Pi Times: Difference between revisions

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 $\pi$ . 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 $\pi$ " appears frequently in mathematical formulas related to a circle or trigonometric functions while $\pi$ raised to some power is rare, which explains the design decision behind this function.

A circular apple pie

Examples

The value of $\pi$ 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)
Operators	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

@@ Line 11: / Line 11: @@
 </syntaxhighlight>
-As a pun, <syntaxhighlight lang=apl inline>○1</syntaxhighlight> is often called ''apple pie'', jokingly using an unconventional pronunciation of [[the name APL]] in conjunction with the [[wikipedia:homophone|homophone]]s ''pi''/''pie''.
+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 ==

Pi Times: Difference between revisions

Latest revision as of 09:20, 9 January 2024

Examples

External links

Documentation

Navigation menu

Search