Manuals/calci/GOLDENRATIO

GOLDENRATIO(phiSmall)

• where 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 phiSmall} is the logical value TRUE or FALSE.

GOLDENRATIO() returns the ratio of the longer part divided by the smaller part is also equal to the whole length divided by the longer part.

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 φ(phi or Smallphi) and its conjugate is represented as Φ(Phi or capitalphi).
• If 'a' and 'b' are two quantities with 'a>b', then

φ = ${\frac {(a+b)}{a}}$ = 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 {a}{b}}

• Using quadratic formula, golden ratio is represented as -

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 \phi}
 = 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 

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 \Phi}
 = 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}}
 = -0.6180339887498948 (Absolute value 0.6180339887498948 is considered as capitalphi)

• Argument 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 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 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 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

Related Videos

GOLDENRATIO

See Also

• GOLDENANGLE

References

• Golden Ratio

• List of Main Z Functions

• Z3 home