FIRST TRANSPARENCY • General Tessellation

He made "time tessellations"

like this graphed model where:

The top three curves show a red,

yellow or green object's flight record.

and

The bottom two curves show the left

and right hand movement.

SECOND TRANSPARENCY • Beek considered a ratio k

Beek considered a ratio, k, of dwell

time divided by hand cycle time.

Hand cycle time is the sum of the

vacant time and dwell time so:

k = D/(V + D)

His research indicated that a novice

juggler tended to have k around 3/4.

While more experienced jugglers

tended to use ratios toward k = 1/2.

You can tell the difference between

these ratios by looking at two

time tessellation models.

They arise from a substitution

of each ratio into Shannon's

special case equation.

ACTION Show two graphs together then separate them to point out the following and put S's graph in hand out:

THIRD TRANSPARENCY • Tessellation For k = 3/4, the toss is made 2/3

For k = 3/4, the toss is made two

thirds into the last ball's flight time.

This is a sixth of the flight time

past the last ball's peak.

ACTION Point to the locations on the graphs as presented or mark them with color.

FOURTH TRANSPARENCY • Tessellation For k = 1/2, the pattern is: toss when

With k = 1/2 the pattern is: toss

when there is a peak, in other words, half

way through the flight of the last ball.

FIFTH TRANSPARENCY • Data Device/Computer or Calculator Assisted Lab Project Chart

Here is a Set of graphs made

with the aid of a modern data collection

device for an Assisted Lab (ComBL) Project

designed to measure Vacant and

Dwell times to find your k values.

You need to make some

gloves. See how close you get

to P. J. Beek's theory!

A novice and an experienced juggler

differ by how one's nervous system links

the wave motion of the flying objects

with the wave motion of the moving hands.

SIXTH TRANSPARENCY • a double harmonic oscillator

This is a physical model of

a double harmonic oscillator.

Notice that as I set one object

in motion the other object starts moving.

Some energy of one is transferred

through this linking bar to the other object.

Ho, the first object has stopped!

Amazing - all of the energy of this

object is now in the motion of the other.

So we have an elementary picture

of how jugglers manage to juggle.

• The Talk Outline