Stretching Your Experience

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Stretching Your Understanding
An Investigation Into Scaling
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Wall
Guy
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Wall
Shadow
Guy
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Shadow
Guy
How many times taller is the shadow than the guy?
Lets call this number the scaling factor for
height.
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So it seems that the shadow is 3 times as tall as
the guy. That is, the scaling factor for height
between the guy and the shadow is 3.
Often, we say that the guys height has been
scaled up by a factor of 3.
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Suppose we measure and determine that the guy is
2 meters tall and shadow is 6 meters tall.
Shadow
Guy
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Suppose we measure and determine that the guy is
2 meters tall and shadow is 6 meters tall.
Shadow
6m
Guy
2m
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Suppose we measure and determine that the guy is
2 meters tall and shadow is 6 meters tall.
Shadow
6m
Guy
2m
How might we determine the scaling factor
mathematically?
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shadows height guys height
So, the scaling factor
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shadows height guys height
So, the scaling factor

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shadows height guys height
6m 2m
So, the scaling factor

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shadows height guys height
6m 2m
So, the scaling factor

3
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What about the width scaling factor?
Shadow
Guy
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What about the width scaling factor?
Shadow
Guy
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Height and width scaled equally
Unscaled
Height scaled more than width
Width scaled more than height
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Similar Figures
Height and width scaled equally
Unscaled
Height scaled more than width
Width scaled more than height
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Not Similar Figures
Height and width scaled equally
Unscaled
Height scaled more than width
Width scaled more than height
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What to remember
How to calculate the scaling factor
Dimension of Big Object
Scaling factor
Dimension of Small Object
What similarity means in this context All
dimensions are scaled by the same factor
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What you will do
Part I Find the scaling factors of the toy car
for each dimension (height, length, and width)
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What you will do
Part I Find the scaling factors of the toy car
for each dimension (height, length, and width)
Part II a Find the area of the parking space
in which the toy car would park as well as that
of the real car. Find the scaling factor for
area. Using string and tape, mark out this
area on the floor.
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What you will do
Part II b Make a box for your toy car by
constructing a net using the graph paper
provided. Find the scaling factor for volume.
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Remember Similarity?
Similar or not?
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Remember Similarity?
Similar or not?
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Remember Similarity?
Similar or not?
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Remember Similarity?
Similar or not?
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Remember Similarity?
Similar or not?
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Remember Similarity?
We call this self-similarity.
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Now we have self-similarity on two scales.
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Now we have self-similarity on two scales.
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Now we have self-similarity on two scales.
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Now we have self-similarity on three scales.
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Now we have self-similarity on three scales.
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Now we have self-similarity on three scales.
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Now we have self-similarity on three scales.
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Here we go.
Lets build Sierpinskis Triangle
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Lets build Sierpinskis Triangle
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Lets build Sierpinskis Triangle
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Lets build Sierpinskis Triangle
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Lets build Sierpinskis Triangle
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Lets build Sierpinskis Triangle
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Lets build Sierpinskis Triangle
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This thing is self-similar across an infinite
number of scales!!!
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This thing is self-similar across an infinite
number of scales!!!
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Here we go again.
Another simple rule, another fractal. This one
is known as the Koch snowflake.
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Another simple rule, another fractal. This one
is known as the Koch snowflake.
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Another simple rule, another fractal. This one
is known as the Koch snowflake.
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Another simple rule, another fractal. This one
is known as the Koch snowflake.
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Another simple rule, another fractal. This one
is known as the Koch snowflake.
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B
A
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B
A
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Check it out for yourself
http//math.rice.edu/lanius/frac/
http//www.coolmath.com/fractals/gallery.htm
http//www.enchgallery.com/fractals/fracthumbs.htm
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