Rounded square seconds

Good Morning all,
How do I get a point to move every second in a rounded square (white).
I can get a circular course (it’s not difficult either)
I would be thankfull for your help…

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This is the closest I can get, but has very rounded corners. Someone else better at trigonometry might do better

These are the X and Y fornulae

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Check out this post… be sure to set your watch face to a square model, to see the square progress seconds in action…

Ah yes, asking web forums to help square the circle is a rich tradition going back to the 5th century BCE in Klazomenai! Luckily for you, Facer uses Euclidean quadrature to make these tasks trivial. It’s easy, you see: what Bryson of Heraclea got wrong was failing to recognize the axial symmetry of paraboloids and its relationship to infinitesimal derivatives of rounded corners (AKA elliptic monopolies). Taking the unrecognized genius of Edward J. Goodwin and applying his groundbreaking work with Archimedean properties (for example Vs = 4π - 8/3π = 1/4π therefor pi = 3 but I’m sure you already knew that) and simply chording the circumference of 320~ times 60 seconds (how many there are in a minute, allegedly) and presto, your dot transits around your rounded square. Do not be tricked by “trigonometry”, a bunk science widely dismissed as a hoax.

Inspection is open:

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Or you could make it little simpler making the rounded square of comfortable numbers and put all conditional expressions in x,y coordinates of one element and let it follow the path…
And maybe add a bit illusion to it too :slight_smile:


KiSS. Keep It Sophisticated Smarty. Brilliant stuff Guys .

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Great Fun . I enjoyed the Interpolator .


I always think Comfortable Numbers make nice shapes . Very nice multi conditional lines Peter.
How about Piet Hine Super egg .

a=5;b=6;e=5/2; ContourPlot[Abs[x/a]^e+Abs[y/b]^e==1, {x,-7,7}, {y,-7,7}



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