Difference between revisions of "Manuals/calci/TORUS"
(Created page with "<div style="font-size:30px">'''TORUS (Radius,TubeRadius,w1) '''</div><br/> *<math>Radius</math> and <math>TubeRadius</math> are radius value of the circle. ==Description== *T...") |
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*A torus can be defined parametrically by: | *A torus can be defined parametrically by: | ||
<math>x(\theta,\phi)=(R+rCos\theta)Cos\phi</math> | <math>x(\theta,\phi)=(R+rCos\theta)Cos\phi</math> | ||
| + | <math>y(\theta,\phi)=(R+rCos\theta)Sin\phi</math> | ||
| + | <math>z(\theta,\phi)=r Sin\theta</math> | ||
where | where | ||
| − | + | <math>\theta</math>,<math>\phi</math> are angles which make a full circle, so that their values start and end at the same point. | |
| − | R is the distance from the center of the tube to the center of the torus | + | *<math>R</math> is the distance from the center of the tube to the center of the torus. |
| − | r is the radius of the tube. | + | *<math>r</math> is the radius of the tube. |
| − | R is known as the | + | *<math>R</math> is known as the "major radius" and <math>r</math> is known as the "minor radius". |
| + | *The ratio R divided by r is known as the aspect ratio. | ||
| + | *The typical doughnut confectionery has an aspect ratio of about 3 to 2. | ||
| + | |||
| + | ==Examples== | ||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/FRACTAL | FRACTAL ]] | ||
| + | *[[Manuals/calci/LISSAJOUS | LISSAJOUS ]] | ||
| + | *[[Manuals/calci/SURFACEGRAPH| SURFACEGRAPH ]] | ||
| + | |||
| + | ==References== | ||
| + | *[https://en.wikipedia.org/wiki/Torus Torus] | ||
| + | |||
| + | |||
| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | *[[ Z3 | Z3 home ]] | ||
Revision as of 12:54, 24 October 2017
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Radius} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle TubeRadius} are radius value of the circle.
Description
- This function shows the Torus for the given value.
- In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle TORUS (Radius,TubeRadius,w1)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Radius} is the radius value of the bigger circle.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle TubeRadius} is the radius value of the smaller circle.
- A torus is a surface of revolution generated by revolving a circle in three dimensional space about an axis co planar with the circle. *If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution.
- For example of TORUS are rings, doughnuts, and bagels.
- A torus can be defined parametrically by:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x(\theta,\phi)=(R+rCos\theta)Cos\phi} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y(\theta,\phi)=(R+rCos\theta)Sin\phi} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z(\theta,\phi)=r Sin\theta} where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta} ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi} are angles which make a full circle, so that their values start and end at the same point.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R} is the distance from the center of the tube to the center of the torus.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} is the radius of the tube.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R} is known as the "major radius" and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} is known as the "minor radius".
- The ratio R divided by r is known as the aspect ratio.
- The typical doughnut confectionery has an aspect ratio of about 3 to 2.
Examples
See Also
References