Difference between revisions of "Manuals/calci/TORUS"
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*For example of TORUS are rings, doughnuts, and bagels. | *For example of TORUS are rings, doughnuts, and bagels. | ||
*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>y(\theta,\phi)=(R+rCos\theta)Sin\phi</math> |
| − | <math>z(\theta,\phi)=r Sin\theta</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. | <math>\theta</math>,<math>\phi</math> are angles which make a full circle, so that their values start and end at the same point. | ||
Revision as of 13:55, 24 October 2017
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} 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 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}
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