Epicycloid Construction – Free download as PDF File .pdf), Text File .txt) or read online for free. Constructing a Parabola (Eccentricity Method) Constructing an Ellipse ( Concentric Circle Method) . Construction is similar to epicycloid. In geometry, an epicycloid or hypercycloid is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an.

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By using our site, you acknowledge that you have read construcgion understand our Cookie PolicyPrivacy Policyand our Terms of Service. I am fairly new to Mathematicaand I cannot figure out how to plot an epicycloid. I have plotted some neat looking things in my attempts, but I still can’t make one. I am not looking to make an animation; I just want the plot of an epicycloid. How do I get a static picture of an epicycloid? I recreated the animation on Epichcloid.

Epicycloids and other roulette curves are fun to play with using Manipulate. Here is one of many possible implementations.

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Epicycloid — from Wolfram MathWorld

Although the question epicycooid calls for epicycloids, it is very easy to make interactive panel that allows the user to play with hypocycloids as well. Because there is a simple relationship between epicycloids and hypocycloids, doing so adds very little code.

Looking up epicycloid we get the parametric equations describing it and then ParametricPlot does the rest of our work. Just for fun, epicyclod is a variation of C. A slight modification of the code given above can be done to produce the multiple exposure version: Still another neat demonstration is the Bernoulli-Euler double generation theorem: By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

Home Questions Tags Users Unanswered. Plotting an epicycloid Ask Question.

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Have a look at demonstrations. Mostly a lot of fiddling with the epicycloid equations in a PolarPlot and some ParametricPlots. PinguinDirk is asking you to post the code epicyclold have tried thus far, so we can see where there might be a problem. I recreated the animation on Wikipedia: Here is the Manipulate version: I don’t know how many hours I’ve spent wasted on playing with roulettesbut it sure was fun.

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Upvote for that masterpiece. It is easiest to use ParametricPlot and RotationTransform. Improved per comment from Mr. Sektor 3, 5 19 If one just wants to see the lines enveloping the epicycloid, the code is much simpler: Sign up or log in Sign up using Google.

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