Difference between revisions of "Christoph Champ Logo"

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(The mathematics behind the logo)
 
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I have always been interested in geometry. This is especially true of symmetry. This is what I had in mind when I designed my logo for this site. It is actually just a Lissajous curve that has been transformed, using the principles of ''sumi-e'', for an artistic effect.
 
I have always been interested in geometry. This is especially true of symmetry. This is what I had in mind when I designed my logo for this site. It is actually just a Lissajous curve that has been transformed, using the principles of ''sumi-e'', for an artistic effect.
  
== The mathematics behind the logo ==
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==The mathematics behind the logo==
In mathematics, a '''Lissajous curve''' is the graph of the system of parametric equations
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In mathematics, a '''Lissajous curve''' is the graph of the system of parametric equations:
  
 
<!--:<math>x=A\sin(at+\delta),\quad y=B\sin(bt),</math>-->
 
<!--:<math>x=A\sin(at+\delta),\quad y=B\sin(bt),</math>-->
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</pre>
 
</pre>
  
== External links ==
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==Sandbox==
* [http://en.wikipedia.org/wiki/Lissajous_curve Wikipedia article on '''Lissajous curve''']
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[[Image:Christoph Champ-beta.png]]
* [http://en.wikipedia.org/wiki/Sumi-e Wikipedia article on '''''Sumi-e''''']
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==External links==
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*[[wikipedia:Lissajous curve]]
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*[[wikipedia:Sumi-e]]
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*[[wikipedia:Harmonograph]]
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[[Category:Personal]]

Latest revision as of 12:54, 24 December 2019

In case you are wondering what this site's logo (or Christoph Champ Logo / Sumi-e Lissajous curve) is all about, this article will attempt to explain it.

I have always been interested in geometry. This is especially true of symmetry. This is what I had in mind when I designed my logo for this site. It is actually just a Lissajous curve that has been transformed, using the principles of sumi-e, for an artistic effect.

In mathematics, a Lissajous curve is the graph of the system of parametric equations:

x = A*sin(at + δ), y = B*sin(bt),

Below is an example of a Lissajous figure with δ = π/2, a = 9, b = 8. Next to it is a sumi-e rendition of this same Lissajous curve (created by Christoph Champ).

You can easily generate a Lissajous curve in Maple by executing the following commands:

x1:= t->sin(9*t): y1:= t->sin(8*t):
plot({[x1(t), y1(t), t=0..2*Pi]});

Sandbox

Christoph Champ-beta.png

External links