Translation for "pallokoordinaateissa" to english

Pallokoordinaateissa

• spherical coordinates
• in spherical coordinates

Translation examples

spherical coordinates

Jos taas toruksen uloimman pinnan sädettä merkitään p:llä ja sisimmän pinnan sädettä q:llä (niin että R = p + q 2 {\displaystyle R={\frac {p+q}{2}}} ja r = p − q 2 {\displaystyle r={\frac {p-q}{2}}} ), toruksen pinta-ala ja toroidin tilavuus on: A = 4 π 2 ( p + q 2 ) ( p − q 2 ) = π 2 ( p + q ) ( p − q ) V = 2 π 2 ( p + q 2 ) ( p − q 2 ) 2 = 1 4 π 2 ( p + q ) ( p − q ) 2 {\displaystyle {\begin{aligned}A&=4\pi ^{2}\left({\frac {p+q}{2}}\right)\left({\frac {p-q}{2}}\right)=\pi ^{2}(p+q)(p-q)\\V&=2\pi ^{2}\left({\frac {p+q}{2}}\right)\left({\frac {p-q}{2}}\right)^{2}={\tfrac {1}{4}}\pi ^{2}(p+q)(p-q)^{2}\end{aligned}}} Koska torus on kahden ympyrän tulo, sen pinnalla olevan pisteen sijainti voidaan ilmoittaa eräänlaisella muunnetulla versiolla pallokoordinaateista.
Expressing the surface area and the volume by the distance p of an outermost point on the surface of the torus to the center, and the distance q of an innermost point (so that R = p + q/2 and r = p − q/2), yields A = 4 π 2 ( p + q 2 ) ( p − q 2 ) = π 2 ( p + q ) ( p − q ) V = 2 π 2 ( p + q 2 ) ( p − q 2 ) 2 = 1 4 π 2 ( p + q ) ( p − q ) 2 {\displaystyle {\begin{aligned}A&=4\pi ^{2}\left({\frac {p+q}{2}}\right)\left({\frac {p-q}{2}}\right)=\pi ^{2}(p+q)(p-q)\\V&=2\pi ^{2}\left({\frac {p+q}{2}}\right)\left({\frac {p-q}{2}}\right)^{2}={\tfrac {1}{4}}\pi ^{2}(p+q)(p-q)^{2}\end{aligned}}} As a torus is the product of two circles, a modified version of the spherical coordinate system is sometimes used.