Stamford
Spinnakers 
High School (U19) Team  Math on Ice 
You can't play this game without mathematics, whether you know it or not. Let's say you're playing defense and an opponent with the puck breaks past your partner across the ice. Do you skate right to where you see the attacker? Of course not, because she won't be there when you arrive. You have to assess her speed, your speed, and her angle of attack, then calculate an angle on which you can intercept her. Angling is a key ingredient of hockey defense. It's amazing how well you do it, considering that none of us can easily explain the underlying math!


Which fraction is largest: 5/4, 4/3, 3/2 or 2/1? If your team has a 5 on 4 advantage, and you have to decide whether to draw an opponent away from the play, it's important to know that 4/3 is a larger fraction (i.e., the numerator is larger in relation to the denominator) than 5/4. Math tells us that 4 skaters have a better advantage over 3 than 5 skaters have over 4.
You're the center, preparing for a faceoff. The referee drops the puck. How soon and how fast do you go for it? You estimate the time it will take for the puck to reach the ice, where it will land, when you have to start moving your stick and how fast you have to move it. Thanks to your math skills, you win another faceoff!


Your teammate is chasing the puck
into her corner of the attacking zone. You're just entering the left side
of the zone at full speed. When your teammate gets the puck, she has to
evaluate your speed and adjust both the speed and direction of her pass to
put the puck on your stick when you're in shooting position. You have to
read what she's doing, factor in her passing ability, and adjust your speed
to make sure you're there when the puck arrives. (You can bring a graphing
calculator to the SAT, but not to hockey. Imagine trying to use one with
those gloves!)


You know your 6th and 7th
teammates on the ice are the boards, right? But how do you know where on
the boards to hit the puck? Mathematically, of course. You know the angle
of incidence equals the angle of reflection. That's why your giveandgo
with these "teammates" always works so well.


Math is involved in your skating
and stick handling, too.
The skater who rolls her ankles has more edge control. Why? Because of the ANGLE of her blades against the ice.


The skater who keeps her knees bent controls more ice with her stick. Why? Because she understands triangles!


The skater who keeps her hips low* gets longer strides. How do we know? More triangles! *We say it that way because some benefits of staying low are not obtained by bending at the waist.


Why do crossunders help us
skate faster while turning? The reason is that, during a turn
without crossunders, the interior skate has less skating to do than
the exterior skate. If the interior skate is fully extended
in the usual way, it works against the
turn. (It's like trying to turn a canoe with paddles working at full force
on both sides.) Instead of
taking short strides with the interior skate, we convert the interior
skate into a second exterior skate, crossing under and
making full strides on its outside edge. What
keeps you from falling into the circle when you use both skates externally?
Well, that's getting into Physics, which is interesting, but not on the SAT.
C =
ΠD. If you skate around a faceoff circle without crossunders, your
outside skate travels about 13 feet further than your inside skate. 

How do you aim a onetimer on a puck


Goaltending and shooting involve
lots of math.
When a goalie faces an attacker on a breakaway, she comes out just enough to "cut off the angles." That requires fast math. It's shown in twodimensions below, but it actually involves three.


By the way, that goalie had 14
saves on 15 shots in her last game, a save percentage of 93.33%. Her team
won their 28th game out of 39. That's hard to compare with another team's
record until you mathematically convert it to an impressive 71.8%.


So, after all these years of getting up early on weekends to practice your mathematics, there's no reason you shouldn't get a perfect score on the Math section of your SAT. Good luck to our Juniors and Seniors!  
Can you think of other applications of math in hockey? Check out the goalie reaction time calculations at http://www.exploratorium.edu/hockey/, where you'll also read that Skating, according to physicist Thomas Humphrey, is "the fastest way to travel on the surface of the earth on your feet." (It doesn't say how he excludes downhill racing.) 

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