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Documentation on polygonal numbers

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Jens Axel Søgaard 2012-10-16 16:53:06 +02:00 committed by Neil Toronto
parent f68cc0ada6
commit 00a886ea0c
1 changed files with 46 additions and 2 deletions
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48
collects/math/scribblings/math-number-theory.scrbl
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@ -20,7 +20,7 @@
(parameterize ([sandbox-output 'string]
[sandbox-error-output 'string])
(make-evaluator 'racket)))
@;(interaction-eval #:eval math-eval (require math))
;(interaction-eval #:eval math-eval (require racket math))
@title[#:tag "number-theory" #:style '(toc)]{Number Theory}
@ -446,7 +446,6 @@ Note: The function @racket[divisor-sum] is multiplicative.
(eulerian-number 5 2)]
}
@defproc[(fibonacci [n Natural]) natural?]{
Returns the @racket[n]th Fibonacci number.
Definition:
@ -507,4 +506,49 @@ Note: The function @racket[divisor-sum] is multiplicative.
(multinomial 5 3 2)]
}
@defproc[(partition-count [n Natural]) natural?]{
Returns the number of partitions of @racket[n].
A partition of a positive integer @racket[n] is a way
of writing @racket[n] as a sum of positive integers.
The number 3 has the partitions @math-style{1+1+1, 1+2, 3}.
See @url{http://en.wikipedia.org/wiki/Partition_(number_theory)}.
@interaction[(require math racket)
(partition-count 3)
(partition-count 4)]
}
@; ----------------------------------------
@section[#:tag "special_numbers"]{Special Numbers}
@subsection{Polygonal Numbers}
@defproc[(triangle? [n Natural]) boolean?]{}
@defproc[(square? [n Natural]) boolean?]{}
@defproc[(pentagonal? [n Natural]) boolean?]{}
@defproc[(hexagonal? [n Natural]) boolean?]{}
@defproc[(heptagonal? [n Natural]) boolean?]{}
@defproc[(octagonal? [n Natural]) boolean?]{
The functions
@racket[triangle?], @racket[square?], @racket[pentagonal?],
@racket[hexagonal?],@racket[heptagonal?] and @racket[octagonal?]
checks whether the input is a polygonal number of the types
triangle, square, pentagonal, hexagonal, heptagonal and octogonal
respectively.
}
@defproc[(triangle [n Natural]) natural?]{}
@defproc[(sqr [n Natural]) natural?]{}
@defproc[(pentagonal [n Natural]) natural?]{}
@defproc[(hexagonal [n Natural]) natural?]{}
@defproc[(heptagonal [n Natural]) natural?]{}
@defproc[(octagonal [n Natural]) natural?]{
The functions @racket[triangle], @racket[sqr], @racket[pentagonal],
@racket[hexagonal],@racket[heptagonal] and @racket[octagonal]
return the @racket[n]th polygonal number of the corresponding
type of polygonal number.
}
@(close-eval untyped-eval)