Manuals/calci/GOLDENRATIO

GOLDENRATIO(phiSmall)

• where $phiSmall$ 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 = ${\frac {(a+b)}{a}}$ = ${\frac {a}{b}}$

• Using quadratic formula, golden ratio is represented as -

$\phi$ = ${\frac {(1+{\sqrt {5}})}{2}}$ = 1.618033988749895 

$\Phi$ = ${\frac {(1-{\sqrt {5}})}{2}}$ = -0.6180339887498948 (Absolute value 0.6180339887498948 is considered as capitalphi)

• 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

Related Videos

GOLDENRATIO

See Also

• GOLDENANGLE

References

• Golden Ratio

• List of Main Z Functions

• Z3 home