Bola pejal (matematika): Perbedaan antara revisi

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[[Berkas:Blue ball.png|thumb|Bola Dalam Matematika bukan dalam Geometri]]
Dalam [[matematika]], '''Bola''' adalah ruang yang dibatasi oleh volume bola tersebut yang disebut juga bola padat.<ref>[{{Cite book|last=Japan|first=Mathematical Society of|last2=Sūgakkai|first2=Nihon|date=1993|url=https://books.google.com.br/books?id=WHjO9K6xEm4C&lpg=PA555&ots=wdYXw-tmOy&dq=great%20circle%20great%20disk%20ball&pg=PA555#v=onepage&q=great%20circle%20great%20disk%20ball&f=false]|title=Encyclopedic Dictionary of Mathematics|publisher=MIT Press|isbn=978-0-262-59020-4|language=en}}</ref> Bisa berupa bola tertutup (termasuk titik batas yang membentuk bola) atau bola terbuka (tidak termasuk mereka).
 
== Dalam Ruang Eucliden ==
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<!--The {{mvar|n}}-dimensional volume of a Euclidean ball of radius {{mvar|R}} in {{mvar|n}}-dimensional Euclidean space is:--><ref>Equation 5.19.4, ''NIST Digital Library of Mathematical Functions.'' http://dlmf.nist.gov/,{{dead link|date=July 2016 |bot=InternetArchiveBot |fix-attempted=yes }} Release 1.0.6 of 2013-05-06.</ref>
:<math>V_n(R) = \frac{\pi^\frac{n}{2}}{\Gamma\left(\frac{n}{2} + 1\right)}R^n,</math>
<!--where&nbsp; {{math|Γ}} is [[Leonhard Euler]]'s [[gamma function]] (which can be thought of as an extension of the [[factorial]] function to fractional arguments). Using explicit formulas for [[particular values of the gamma function]] at the integers and half integers gives formulas for the volume of a Euclidean ball that do not require an evaluation of the gamma function. These are:-->
:<math>\begin{align}V_{2k}(R) &= \frac{\pi^k}{k!}R^{2k}\,,\\
V_{2k+1}(R) &= \frac{2^{k+1}\pi^k}{(2k+1)!!}R^{2k+1} = \frac{2(k!)(4\pi)^k}{(2k+1)!}R^{2k+1}\,.\end{align}</math>
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== Lihat pula ==
* [[Bola]] - dalam pengertian biasa
<br>
* [[BolaCakram (matematika)]]
* [[Disk (matematika)]]
* [[Bola formal]]
* [[Lingkungan (matematika)]]
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* [[Volume HiperBola]]
* [[Oktahedron]]
* [[Ruang EuclideanEuklides]]
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