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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A195477 Decimal expansion of shortest length, (C), of segment from side CA through centroid to side CB in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(3),2).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 19 2011

Keywords

Comments

See A195304 for definitions and a general discussion.

Examples

			(C)=0.98865926298193884171309586388382524030...

Crossrefs

Cf. A195304.

Programs

  • Mathematica
    a = 1; b = Sqrt[3]; h = 2 a/3; k = b/3;
f[t_] := (t - a)^2 + ((t - a)^2) ((a*k - b*t)/(a*h - a*t))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f1 = (f[t])^(1/2) /. Part[s, 4]
RealDigits[%, 10, 100] (* (A) A195575 *)
f[t_] := (t - a)^2 + ((t - a)^2) (k/(h - t))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f2 = (f[t])^(1/2) /. Part[s, 4]
RealDigits[%, 10, 100] (* (B) A195576 *)
f[t_] := (b*t/a)^2 + ((b*t/a)^2) ((a*h - a*t)/(b*t - a*k))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f3 = (f[t])^(1/2) /. Part[s, 4]
RealDigits[%, 10, 100] (* (C) A195577 *)
c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
RealDigits[%, 10, 100] (* Philo(ABC,G) A195578 *)

A195478 Decimal expansion of normalized Philo sum, Philo(ABC,G), where G=centroid of the 1,sqrt(3),2 right triangle ABC.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 19 2011

Keywords

Comments

See A195304 for definitions and a general discussion.

Examples

			Philo(ABC,G)=0.61384172539418681066036724600139402660748...

Crossrefs

Cf. A195304.

Programs

  • Mathematica
    a = 1; b = Sqrt[3]; h = 2 a/3; k = b/3;
f[t_] := (t - a)^2 + ((t - a)^2) ((a*k - b*t)/(a*h - a*t))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f1 = (f[t])^(1/2) /. Part[s, 4]
RealDigits[%, 10, 100] (* (A) A195575 *)
f[t_] := (t - a)^2 + ((t - a)^2) (k/(h - t))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f2 = (f[t])^(1/2) /. Part[s, 4]
RealDigits[%, 10, 100] (* (B) A195576 *)
f[t_] := (b*t/a)^2 + ((b*t/a)^2) ((a*h - a*t)/(b*t - a*k))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f3 = (f[t])^(1/2) /. Part[s, 4]
RealDigits[%, 10, 100] (* (C) A195577 *)
c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
RealDigits[%, 10, 100] (* Philo(ABC,G) A195578 *)

A195475 Decimal expansion of shortest length, (A), of segment from side AB through centroid to side AC in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(3),2) and angles 30,60,90.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 19 2011

Keywords

Comments

See A195304 for definitions and a general discussion.

Examples

			(A)=0.643846313298743531569372107211809720...

Crossrefs

Cf. A195304, A195476, A195477, A195478.

Programs

  • Mathematica
    a = 1; b = Sqrt[3]; h = 2 a/3; k = b/3;
f[t_] := (t - a)^2 + ((t - a)^2) ((a*k - b*t)/(a*h - a*t))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f1 = (f[t])^(1/2) /. Part[s, 4]
RealDigits[%, 10, 100] (* (A) A195575 *)
f[t_] := (t - a)^2 + ((t - a)^2) (k/(h - t))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f2 = (f[t])^(1/2) /. Part[s, 4]
RealDigits[%, 10, 100] (* (B) A195576 *)
f[t_] := (b*t/a)^2 + ((b*t/a)^2) ((a*h - a*t)/(b*t - a*k))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f3 = (f[t])^(1/2) /. Part[s, 4]
RealDigits[%, 10, 100] (* (C) A195577 *)
c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
RealDigits[%, 10, 100] (* Philo(ABC,G) A195578 *)
Previous Showing 61-63 of 63 results.

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