Editing Number (section)

===Periods and exponential periods===
{{Main|Period (algebraic geometry)}}
A period is a complex number that can be expressed as an [[integral]] of an [[algebraic function]] over an algebraic [[Domain of a function|domain]]. The periods are a class of numbers which includes, alongside the algebraic numbers, many well known [[Mathematical constant|mathematical constants]] such as the [[Pi|number ''π'']]. The set of periods form a countable [[Ring (mathematics)|ring]] and bridge the gap between algebraic and transcendental numbers.<ref name=":1">{{Citation |last1=Kontsevich |first1=Maxim |title=Periods |date=2001 |work=Mathematics Unlimited — 2001 and Beyond |pages=771–808 |editor-last=Engquist |editor-first=Björn |url=https://link.springer.com/chapter/10.1007/978-3-642-56478-9_39 |access-date=2024-09-22 |place=Berlin, Heidelberg |publisher=Springer |language=en |doi=10.1007/978-3-642-56478-9_39 |isbn=978-3-642-56478-9 |last2=Zagier |first2=Don |editor2-last=Schmid |editor2-first=Wilfried}}</ref><ref>{{Cite web |last=Weisstein |first=Eric W. |title=Algebraic Period |url=https://mathworld.wolfram.com/AlgebraicPeriod.html |access-date=2024-09-22 |website=mathworld.wolfram.com |language=en}}</ref> 

The periods can be extended by permitting the integrand to be the product of an algebraic function and the [[Exponential function|exponential]] of an algebraic function. This gives another countable ring: the exponential periods. The [[E (mathematical constant)|number ''e'']] as well as [[Euler's constant]] are exponential periods.<ref name=":1" /><ref>{{Cite journal |last=Lagarias |first=Jeffrey C. |date=2013-07-19 |title=Euler's constant: Euler's work and modern developments |journal=Bulletin of the American Mathematical Society |volume=50 |issue=4 |pages=527–628 |doi=10.1090/S0273-0979-2013-01423-X |arxiv=1303.1856 |issn=0273-0979}}</ref>