GoldenAngle¶

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description¶

GoldenAngle
    is the golden angle (3 - Sqrt[5]) Pi = 2 Pi / GoldenRatio^2, with
    numerical value ~= 2.39996 radians (~= 137.5 degrees).
GoldenAngle is a mathematical constant: it has attributes Constant and
Protected, NumericQ[GoldenAngle] is True, and D[GoldenAngle, x] is 0.
N[GoldenAngle, prec] evaluates it to any precision.

Examples¶

No verified examples yet for this function.

Implementation notes¶

Attributes Constant, Protected. `Attributes[GoldenAngle] = {Constant,

Attributes: Constant, Protected.

Implementation status¶

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References¶

Source: src/info.c
Specification: docs/spec/builtins/mathematical-constants.md

Notes & additional examples¶

Worked examples¶

In[1]:= N[GoldenAngle]
Out[1]= 2.39996

In[1]:= N[GoldenAngle, 40]
Out[1]= 2.399963229728653322231555506633613853125

In[1]:= N[GoldenAngle/Degree, 30]
Out[1]= 137.5077640500378546463487396284

In[1]:= N[GoldenAngle - (3 - Sqrt[5]) Pi, 40]
Out[1]= 0.0

Notes¶

GoldenAngle is (3 - Sqrt[5]) Pi = 2 Pi / GoldenRatio^2, the angle that divides a full turn in the golden ratio — about 137.5 degrees, the divergence angle that governs optimal phyllotactic spiral packing in plants. Dividing by Degree shows the familiar 137.5..., and subtracting the closed form (3 - Sqrt[5]) Pi numerically returns 0.0. It is a protected Constant (so D[GoldenAngle, x] is 0) that N evaluates to any precision.