A356418 Decimal expansion of sqrt(4/3 + 1/sqrt(3)).

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

Offset: 1

Author

Christoph B. Kassir, Aug 21 2022

Keywords

• nonn
• cons
• easy

Comments

This is the radius of the smallest circle containing a system of three unit squares which intersect at the vertices to form an equilateral triangle at the center.

Examples

			1.382274792696068482365108044918041903951415152171813...
		

Links

• Presh Talwalkar, Very few people solved this test problem from Australia, YouTube video, 2022.

Crossrefs

Cf. A002194, A020760.

Programs

Magma

Sqrt(4/3 + 1/Sqrt(3));

Maple

evalf(sqrt(4/3 + 1/sqrt(3)), 120);

Mathematica

RealDigits[Sqrt[4/3 + 1/Sqrt[3]], 10, 120][[1]]

Maxima

fpprec: 100$ ev(bfloat(sqrt(4/3 + 1/sqrt(3))));

PARI

sqrt(4/3 + 1/sqrt(3))