Transcript HowtomakeaHOLE-in-One2009

Mini
Golf
Laurie DiGregorio
Germantown Hills Middle School, Metamora, IL 61548
Teresa Yazujian
Eureka Middle School, Eureka, IL 61530
Nancy Powell
Bloomington High School, Bloomington, IL 61704
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How to Get a Hole - in - one!
What a great day
for a game of golf!
This will be a piece
of cake!
It looks like I need to
bank this shot…
…the trick is to
find the right
angle.
Hmm…..
…not exactly as I
planned.
I’ll have to try a
new angle.
This could
take years
before I get
it right!
Did you ever think you could
use math to get a hole-in-one?
At this point…
I’d try anything!
First, let’s look at some properties
of angles.
When the ball
hits the wall,
it creates an
angle of
incidence.
As the ball bounces off the wall,
an angle of reflection is created.
Something really cool!
The angle of incidence
and the
angle of reflection
are ALWAYS
congruent.
We know that these angles are congruent
because they are reflections of each other.
Can our knowledge of
reflections help us solve
the puzzle?
Remember, we are trying to get a
hole-in-one!
Since a direct
shot is not an
option, we will
have to bank it
off a wall if we
want to make
a hole-in-one.
We know we want to bank
the ball off the left wall of
the green.
But how can we use math to
determine where the ball
should bounce off the wall?
Guess and check
sure doesn’t
work.
Too bad we
can’t just
move the flag!
Wait a
minute!!!
What if we...
MOVED THE FLAG?
But WHERE do we move it???
Think about this: If we move the
flag anywhere INSIDE the hole, we
have changed the hole…
…therefore we have
changed the problem.
Hint:
Think outside
the box!
Literally!!!
What if we reflected the hole across
the side we want to bank off?
What would that do for us?
Do you realize the ball is now in
a straight line with the hole?
Ok, ok. It is in line with the reflected hole.
Here is the $100,000.00
question of the day:
What can a reflection tell us?
If the hole is point H, then
let’s label the reflection of the
hole as point H’. (H prime)
H’
H
We can also label the intersection of the
ball’s path and the wall as point W.
H
H’
.
W
See what happens when we
connect H and H’.
H
H’
.
W
A right triangle is formed.
H
H’
.
W
What would happen if we reflect this
triangle over the wall?
H
H’
.
W
Let’s find out!
(drum roll, please)
It’s no surprise that the reflected
triangle reveals a path to the hole!
H
H’
.
W
How, you ask?
Remember, if two triangles are
congruent, then their corresponding
sides and angles are congruent.
H
H’
.
W
The ball is hit towards H’. Since it can’t go
through the wall, it will reflect off the wall
and travel towards point H.
H
H’
.
W
The End!
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