Jump to navigation Jump to search

General

Display information for equation id:math.220965.4 on revision:220965

* Page found: Surface area (eq math.220965.4)

(force rerendering)

Occurrences on the following pages:

Hash: c10abad78cf92d129f9f5a906d848ebf

TeX (original user input): 

 S_D: \vec{r}=\vec{r}(u,v), \quad (u,v)\in D

TeX (checked): 

S_{D}:{\vec {r}}={\vec {r}}(u,v),\quad (u,v)\in D

LaTeXML (experimental; uses MathML) rendering

MathML (4.997 KB / 994 B) :

S D : r → = r → ⁢ ( u , v ) , ( u , v ) ∈ D : subscript 𝑆 𝐷 formulae-sequence → 𝑟 → 𝑟 𝑢 𝑣 𝑢 𝑣 𝐷 {\displaystyle S_{D}:{\vec{r}}={\vec{r}}(u,v),\quad(u,v)\in D} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle S_{D}:{\vec{r}}={\vec{r}}(u,v),\quad(u,v)\in D}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">
      <msub id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml">
        <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">S</mi>
        <mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">D</mi>
      </msub>
      <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">:</mo>
      <mrow id="p1.1.m1.1.21.2" xref="p1.1.m1.1.21.2.1.cmml">
        <mrow id="p1.1.m1.1.21.2.2" xref="p1.1.m1.1.21.2.2.cmml">
          <mover accent="true" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">
            <mi id="p1.1.m1.1.4.2" xref="p1.1.m1.1.4.2.cmml">r</mi>
            <mo stretchy="false" id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">→</mo>
          </mover>
          <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">=</mo>
          <mrow id="p1.1.m1.1.21.2.2.1" xref="p1.1.m1.1.21.2.2.1.cmml">
            <mover accent="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
              <mi id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">r</mi>
              <mo stretchy="false" id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">→</mo>
            </mover>
            <mo id="p1.1.m1.1.21.2.2.1.1" xref="p1.1.m1.1.21.2.2.1.1.cmml">⁢</mo>
            <mrow id="p1.1.m1.1.21.2.2.1.2" xref="p1.1.m1.1.21.2.2.1.2.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.7" xref="p1.1.m1.1.21.2.2.1.2.1.cmml">(</mo>
              <mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">u</mi>
              <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.21.2.2.1.2.1.cmml">,</mo>
              <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">v</mi>
              <mo stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.21.2.2.1.2.1.cmml">)</mo>
            </mrow>
          </mrow>
        </mrow>
        <mo rspace="12.5pt" id="p1.1.m1.1.12" xref="p1.1.m1.1.21.2.1a.cmml">,</mo>
        <mrow id="p1.1.m1.1.21.2.3" xref="p1.1.m1.1.21.2.3.cmml">
          <mrow id="p1.1.m1.1.21.2.3.1" xref="p1.1.m1.1.21.2.3.1.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.14" xref="p1.1.m1.1.21.2.3.1.1.cmml">(</mo>
            <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">u</mi>
            <mo id="p1.1.m1.1.16" xref="p1.1.m1.1.21.2.3.1.1.cmml">,</mo>
            <mi id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">v</mi>
            <mo stretchy="false" id="p1.1.m1.1.18" xref="p1.1.m1.1.21.2.3.1.1.cmml">)</mo>
          </mrow>
          <mo id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">∈</mo>
          <mi id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">D</mi>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">
        <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">:</ci>
        <apply id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1">
          <csymbol cd="ambiguous" id="p1.1.m1.1.21.1.1.cmml" xref="p1.1.m1.1.21.1">subscript</csymbol>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑆</ci>
          <ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">𝐷</ci>
        </apply>
        <apply id="p1.1.m1.1.21.2.1.cmml" xref="p1.1.m1.1.21.2">
          <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.1a.cmml" xref="p1.1.m1.1.12">formulae-sequence</csymbol>
          <apply id="p1.1.m1.1.21.2.2.cmml" xref="p1.1.m1.1.21.2.2">
            <eq id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
            <apply id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">
              <ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">→</ci>
              <ci id="p1.1.m1.1.4.2.cmml" xref="p1.1.m1.1.4.2">𝑟</ci>
            </apply>
            <apply id="p1.1.m1.1.21.2.2.1.cmml" xref="p1.1.m1.1.21.2.2.1">
              <times id="p1.1.m1.1.21.2.2.1.1.cmml" xref="p1.1.m1.1.21.2.2.1.1"/>
              <apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
                <ci id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">→</ci>
                <ci id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">𝑟</ci>
              </apply>
              <interval closure="open" id="p1.1.m1.1.21.2.2.1.2.1.cmml" xref="p1.1.m1.1.21.2.2.1.2">
                <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">𝑢</ci>
                <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝑣</ci>
              </interval>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.21.2.3.cmml" xref="p1.1.m1.1.21.2.3">
            <in id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19"/>
            <interval closure="open" id="p1.1.m1.1.21.2.3.1.1.cmml" xref="p1.1.m1.1.21.2.3.1">
              <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">𝑢</ci>
              <ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">𝑣</ci>
            </interval>
            <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">𝐷</ci>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle S_{D}:{\vec{r}}={\vec{r}}(u,v),\quad(u,v)\in D}</annotation>
  </semantics>
</math>

SVG (8.878 KB / 3.118 KB) :

upper S Subscript upper D Baseline colon ModifyingAbove r With right-arrow equals ModifyingAbove r With right-arrow times left-parenthesis u comma v right-parenthesis comma left-parenthesis u comma v right-parenthesis element-of upper D

SVG (MathML can be enabled via browser plugin) rendering

MathML (1.401 KB / 417 B) :

S D : r → = r → ( u , v ) , ( u , v ) ∈ D {\displaystyle S_{D}:{\vec {r}}={\vec {r}}(u,v),\quad (u,v)\in D} 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle S_{D}:{\vec {r}}={\vec {r}}(u,v),\quad (u,v)\in D}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msub>
          <mi>S</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>D</mi>
          </mrow>
        </msub>
        <mo>:</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mrow class="MJX-TeXAtom-ORD">
            <mover>
              <mi>r</mi>
              <mo stretchy="false">&#x2192;<!-- → --></mo>
            </mover>
          </mrow>
        </mrow>
        <mo>=</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mrow class="MJX-TeXAtom-ORD">
            <mover>
              <mi>r</mi>
              <mo stretchy="false">&#x2192;<!-- → --></mo>
            </mover>
          </mrow>
        </mrow>
        <mo stretchy="false">(</mo>
        <mi>u</mi>
        <mo>,</mo>
        <mi>v</mi>
        <mo stretchy="false">)</mo>
        <mo>,</mo>
        <mspace width="1em" />
        <mo stretchy="false">(</mo>
        <mi>u</mi>
        <mo>,</mo>
        <mi>v</mi>
        <mo stretchy="false">)</mo>
        <mo>&#x2208;<!-- ∈ --></mo>
        <mi>D</mi>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle S_{D}:{\vec {r}}={\vec {r}}(u,v),\quad (u,v)\in D}</annotation>
  </semantics>
</math>

SVG (6.715 KB / 2.825 KB) :

{\displaystyle S_{D}:{\vec {r}}={\vec {r}}(u,v),\quad (u,v)\in D}

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Surface area page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Retrieved from "https://en.formulasearchengine.com/wiki/Special:FormulaInfo"