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Isaac0427

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Isaac0427

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- #2

ProfuselyQuarky

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Oh, those are a lot of fun -- even better than polar graphing! My favorite is the Hypotrochoid:

x(t) = (a - b) cos t + c cos ((a/b - 1)t)

x(t) = (a - b) sin t + c sin ((a/b - 1)t)

Sorry, I haven't learned LaTeX, yet . . . Here's a bunch of lovely equations you can try:

https://elepa.files.wordpress.com/2013/11/fifty-famous-curves.pdf

What calculator do you have?

Last edited:

- #3

ProfuselyQuarky

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x(t) = sin(7πt)

y(t) = cos(5πt)

Not so sure if it has a name, but it looks way cool. You can always experiment and make up your own, too :)

- #4

Ssnow

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The astroid:

##x(t)=a\cos^{3}{t}##

##y(t)=a\sin^{3}{t}##

##x(t)=a\cos^{3}{t}##

##y(t)=a\sin^{3}{t}##

- #5

ProfuselyQuarky

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That one is lovely.The astroid:

##x(t)=a\cos^{3}{t}##

##y(t)=a\sin^{3}{t}##

- #6

pwsnafu

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##\left| \frac{x}{a}\right|^n + \left| \frac{y}{b}\right|^n = 1##

which has parametric equations

##x(t) = \pm a \cos^{2/n}(t)##

##y(t) = \pm b \sin^{2/n}(t)##

It contains a number of equations above as special cases.

In turn this is generalized by the superformula.

As I understand it the 3d version is used by No Man's Sky.

- #7

Ssnow

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##x=t\cos{t}##

##y=t\sin{t}##

with ##t\in [0,+\infty)##. Have good painting ...

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