Manuals/calci/GOLDENRATIO

GOLDENRATIO(phismall)

• where $phismall$ is the logical value TRUE or FALSE.

GOLDENRATIO() returns the golden ratio value.

Description

• Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
• Golden ratio is represented as phi(φ) and its conjugate is represented as Phi (&Phi).
• If 'a' and 'b' are two quantities with 'a>b', then

(φ) = Failed to parse (syntax error): {\displaystyle \frac{\(a + b)}{a}}
 = Failed to parse (unknown function "\a"): {\displaystyle \frac{\a}{b}}

• Using quadratic formula, golden ratio is represented as -

φ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1+&sqrt; 5}{2}} = 1.618033988749895

Φ = Failed to parse (syntax error): {\displaystyle \frac{1-&sqrt; 5}{2}} = 0.6180339887498948

• Argument $phismall$ can be logical values TRUE (or 1) or FALSE (or 0). Any other argument values are ignored and Calci assumes it to be TRUE or 1.
• If argument $phismall$ is omitted, Calci assumes it as TRUE or 1 and displays the output as 0.6180339887498948.
• If argument is invalid, Calci returns a #NULL error message.

Examples

GOLDENRATIO(TRUE) returns 0.6180339887498948, value of capitalphi Φ

GOLDENRATIO(1) returns 0.6180339887498948, value of capitalphi Φ

GOLDENRATIO(FALSE) returns 1.618033988749895, value of smallphi φ

GOLDENRATIO() returns 0.6180339887498948, value of capitalphi Φ

See Also

• GOLDENANGLE

References

• Golden Ratio