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Difference between revisions of "Manuals/calci/GOLDENRATIO"

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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.
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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.
  
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'''GOLDENRATIO'''(phismall)
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== Description ==
  
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where
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*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.
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*Golden ratio is represented as '''&phi;(phi or Smallphi)''' and its conjugate is represented as '''&Phi;(Phi or capitalphi)'''.
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*If 'a' and 'b' are two quantities with 'a>b', then
  
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'''phismall''' is true or false
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&phi; = <math>\frac{(a + b)}{a}</math> = <math>\frac {a}{b}</math>
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*Using quadratic formula, golden ratio is represented as -
  
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</div>
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<math>\phi</math> = <math>\frac{(1 + \sqrt 5)}{2}</math> = 1.618033988749895
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----
 
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GOLDENRATIO function returns goldenratio in smallphi  or capitalphi depending on the argument.
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<math>\Phi</math> = <math>\frac{(1 - \sqrt 5)}{2}</math> = -0.6180339887498948 (Absolute value 0.6180339887498948 is considered as capitalphi)
  
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</div>
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*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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----
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*If argument <math>phismall</math> is omitted, Calci assumes it as TRUE or 1 and displays the output as ''0.6180339887498948''.
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*If argument is invalid, Calci returns a #NULL error message.
  
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GOLDENRATIO returns goldenratio in smallphi if argument is not given.
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== Examples ==
  
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</div>
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GOLDENRATIO(TRUE) ''returns 0.6180339887498948'', value of capitalphi &Phi;
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----
 
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<div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">
 
  
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GOLDENRATIO
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GOLDENRATIO(1) ''returns 0.6180339887498948'', value of capitalphi &Phi;
  
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</div></div>
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GOLDENRATIO(FALSE) ''returns 1.618033988749895'', value of smallphi &phi;
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<div id="8SpaceContent" class="zcontent" align="left">
 
  
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Lets see an example in (Column2Row1)
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GOLDENRATIO() ''returns 0.6180339887498948'', value of capitalphi &Phi;
  
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<nowiki>=GOLDENANGLE(false)</nowiki>
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==Related Videos==
  
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Returns 0.618034 for GOLDENRATIO(false)
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{{#ev:youtube|5zosU6XTgSY|280|center|GOLDENRATIO}}
  
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Consider another example in (Column2Row2)
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== See Also ==
  
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<nowiki>=GOLDENRATIO(true)</nowiki>
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*[[Manuals/calci/GOLDENANGLE  | GOLDENANGLE]]
  
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Returns 1.618034 for =GOLDENRATIO(true)
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== References ==
  
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</div>
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*[http://en.wikipedia.org/wiki/Golden_ratio Golden Ratio]
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----
 
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<div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Syntax </div><div class="ZEditBox"><center></center></div></div>
 
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<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
 
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<div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div>
 
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<div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div>
 
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{| id="TABLE3" class="SpreadSheet blue"
 
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|+ Default Calci
 
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|- class="even"
 
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| class="sshl_f" | 0.618034
 
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<div id="2Space_Handle" class="zhandles" title="Click and Drag to resize CALCI Column/Row/Cell. It is EZ!"></div><div id="2Space_Copy" class="zhandles" title="Click and Drag over to AutoFill other cells."></div><div id="2Space_Drag" class="zhandles" title="Click and Drag to Move/Copy Area.">[[Image:copy-cube.gif]]  </div>
 
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</div>
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----
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 16:25, 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



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