Jump to navigation Jump to search

General

Display information for equation id:math.223722.1 on revision:223722

* Page found: Torus (eq math.223722.1)

(force rerendering)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: b98ecbcb75b9522f21fd32b419b06521

TeX (original user input):

y(\theta, \varphi) = (R + r \cos \theta) \sin{\varphi}

TeX (checked):

y(\theta ,\varphi )=(R+r\cos \theta )\sin {\varphi }

LaTeXML (experimental; uses MathML) rendering

MathML (4.342 KB / 846 B) :

y ( θ , φ ) = ( R + r cos θ ) sin φ 𝑦 𝜃 𝜑 𝑅 𝑟 𝜃 𝜑 {\displaystyle{\displaystyle y(\theta,\varphi)=(R+r\cos\theta)\sin{\varphi}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle y(\theta,\varphi)=(R+r\cos\theta)\sin{\varphi}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">
      <mrow id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">
        <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">y</mi>
        <mo id="p1.1.m1.1.17.1.1" xref="p1.1.m1.1.17.1.1.cmml"></mo>
        <mrow id="p1.1.m1.1.17.1.2" xref="p1.1.m1.1.17.1.2.1.cmml">
          <mo stretchy="false" id="p1.1.m1.1.2" xref="p1.1.m1.1.17.1.2.1.cmml">(</mo>
          <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">θ</mi>
          <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.17.1.2.1.cmml">,</mo>
          <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">φ</mi>
          <mo stretchy="false" id="p1.1.m1.1.6" xref="p1.1.m1.1.17.1.2.1.cmml">)</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">=</mo>
      <mrow id="p1.1.m1.1.17.2" xref="p1.1.m1.1.17.2.cmml">
        <mrow id="p1.1.m1.1.17.2.2" xref="p1.1.m1.1.17.2.2.2.cmml">
          <mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.17.2.2.2.cmml">(</mo>
          <mrow id="p1.1.m1.1.17.2.2.2" xref="p1.1.m1.1.17.2.2.2.cmml">
            <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">R</mi>
            <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">+</mo>
            <mrow id="p1.1.m1.1.17.2.2.2.1" xref="p1.1.m1.1.17.2.2.2.1.cmml">
              <mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">r</mi>
              <mo id="p1.1.m1.1.17.2.2.2.1.1" xref="p1.1.m1.1.17.2.2.2.1.1.cmml"></mo>
              <mrow id="p1.1.m1.1.17.2.2.2.1.2" xref="p1.1.m1.1.17.2.2.2.1.2.cmml">
                <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">cos</mi>
                <mo id="p1.1.m1.1.17.2.2.2.1.2a" xref="p1.1.m1.1.17.2.2.2.1.2.cmml"></mo>
                <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">θ</mi>
              </mrow>
            </mrow>
          </mrow>
          <mo stretchy="false" id="p1.1.m1.1.14" xref="p1.1.m1.1.17.2.2.2.cmml">)</mo>
        </mrow>
        <mo id="p1.1.m1.1.17.2.1" xref="p1.1.m1.1.17.2.1.cmml"></mo>
        <mrow id="p1.1.m1.1.17.2.3" xref="p1.1.m1.1.17.2.3.cmml">
          <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">sin</mi>
          <mo id="p1.1.m1.1.17.2.3a" xref="p1.1.m1.1.17.2.3.cmml"></mo>
          <mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">φ</mi>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">
        <eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
        <apply id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">
          <times id="p1.1.m1.1.17.1.1.cmml" xref="p1.1.m1.1.17.1.1"/>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑦</ci>
          <interval closure="open" id="p1.1.m1.1.17.1.2.1.cmml" xref="p1.1.m1.1.17.1.2">
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝜃</ci>
            <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝜑</ci>
          </interval>
        </apply>
        <apply id="p1.1.m1.1.17.2.cmml" xref="p1.1.m1.1.17.2">
          <times id="p1.1.m1.1.17.2.1.cmml" xref="p1.1.m1.1.17.2.1"/>
          <apply id="p1.1.m1.1.17.2.2.2.cmml" xref="p1.1.m1.1.17.2.2">
            <plus id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10"/>
            <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝑅</ci>
            <apply id="p1.1.m1.1.17.2.2.2.1.cmml" xref="p1.1.m1.1.17.2.2.2.1">
              <times id="p1.1.m1.1.17.2.2.2.1.1.cmml" xref="p1.1.m1.1.17.2.2.2.1.1"/>
              <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">𝑟</ci>
              <apply id="p1.1.m1.1.17.2.2.2.1.2.cmml" xref="p1.1.m1.1.17.2.2.2.1.2">
                <cos id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12"/>
                <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">𝜃</ci>
              </apply>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.17.2.3.cmml" xref="p1.1.m1.1.17.2.3">
            <sin id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15"/>
            <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">𝜑</ci>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle y(\theta,\varphi)=(R+r\cos\theta)\sin{\varphi}}}</annotation>
  </semantics>
</math>

SVG (10.297 KB / 3.96 KB) :

y times left-parenthesis theta comma phi right-parenthesis equals left-parenthesis upper R plus r times cosine theta right-parenthesis times sine phi

MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple: y*(theta , varphi)=(R + r*cos(theta))* sin(varphi)

Information about the conversion process:

\cos: Cosine; Example: \cos@@{z}

Will be translated to: cos($0)

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E2

Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos


\sin: Sine; Example: \sin@@{z}

Will be translated to: sin($0)

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E1

Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin



Translation to Mathematica

In Mathematica: y*(\[Theta], \[CurlyPhi])=(R + r*Cos[\[Theta]])* Sin[\[CurlyPhi]]

Information about the conversion process:

\cos: Cosine; Example: \cos@@{z}

Will be translated to: Cos[$0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E2

Mathematica: https://reference.wolfram.com/language/ref/Cos.html


\sin: Sine; Example: \sin@@{z}

Will be translated to: Sin[$0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E1

Mathematica: https://reference.wolfram.com/language/ref/Sin.html



Similar pages

Calculated based on the variables occurring on the entire Torus page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results