The On-Line Encyclopedia of Integer Sequences (OEIS)

A343236 revision #9

A343236

Decimal expansion of (A010476 - 3*A228496)/(4*Pi) - 1/8.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

-1,1

COMMENTS

This constant gives the ratio of the area between three touching circles, one with half of the radius of the two others, and the area of one of the large circular disks.

See A343235 for the same problem with three identical circular disks, where also links on the Descartes-Steiner five circle theorem and the Soddy circles are given.

The isosceles triangle with the centers of the circles as corners has two angles alpha = arctan(sqrt(5)/2) = A228496 (about 48.2 degrees).

The ratio of the perimeter of the boundary of this circular cuspodial triangle and the perimeter of the large circle is alpha/(2*Pi) + 1/4 = 0.3838602364...

The radii of the inner and outer Soddy circles, normalized to the radius r of one of the two large circles are s_i = S_i/r = -3/2 + phi = A176055 - 2 = 0.1180339887... and s_o = S_o/r = 1/2 + phi = A176055 = 2 + s_i = 2.1180339887... Here phi = A001622 (golden ratio).

LINKS

Table of n, a(n) for n=-1..74.

FORMULA

Equals A/(Pi*r^2) = (sqrt(5)/Pi - 3*arctan(sqrt(5)/2)/(2*Pi) - 1/4)/2, where A is the area between three mutually touching circular disks with radii r, r, and r/2 (in some length unit).

Equals sqrt(5)/(2*Pi) - 3*A228496/(4*Pi) - 1/8.

EXAMPLE

0.03009091710766602117945599124597761...

CROSSREFS

Cf. A001622, A010476, A176055, A228496, A343235.

Sequence in context: A166244 A022001 A265832 * A363767 A011073 A200287

Adjacent sequences: A343233 A343234 A343235 * A343237 A343238 A343239

KEYWORD

nonn,easy,cons

AUTHOR

Wolfdieter Lang, Apr 20 2021

STATUS

proposed