Daily Equation #2 – Astroid x^(2/3) + y^(2/3) = a


Description

This is Day 2 of my collection of printable equations. To see the whole collection, go to:http://www.thingiverse.com/thing:227210

Found a great site of famous & interesting equations: http://www-groups.dcs.st-and.ac.uk/~history/Curves/Curves.html. For today's equation, I picked the Astroid: x^(2/3) + y^(2/3) = a where a = r^2/3

From the site (edited & shortened for clarity):

The astroid can be formed by rolling a circle of radius r/4 on the inside of a circle of radius r. It can also be formed as the envelope produced when a line segment is moved with each end on one of a pair of perpendicular axes. It is therefore a glissette.

The length of the astroid is 6r and its area is 3€r^2/8.

The astroid was first discussed by Johann Bernoulli in 1691-92. It also appears in Leibniz's correspondence of 1715. It is sometimes called the tetracuspid for the obvious reason that it has four cusps. The astroid only acquired its present name in 1836 in a book published in Vienna. It has been known by various names in the literature, even after 1836, including cubocycloid and paracycle.

Details:

  • units are in mm
  • a = 70
  • Range(x) = -50 to 50
  • stl resized to make x axis = 100 mm

As always, I'm going to continue to post one equation per day until get bored or people lose interest. If there's a particular equation you'd like to see, leave a comment and I'll give it a shot.

Technical Note:

  • The thickness in the y-direction is created by plotting a second curve whose points are a constant distance in the direction perpendicular to the tangent of the first curve. This can create artifacts at regions of rapidly changing slope. However, the lower or inner curve is always correct.

Daily Equation #2 - Astroid x^(2/3) + y^(2/3) = aby skaye is licensed under the Creative Commons - Attribution - Non-Commercial license

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