Recursion

Guerino Mazzola; Maria Mannone; Yan Pang

doi:10.1007/978-3-319-42937-3_7

Recursion

Guerino Mazzola, Maria Mannone, Yan Pang

Music (Twin Cities)

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

Recursion is a technique to define concepts that depend on natural numbers. First, such a concept is defined for n = 0. Then, the concept for n is supposed to be defined, and we use the concept for n to define the concept for n+1. Therefore, it is defined for all natural numbers n. This is the idea of recursion, namely the definition by induction. We will prove that this mathematical process is possible. We then apply recursion to create musical compositions.

Original language	English (US)
Title of host publication	Computational Music Science
Publisher	Springer Nature
Pages	77-81
Number of pages	5
DOIs	https://doi.org/10.1007/978-3-319-42937-3_7
State	Published - 2016

Publication series

Name	Computational Music Science
ISSN (Print)	1868-0305
ISSN (Electronic)	1868-0313

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing Switzerland.

Keywords

Fibonacci Number
Golden Ratio
Natural Number
Recursive Function
Recursive Method

Publisher link

10.1007/978-3-319-42937-3_7

Find It

Find It at U of M Libraries

Cite this

@inbook{1aa39024594546d1933c2b1b2ae18812,

title = "Recursion",

abstract = "Recursion is a technique to define concepts that depend on natural numbers. First, such a concept is defined for n = 0. Then, the concept for n is supposed to be defined, and we use the concept for n to define the concept for n+1. Therefore, it is defined for all natural numbers n. This is the idea of recursion, namely the definition by induction. We will prove that this mathematical process is possible. We then apply recursion to create musical compositions.",

keywords = "Fibonacci Number, Golden Ratio, Natural Number, Recursive Function, Recursive Method",

author = "Guerino Mazzola and Maria Mannone and Yan Pang",

note = "Publisher Copyright: {\textcopyright} 2016, Springer International Publishing Switzerland.",

year = "2016",

doi = "10.1007/978-3-319-42937-3_7",

language = "English (US)",

series = "Computational Music Science",

publisher = "Springer Nature",

pages = "77--81",

booktitle = "Computational Music Science",

address = "United States",

}

TY - CHAP

T1 - Recursion

AU - Mazzola, Guerino

AU - Mannone, Maria

AU - Pang, Yan

PY - 2016

Y1 - 2016

N2 - Recursion is a technique to define concepts that depend on natural numbers. First, such a concept is defined for n = 0. Then, the concept for n is supposed to be defined, and we use the concept for n to define the concept for n+1. Therefore, it is defined for all natural numbers n. This is the idea of recursion, namely the definition by induction. We will prove that this mathematical process is possible. We then apply recursion to create musical compositions.

AB - Recursion is a technique to define concepts that depend on natural numbers. First, such a concept is defined for n = 0. Then, the concept for n is supposed to be defined, and we use the concept for n to define the concept for n+1. Therefore, it is defined for all natural numbers n. This is the idea of recursion, namely the definition by induction. We will prove that this mathematical process is possible. We then apply recursion to create musical compositions.

KW - Fibonacci Number

KW - Golden Ratio

KW - Natural Number

KW - Recursive Function

KW - Recursive Method

UR - http://www.scopus.com/inward/record.url?scp=85136709425&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85136709425&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-42937-3_7

DO - 10.1007/978-3-319-42937-3_7

M3 - Chapter

AN - SCOPUS:85136709425

T3 - Computational Music Science

SP - 77

EP - 81

BT - Computational Music Science

PB - Springer Nature

ER -

Recursion

Abstract

Publication series

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this