Xah Lee, 2006-11
Video of juggling inside a conical enclosure http://youtube.com/watch?v=MqDAf_lg9Xs (by Greg Kennedy)
It looks like juggling in wonderland, doesn't it?
You may not know, that when a cone is cut by a plane, their intersection forms a curve on the cutting plane, and this curve are mathematically classified into 3 types: ellipse (closed), hyperbola (open), parabola (open), depending the angle of the cutting plane with respect to the cone.
In general, these curves are literally and collectively called Conic Sections, or just Conics, and are know since ancient Greeks.
You can see illustrations and their math details here: conic sections, ellipse, hyperbola, parabola.
Now, this is why, when the guy throws the ball even towards the ground, the ball comes up higher.
If he throws the ball directly toward the ground (which he didn't do in the video), it will make a dip and come up! (provided he's not directing it towards the apex of the cone.)
Also of interest, is that the intersection of a cylinder and a plane is also a ellipse. This means, if the glass wall is a cylinder, then a ball thrown in the downward direction will also come up on the opposite side. Similar to the juggling inside the cone.
Greg Kennedy's conics juggling is interesting because it force the balls on a surface. Normal juggling, is a 3D affair. By making balls roll on a surface, the juggling becomes a 2D affair, and consequently much easier.
However, note that in practice, most juggling of more than 3 balls are essentially planar. For example, imaging juggling 5 balls. Although there are no constraints on where the ball would fly, but in practice it is thrown such that its path lies on the plane parallel to the juggler's face.
Greg's juggling is interesting because by forcing the balls to roll on a surface, it visually accentuate one beautiful aspect of juggling: the mathematical patterns made by the ball's paths.
Other mathematically interesting jugglings by Greg Kennedy:
Page created: 2006-06. © 2006 by Xah Lee.