A195284 -id:A195284 - cp's OEIS frontend

A195361 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)=(2,5,sqrt(29)).

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

Offset: 1

Clark Kimberling, Sep 16 2011

See A195284 for definitions and a general discussion.

			(C)=2.2837218307477570559504100423095635446269975...

Cf. A195284.

a = 2; b = 5; c = Sqrt[29]; 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) A195359 *)
N[x2, 100]
RealDigits[%]    (* (B) A195360 *)
N[x3, 100]
RealDigits[%]    (* (C) A195361 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (* Philo(ABC,I)  A195362 *)

A195362 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 2,5,sqrt(29) right triangle ABC.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Sep 16 2011

See A195284 for definitions and a general discussion.

			Philo(ABC,I)=0.4746287747584270516471193113995166804876...

Cf. A195284.

a = 2; b = 5; c = Sqrt[29]; 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) A195359 *)
N[x2, 100]
RealDigits[%]    (* (B) A195360 *)
N[x3, 100]
RealDigits[%]    (* (C) A195361 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (* Philo(ABC,I)  A195362 *)

A195365 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(2),sqrt(3),sqrt(5)).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Sep 16 2011

See A195284 for definitions and a general discussion.

			(A)=0.96627396157671295720938864900921248163444...

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

Cf. A195284, A195366, A195367, A195368.

a = Sqrt[2]; b = Sqrt[3]; c = Sqrt[5];
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) A195365 *)
N[x2, 100]
RealDigits[%]    (* (B) A195366 *)
N[x3, 100]
RealDigits[%]    (* (C) A195367 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]     (* Philo(ABC,I) A195368 *)

A195366 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(2),sqrt(3),sqrt(5)).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Sep 16 2011

See A195284 for definitions and a general discussion.

			(B)=1.007463748030051594292118840267066181580...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A195284.

a = Sqrt[2]; b = Sqrt[3]; c = Sqrt[5];
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) A195365 *)
N[x2, 100]
RealDigits[%]    (* (B) A195366 *)
N[x3, 100]
RealDigits[%]    (* (C) A195367 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (* Philo(ABC,I) A195368 *)

A195367 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(2),sqrt(3),sqrt(5)).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Sep 16 2011

See A195284 for definitions and a general discussion.

			(C)=1.2872120826147987661983905302731728582463923413314...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A195284.

a = Sqrt[2]; b = Sqrt[3]; c = Sqrt[5];
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) A195365 *)
N[x2, 100]
RealDigits[%]    (* (B) A195366 *)
N[x3, 100]
RealDigits[%]    (* (C) A195367 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (* Philo(ABC,I) A195368 *)

A195368 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(2),sqrt(3),sqrt(5) right triangle ABC.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Sep 16 2011

See A195284 for definitions and a general discussion.

			Philo(ABC,I)=0.6058618423612399338566241911182750750678...

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

Cf. A195284.

a = Sqrt[2]; b = Sqrt[3]; c = Sqrt[5];
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) A195365 *)
N[x2, 100]
RealDigits[%]    (* (B) A195366 *)
N[x3, 100]
RealDigits[%]    (* (C) A195367 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (* Philo(ABC,I) A195368 *)

A195369 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(2),sqrt(3)).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Sep 17 2011

See A195284 for definitions and a general discussion.

			(A)=0.7157901359899149545954926723334324945663...

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

Cf. A195284, A195370, A195371, A195372.

a = 1; b = Sqrt[2]; c = Sqrt[3];
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) A195369 *)
N[x2, 100]
RealDigits[%]    (* (B) A195370 *)
N[x3, 100]
RealDigits[%]    (* (C) A195371 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (* Philo(ABC,I) A195372 *)

A195370 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(2),sqrt(3)).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Sep 17 2011

See A195284 for definitions and a general discussion.

			(B)=0.76813743261553676070153452111928795509267198845...

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

Cf. A195284, A195369, A195371, A195372.

a = 1; b = Sqrt[2]; c = Sqrt[3];
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) A195369 *)
N[x2, 100]
RealDigits[%]    (* (B) A195370 *)
N[x3, 100]
RealDigits[%]    (* (C) A195371 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (* Philo(ABC,I) A195372 *)

A195371 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(2),sqrt(3)).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Sep 17 2011

See A195284 for definitions and a general discussion.

			(C)=0.96472381958991695060440464950380668660...

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

Cf. A195284, A195369, A195370, A195372.

a = 1; b = Sqrt[2]; c = Sqrt[3];
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) A195369 *)
N[x2, 100]
RealDigits[%]    (* (B) A195370 *)
N[x3, 100]
RealDigits[%]    (* (C) A195371 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (* Philo(ABC,I) A195372 *)

A195372 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,sqrt(2),sqrt(3) right triangle ABC.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Sep 17 2011

See A195284 for definitions and a general discussion.

			Philo(ABC,I)=0.590568080015997134374704644164650566944103294...

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

Cf. A195284, A195369, A195370, A195371.

a = 1; b = Sqrt[2]; c = Sqrt[3];
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) A195369 *)
N[x2, 100]
RealDigits[%]    (* (B) A195370 *)
N[x3, 100]
RealDigits[%]    (* (C) A195371 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (* Philo(ABC,I) A195372 *)

cp's OEIS Frontend

A195361 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)=(2,5,sqrt(29)).

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Mathematica

A195362 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 2,5,sqrt(29) right triangle ABC.

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Mathematica

A195365 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(2),sqrt(3),sqrt(5)).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A195366 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(2),sqrt(3),sqrt(5)).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A195367 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(2),sqrt(3),sqrt(5)).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A195368 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(2),sqrt(3),sqrt(5) right triangle ABC.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A195369 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(2),sqrt(3)).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A195370 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(2),sqrt(3)).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A195371 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(2),sqrt(3)).