Difference between revisions of "Manuals/calci/GOLDENRATIO"

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=GOLDENRATIO(phismall)=
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<div style="font-size:30px">'''GOLDENRATIO(phiSmall)'''</div><br/>
 
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*where <math>phiSmall</math> is the logical value TRUE or FALSE.
*where <math>phismall</math> is the logical value TRUE or FALSE.
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**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.
 
 
GOLDENRATIO() returns the golden ratio value.
 
  
 
== Description ==
 
== 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.
 
*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(&phi;)''' and its conjugate is represented as '''Phi (&Phi)'''.  
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*Golden ratio is represented as '''&phi;(phi or Smallphi)''' and its conjugate is represented as '''&Phi;(Phi or capitalphi)'''.  
 
*If 'a' and 'b' are two quantities with 'a>b', then
 
*If 'a' and 'b' are two quantities with 'a>b', then
  
  (&phi;) = <math>\frac{\(a + b)}{a}</math> = <math>\frac{\a}{b}</math>
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  &phi; = <math>\frac{(a + b)}{a}</math> = <math>\frac {a}{b}</math>
 
*Using quadratic formula, golden ratio is represented as -
 
*Using quadratic formula, golden ratio is represented as -
  
&phi; = <math>\frac{1+&sqrt; 5}{2}</math> = 1.618033988749895
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<math>\phi</math> = <math>\frac{(1 + \sqrt 5)}{2}</math> = 1.618033988749895  
  
&Phi; = <math>\frac{1-&sqrt; 5}{2}</math> = 0.6180339887498948
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<math>\Phi</math> = <math>\frac{(1 - \sqrt 5)}{2}</math> = -0.6180339887498948 (Absolute value 0.6180339887498948 is considered as capitalphi)
  
 
*Argument <math>phismall</math> 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.
 
*Argument <math>phismall</math> 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.
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GOLDENRATIO() ''returns 0.6180339887498948'', value of capitalphi &Phi;
 
GOLDENRATIO() ''returns 0.6180339887498948'', value of capitalphi &Phi;
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==Related Videos==
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{{#ev:youtube|5zosU6XTgSY|280|center|GOLDENRATIO}}
  
 
== See Also ==
 
== See Also ==
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*[http://en.wikipedia.org/wiki/Golden_ratio Golden Ratio]
 
*[http://en.wikipedia.org/wiki/Golden_ratio Golden Ratio]
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 17:25, 17 August 2018

GOLDENRATIO(phiSmall)


  • where 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 =  = 
  • Using quadratic formula, golden ratio is represented as -
 =  = 1.618033988749895 
 =  = -0.6180339887498948 (Absolute value 0.6180339887498948 is considered as capitalphi)
  • Argument 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 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

References