Shear transformation: Difference between revisions
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A WASSERMANN (talk | contribs) No edit summary |
A WASSERMANN (talk | contribs) No edit summary |
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\varphi: {\cal A}(\mathbb{R}^2) \to {\cal A}(\mathbb{R}^2), \; x \mapsto \begin{pmatrix}1 & 1 \\ 0& 1\end{pmatrix} | \varphi: {\cal A}(\mathbb{R}^2) \to {\cal A}(\mathbb{R}^2), \; x \mapsto \begin{pmatrix}1 & 1 \\ 0& 1\end{pmatrix} | ||
</math> | </math> | ||
Points of | Points of the form <math>{x\choose \lambda}</math> are mapped to: | ||
:<math> | :<math> | ||
\varphi{x\choose \lambda} = | \varphi({x\choose \lambda}) = {x + \lambda\choose} | ||
</math> | </math> | ||
<jsxgraph width="500" height="500"> | <jsxgraph width="500" height="500"> | ||
JXG.Options.label.autoPosition = true; | JXG.Options.label.autoPosition = true; | ||
JXG.Options.text.fontSize = 20; | JXG.Options.text.fontSize = 20; | ||
var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-5, 5, 5, -5], axis: true}); | |||
var y = board.defaultAxes.y; | |||
var g0 = board.create('glider', [0, 2, y]); | |||
</jsxgraph> | </jsxgraph> | ||
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<source lang="javascript"> | <source lang="javascript"> | ||
</source> | </source> | ||
[[Category:Examples]] | [[Category:Examples]] | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
Revision as of 07:11, 31 May 2021
Shear transformation
- [math]\displaystyle{ \varphi: {\cal A}(\mathbb{R}^2) \to {\cal A}(\mathbb{R}^2), \; x \mapsto \begin{pmatrix}1 & 1 \\ 0& 1\end{pmatrix} }[/math]
Points of the form [math]\displaystyle{ {x\choose \lambda} }[/math] are mapped to:
- [math]\displaystyle{ \varphi({x\choose \lambda}) = {x + \lambda\choose} }[/math]
