

A344363


Decimal expansion of (5^(1/4) + 5^(3/4))/2.


1



2, 4, 1, 9, 5, 2, 5, 1, 5, 3, 0, 5, 1, 6, 6, 5, 3, 3, 0, 9, 6, 4, 0, 3, 2, 1, 8, 0, 2, 1, 7, 0, 7, 6, 5, 3, 8, 6, 5, 1, 8, 1, 7, 8, 5, 7, 9, 3, 8, 5, 4, 7, 0, 8, 4, 6, 8, 3, 2, 5, 5, 3, 8, 2, 8, 9, 5, 8, 8, 4, 0, 4, 2, 5, 3, 9, 8, 9, 9, 6, 8, 5, 7, 3, 5, 8, 0, 1, 5, 5, 0, 8, 2, 4, 1, 8, 4, 6, 7, 8, 4, 8, 7, 3, 8
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Solution for z in the system {x = 1/y + 1/z, y = x + 1/z, z = y + 1/x}. The corresponding values of x and y are (5^(1/4) + 5^(1/4))/2 and 5^(1/4).
The largest aspect ratio of a set of three rectangles which have the property that any two of them can be scaled, rotated, and joined at an edge to obtain a rectangle with the third aspect ratio. The other two aspect ratios are given in the comment above.


LINKS



FORMULA



EXAMPLE

2.419525153051665330964032180217076538651...


MATHEMATICA

RealDigits[(Surd[5, 4]+Surd[5^3, 4])/2, 10, 120][[1]] (* Harvey P. Dale, Jan 01 2023 *)


PROG

(PARI) my(c=250+150*quadgen(20)); a_vector(len) = digits(sqrtint(floor(c*100^(len2)))); \\ Kevin Ryde, May 28 2021


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



