (C) A195401 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195402 *)
  • PARI
    sqrt(8)*(7-sqrt(7))/7 \\ Charles R Greathouse IV, Nov 26 2024
  • PARI
    polrootsreal(49*x^4-896*x^2+2304)[3] \\ Charles R Greathouse IV, Nov 26 2024

A195400 Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(sqrt(7),3,4).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 17 2011

Keywords

Comments

See A195284 for definitions and a general discussion.

Examples

			(B)=1.80566491858054587933117899514765276...

Crossrefs

Cf. A195284.

Programs

  • Mathematica
    a = Sqrt[7]; b = 3; c = 4;
f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%]    (* (A) A195399 *)
N[x2, 100]
RealDigits[%]    (* (B) A195400 *)
N[x3, 100]
RealDigits[%]    (* (C) A195401 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195402 *)

A195401 Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(sqrt(7),3,4).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 17 2011

Keywords

Comments

See A195284 for definitions and a general discussion.

Examples

			(C)=2.32744382440084633678206000810685122318...

Crossrefs

Cf. A195284.

Programs

  • Mathematica
    a = Sqrt[7]; b = 3; c = 4;
f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%]    (* (A) A195399 *)
N[x2, 100]
RealDigits[%]    (* (B) A195400 *)
N[x3, 100]
RealDigits[%]    (* (C) A195401 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195402 *)

A195402 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(7),3,4 right triangle ABC.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 17 2011

Keywords

Comments

See A195284 for definitions and a general discussion.

Examples

			Philo(ABC,I)=0.6108897803863800074424128886740422330...

Crossrefs

Cf. A195284.

Programs

  • Mathematica
    a = Sqrt[7]; b = 3; c = 4;
f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%]    (* (A) A195399 *)
N[x2, 100]
RealDigits[%]    (* (B) A195400 *)
N[x3, 100]
RealDigits[%]    (* (C) A195401 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195402 *)

A195403 Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(r),r), where r=(1+sqrt(5))/2 (the golden ratio).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 17 2011

Keywords

Comments

See A195284 for definitions and a general discussion.

Examples

			(A)=0.69202867847165176790432874525629325200...

Crossrefs

Cf. A195284, A195404, A195405, A195406.

Programs

  • Mathematica
    a = 1; b = Sqrt[c]; c = (1 + Sqrt[5])/2;
f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%]    (* (A) A195403 *)
N[x2, 100]
RealDigits[%]    (* (B) A195404 *)
N[x3, 100]
RealDigits[%]    (* (C) A195405 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195406 *)

Extensions

a(99) corrected by Georg Fischer, Jul 18 2021

A195404 Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(r),r), where r=(1+sqrt(5))/2 (the golden ratio).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 17 2011

Keywords

Comments

See A195284 for definitions and a general discussion.

Examples

			(B)=0.72709206292807012052455723638058094...

Crossrefs

Cf. A195284.

Programs

  • Mathematica
    a = 1; b = Sqrt[c]; c = (1 + Sqrt[5])/2;
f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%]    (* (A) A195403 *)
N[x2, 100]
RealDigits[%]    (* (B) A195404 *)
N[x3, 100]
RealDigits[%]    (* (C) A195405 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195406 *)

Extensions

a(99) corrected by Georg Fischer, Jul 18 2021

A195405 Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(r),r), where r=(1+sqrt(5))/2 (the golden ratio).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 17 2011

Keywords

Comments

See A195284 for definitions and a general discussion.

Examples

			(C)=0.92487539105022513066262517351274541075260...

Crossrefs

Cf. A195284.

Programs

  • Mathematica
    a = 1; b = Sqrt[c]; c = (1 + Sqrt[5])/2;
f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%]    (* (A) A195403 *)
N[x2, 100]
RealDigits[%]    (* (B) A195404 *)
N[x3, 100]
RealDigits[%]    (* (C) A195405 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195406 *)

A195406 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of the right triangle ABC having sidelengths (a,b,c)=(1,sqrt(r),r), where r=(1+sqrt(5))/2 (the golden ratio).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 17 2011

Keywords

Comments

See A195284 for definitions and a general discussion.

Examples

			Philo(ABC,I)=0.6025613912861148617941572291168471786...

Crossrefs

Cf. A195284.

Programs

  • Mathematica
    a = 1; b = Sqrt[c]; c = (1 + Sqrt[5])/2;
f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%]    (* (A) A195403 *)
N[x2, 100]
RealDigits[%]    (* (B) A195404 *)
N[x3, 100]
RealDigits[%]    (* (C) A195405 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195406 *)

Extensions

a(99) corrected by Georg Fischer, Jul 18 2021
Previous Showing 41-50 of 94 results. Next

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