I came up with a cool parametric equation

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The discussion centers around a unique parametric equation defined by the equations y = 2.5*(fresnelC(t*2) - arcsinh(t/2)) and x = 2.5*(fresnelS(t) + arcsinh(t/2)). The graph of this equation spans t from -2π to 2π, with x and y values ranging from -7 to 7. The conversation highlights the potential for creating various interesting curves using Fresnel integrals, while also referencing Wolfram Alpha as a resource for exploring additional plane curves.

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  • Understanding of parametric equations
  • Familiarity with Fresnel integrals
  • Knowledge of the arcsinh function
  • Ability to graph mathematical functions
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  • Explore advanced properties of Fresnel integrals
  • Learn how to graph parametric equations using software like Desmos or MATLAB
  • Investigate additional mathematical resources on Wolfram Alpha
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y = 2.5*(fresnelC(t*2) - arcsinh(t/2))
x = 2.5*(fresnelS(t) + arcsinh(t/2))

In case you don't have anything that can graph this, this is what it looks like from t = -2*pi to 2*pi, from y = -7 to 7, and from x= -7 to 7:

Z6dhV9R.png


There are a lot of interesting ones that can be made with the fresnel integrals, but I won't list the other ones that I found because they are all pretty similar.

Do you have any cool equations? I tried looking online, but the ones I could find weren't all that great.
 
Last edited:
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sgfw said:
y = 2.5*(fresnelC(t*2) - arcsinh(t/2))
x = 2.5*(fresnelS(t) + arcsinh(t/2))

In case you don't have anything that can graph this, this is what it looks like from t = -2*pi to 2*pi, from y = -7 to 7, and from x= -7 to 7:

Z6dhV9R.png


There are a lot of interesting ones that can be made with the fresnel integrals, but I won't list the other ones that I found because they are all pretty similar.

Do you have any cool equations? I tried looking online, but the ones I could find weren't all that great.
Wolfram Alpha has a LOT of cool plane curves. Many of them are rather amusing. For example, this one.

As a side note, this probably should go in the lounge.
 
Last edited:

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