Marching TRANSPARENCY 1 • Marching Onto Stage

Ladies and Gentleman - students of all ages:
Welcome to “Out Juggling In My Class ”

A celebration of my thirty eight years of teaching mathematics.

That you are here for this NCTM 2002 ANNUAL CONVENTION means you are outstanding.

We all enjoy a parade!         Right?

Physics of WMT TRANSPARENCY 2 • Physics of WMT

My students inspired this parade graphic.

When I march and toss an object, the flight path looks
like a parabola to me.

The ball is moving back and forth from hand to hand.

Perhaps the parabola is y = 16 - x²/4 inches.

But you see a different parabola due to my body motion.

As I march approximately "pi" mph, you may see
the parabola y = 16 - x²/20 inches.

Isn't that a striking difference in viewpoint about this motion?

Physicist John A. Wheeler* holds a viewpoint about this motion which is different from Newtonian physics.

Wheeler* uses a moving object's slight change in aging due to gravity to explain a parabolic distance versus time relationship.

His "Principle Of Maximal Aging" selects the curve that maximizes an object's height from the earth while minimizing its velocity getting there.

Tossed objects age longer when remaining
more distant from the earth.

Also, tossed objects age longer at slower velocities.

Wheeler* demonstrated a parabolic relation
between height and time for a tossed object
as shown in this graphic:

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PMA TRANSPARENCY 3 • The Principle Of Maximal Aging

The top green curve has the advantage of aging
longer due to a longer height interval.

The bottom blue curve has the advantage of aging
longer due to slower velocities getting there.

The best balance for longer aging is the
middle red geodesic parabola.         YES !

Free fall position equaling a constant times time squared
relates to maximizing the object's aging.

Let's simulate a Gregorian chant to remember this concept:

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CHANT PMA TRANSPARENCY 3A
"Principle Of Maximal Aging" - Get higher but go slower.

I know you can be louder than that!         Please try again.

CHANT
"Principle Of Maximal Aging" - Get higher but go slower.

Good For You!

How does the geometry of a tossed
object follow a parabolic pattern?

Galileo found that a linear model fit the
horizontal component of the flight path.

          x = rate * time

GHM CHANT TRANSPARENCY 4 • Chanting the distance formula

Try Chanting: Distance Equals Rate Times Time.

CHANT       X EQUALS RATE TIMES TIME!

WOW - Some outstanding chanters here!

So replace the variable time in y = ( constant ) t²
with x/(a constant rate).

Then we have: y = ( a new konstant) x²

Therefore, Wheeler's Principle Of Maximal Aging
and Galileo's Horizontal Linear Motion Model
combine to give parabolic flight paths.

Your chanting sounds really good!

I can tell that you will be
outstanding in my next topic.

PROP - SHEET OF PAPER or plastic ball

• The Talk Outline

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