A230582 - OEIS

A230582

Decimal expansion of the ratio of height to width of the bounding rectangle of the national flag of Nepal, as defined in Schedule 1 of Article 5 of its Constitution.

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

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

OFFSET

1,2

COMMENTS

The red field of the Nepalese flag consists of two overlapping triangles:

A...D

|\ .

| \ .

| \.

| E-F

| \.

B---C

where C and F lie on a vertical line. There is a blue border around this field which makes point F extend slightly further than point C when the entire flag is considered, since angle AFE is smaller than angle ECB. - Jeremy Tan, Apr 06 2015

This constant is algebraic, specifically quartic. In particular it is the least root of 243356742235044x^4 - 1325568548812608x^3 + 2700899847521244x^2 - 2439951444086880x + 824634725389225. - Charles R Greathouse IV, Oct 24 2013

Denominator is 4506606337686 = 2 * 3 * 2791 * 13591 * 19801. - Charles R Greathouse IV, Jun 16 2020

REFERENCES

John D. Barrow, 100 Essential Things You Didn't Know about Math and the Arts, W. W. Norton & Company, 2015. See Chapter 26: Why the Nepal Flag is Unique, pp. 102-105.

Constitution of Nepal, Article 5, Schedule 1.

LINKS

Daniel Arribas, Table of n, a(n) for n = 1..250

Pawan Dhakal and Peter Doyle, Construction of the Flag of Nepal in the Conjugate Coordinate System using Mathematica.

Brady Haran and James Grime, The Most Mathematical Flag, Numberphile video, 2012.

0xc.de (pseudonymous owner "Achim"), Nationalflagge von Nepal (with derivation of ratio).

Wikipedia, Flag of Nepal.

Index entries for algebraic numbers, degree 4.

FORMULA

Equals (6136891429688-306253616715*sqrt(2)-(934861968+20332617192*sqrt(2)) * sqrt(118-48*sqrt(2)))/4506606337686.

EXAMPLE

1.219010337829452184570024869930988566...

MATHEMATICA

RealDigits[(6136891429688 - 306253616715*Sqrt[2] - (934861968+20332617192*Sqrt[2]) * Sqrt[118 - 48*Sqrt[2]])/4506606337686, 10, 120][[1]] (* Amiram Eldar, Apr 01 2026 *)

CROSSREFS

Sequence in context: A359625 A009349 A334254 * A011186 A388364 A395734

Adjacent sequences: A230579 A230580 A230581 * A230583 A230584 A230585

KEYWORD

nonn,cons

AUTHOR

Jeremy Tan, Oct 23 2013

STATUS

approved