Mom! There's an Astroid in My Closet!

A New Look at the So-Called Trammel of Archimedes

“…The seemingly unexpected appearances of the same astroid and various ellipses associated with bifold closet doors treated in [5] are easily explained as consequences of Property 1. In [5] the floor area swept out by the right panel of a bifold closet door was found using calculus. That result follows directly from the discussion related to Figures 10b and 10c.…”

“…Zigzag trammels can be realized physically as folding doors. Examples are those treated in [5], where the left endpoint Z is kept fixed. The seemingly unexpected appearances of the same astroid and various ellipses associated with bifold closet doors treated in [5] are easily explained as consequences of Property 1.…”

“…Examples are those treated in [5], where the left endpoint Z is kept fixed. The seemingly unexpected appearances of the same astroid and various ellipses associated with bifold closet doors treated in [5] are easily explained as consequences of Property 1. In [5] the floor area swept out by the right panel of a bifold closet door was found using calculus.…”

“…For calculus derivations of this envelope see [5] and [6]. from the origin making angle α with the x axis is related to the coordinates of a point E = (x, y) on the ellipse by the parametric equations…”