Pi Times: Difference between revisions

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{{Built-in|Pi Times|○}} is a [[monadic]] [[scalar function]] which gives the [[argument]] [[times]] the mathematical constant [[wikipedia:pi|<math>\pi</math>]]. It shares the [[glyph]] <source lang=apl inline>○</source> with the dyadic arithmetic function [[Circular]]. The phrase "some value times <math>\pi</math>" appears frequently in mathematical formulas related to a [[wikipedia:circle|circle]] or [[wikipedia:trigonometric functions|trigonometric functions]] while <math>\pi</math> raised to some [[power]] is rare, which explains the design decision behind this function.
{{Built-in|Pi Times|○}} is a [[monadic]] [[scalar function]] which gives the [[argument]] [[times]] the mathematical constant [[wikipedia:pi|pi]] <math>\pi</math>. Its [[glyph]] <syntaxhighlight lang=apl inline>○</syntaxhighlight>, which is shared with the dyadic arithmetic function [[Circular]], alludes to pi being the ratio of a circle's circumference to its diameter. The phrase "some value times <math>\pi</math>" appears frequently in mathematical formulas related to a [[wikipedia:circle|circle]] or [[wikipedia:trigonometric functions|trigonometric functions]] while <math>\pi</math> raised to some [[power]] is rare, which explains the design decision behind this function.


[[File:Applepie.jpg|thumb|right|A circular apple pie]]
== Examples ==
== Examples ==


The value of <math>\pi</math> can be obtained by giving the argument of 1.
The value of <math>\pi</math> can be obtained by giving the argument of 1.


<source lang=apl>
<syntaxhighlight lang=apl>
       ○1
       ○1
3.141592654
3.141592654
</source>
</syntaxhighlight>
 
As a pun, <syntaxhighlight lang=apl inline>○1</syntaxhighlight> is often called ''apple pie'', jokingly using [[Humour#Apples|an unconventional pronunciation]] of [[the name APL]] in conjunction with the [[wikipedia:homophone|homophone]]s ''pi''/''pie''.


== External links ==
== External links ==
Line 14: Line 17:
=== Documentation ===
=== Documentation ===


* [http://help.dyalog.com/latest/#Language/Primitive%20Functions/Pi%20Times.htm Dyalog]
* [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Pi%20Times.htm Dyalog]
* [http://microapl.com/apl_help/ch_020_020_230.htm APLX]
* [http://microapl.com/apl_help/ch_020_020_230.htm APLX]
* [https://www.jsoftware.com/help/dictionary/dodot.htm J Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/odot NuVoc]
* [https://www.jsoftware.com/help/dictionary/dodot.htm J Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/odot NuVoc]
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]

Latest revision as of 09:20, 9 January 2024

○

Pi Times (○) is a monadic scalar function which gives the argument times the mathematical constant pi . Its glyph ○, which is shared with the dyadic arithmetic function Circular, alludes to pi being the ratio of a circle's circumference to its diameter. The phrase "some value times " appears frequently in mathematical formulas related to a circle or trigonometric functions while raised to some power is rare, which explains the design decision behind this function.

A circular apple pie

Examples

The value of can be obtained by giving the argument of 1. 

      ○1
3.141592654

As a pun, ○1 is often called apple pie, jokingly using an unconventional pronunciation of the name APL in conjunction with the homophones pi/pie.

External links

Documentation

APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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