A395397 - OEIS

A395397

Decimal expansion of the volume of the solid of revolution formed by rotating the loop part of a Folium of Descartes about its axis of symmetry.

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

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OFFSET

0,1

COMMENTS

The Folium of Descartes is a plane curve that can be described by x^3 + y^3 = 3*a*x*y. Here we take a = 1.

Its axis of symmetry is the line y = x.

REFERENCES

N. P. Bali and Usha Paul, A Textbook of Engineering Mathematics: for B.E., B.Tech. Semester I, Laxmi Publications (P) Ltd, 8th ed., 2014, pp. 139-140.

LINKS

Table of n, a(n) for n=0..104.

Doand A. Cole, The Mystery of the SOR.

Amiram Eldar, Illustration of the solid of revolution.

Eric Weisstein's World of Mathematics, Folium of Descartes.

Wikipedia, Folium of Descartes.

FORMULA

Equals (Pi/(6*sqrt(2))) * (8*log(2)-3).

EXAMPLE

0.942327120221980050937942470001364918699075701037367...

MATHEMATICA

RealDigits[(Pi/(6*Sqrt[2])) * (8*Log[2]-3), 10, 120][[1]]