# parametric equation

Another harmonograph. This time it only has 3 pendulums (Hence the zeroed-out values of one of the pendulums in the formulae). Another change is that the damping is now 0.02.

this is probably the most entp thing of my life but i solved a parametric equation for the first time in my life during an exam and got 100/100 and translated by heart a latin text i had translated 3 years before and had never revised again and got 90/100 [and all my classmates hate me for this]

Haha! I always do so well on exams too. We don’t deserve this. I’ll kind of glance at the book and just tell myself, be logical… and then I’ll go to bed at 8 or watch a movie or something, and then perfectly derive a dimensionless number the next day.

Those of us who can do this are seriously lucky. Like. My school luck… it’s ridiculous.

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I literally watch these for hours.

For those who are curious, they are parametric equations I programmed in Processing 2. The color defined by the derivatives (speed).

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The image is not mine. It is a fantastic creation by bigblueboo that has caught some attention outside of the usual math tumblverse. You should definitely check out eir blog and if you like this post you should (also?) reblog the original. With that out of the way:

Linear Algebra. Linear algebra is the study of vector spaces, which are “flat” structures that have a notion of addition and dimension.

L^2(S^1) is the space of “square integrable functions on the circle”. Every continuous function from the closed interval [-π,π] is in L^2(S^1), but the space also includes some functions which have discontinuities, so long as they are not too extreme.

bigblueboo’s image happens to be an excellent source of mathematical content: this post is final post in a series in which I discover some of its secrets. In the first post you can see a derivation of its symbolic equations of motion, and part two contains a sweet characterization. The third post, which explains that the non-constant speed in the gif is not (entirely) a result of the viewing angle, and the fourth post quantifies the variation.

I have some more questions about HTPs; there are certainly natural questions to look at. Therefore, I am planning on doing an epilogue post which will lay out some of the questions I have. If you have any questions you’d like me to share, please reblog and I’ll (probably) include them! However, that post will not be written in fancy images like usual but I’ll just do the best I can in plaintext so that it can be a legitimate reblog of the OP (hopefully he’ll see some of the work that his wonderful piece inspired!)

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When you’ve got a test on parametric equations, but ur still swan queen af.

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If anyone’s curious, here’s a blown up version of that math-y heart and the parametric equations for it in the form {x(t), y(t)}

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9/7 - breakfast and set up for today. Need to get through parametric equations (kind of struggling) and an essay about Kurt Cobain. Also, hello to all my new followers!

An animation of the curve adaptation with continuously increasing a/b fraction from 0 to 1 in steps of 0.01

Where δ=0 and parametric equations x=sin(at +  δ) and y=sin(bt)

Courtesy: http://en.wikipedia.org/wiki/File:Lissajous_animation.gif