Skating and Geometry..

[xofivebyfive]

For my Geometry Honors class, we have to choose a topic and explain how geometry is used with it. Others who have gone before me have done theme parks, frisbee, swimming, field hockey, food plating.. etc.. I decided that I wanted to do skating, since I'm interested in that. I'm having some problems coming up with different geometric things. It has to be five to ten minutes long.. and I know that everything is done on the arc of a circle, t-stops, when you spin your feet are parallel.. and the area and perimeter of the actual rink. Can you come up with anything else? I mean anything that has even the tiniest thing to do with geometry. Angles, shapes, area.. I need some assistance.

[Casey]

The various patterns that 3-turns, rockers, counters, mohawks leave on the ice all correspond to various geometric terms, I think...

[jenlyon60]

If you can find an old USFS rulebook that still includes the figures patterns, there is a lot of geometry involved with figures.

Actually there is a lot of geometry principles that you can illustrate with the various USFS moves in the field patterns, as well. It's just not as obvious as with school figures.

[dcden]

If you're familiar with some of the school figures (figure 8's), try these as jumping off points:

Cardioid - looks like the 3 turn figure
http://mathworld.wolfram.com/Cardioid.html

Limacon - looks like 3 turn or loop figures.
http://mathworld.wolfram.com/Limacon.html

[Joan]

Tom Zakrajsek (elite coach from Colorado Springs) talks about a "power angle" just before jump takeoff. The skating knee is bent with knee over toes, the free leg is back, the arm on the side of the skating leg is cross-checked, the other arm is extended back and the body forms an angle, say about 75 degrees, to the ice.

[doubletoe]

Ask your coach to draw a serpentine spiral sequence or footwork sequence exactly how it has to be laid out on the ice rink. Each "lobe" is a half circle (an "arc" of a circle, in geometric terms), even though the pattern you make with the arcs ends up being a serpentine pattern, not a circular pattern. But you can also use two large arcs of a circle to do a circular spiral or footwork sequence instead. Because it's a circle contained within a rectangular shape (the rink), the diameter of the circle will be just slighly less than the width of the rectangle (the rink).

As someone else mentioned, you can talk about body positions, too. The goal on a sitspin position is to have your skating leg "parallel" to the ice. You also want the free leg to be parallel to the ice (at a 90-degree angle) or higher when you do a camel or flying camel spin. The minimum requirement for a spiral position is having the free leg higher than parallel and at greater than a 90 degree angle (since it needs to be above the hip), and one of the big point-getters under the new judging system is a spiral where the split is 180 degrees, completely vertical, and perpendicular to the ice. Hey, that's a lot of geometry we have to think about!

Here's something else you can mention: When you skate, you are hardly ever traveling the shortest distance between two points on the ice because you are almost always on an edge, which means you are skating on the arc of a circle, not a straight line. Since we need our edges to push against the ice, the fastest way for us to get between to points is to skate on a curve, even though the "shortest distance" may be a straight line.

[mikawendy]

And for most lobes in MIF patterns and figures, the lobe begins perpendicular to an axis. For example, the lobes of MIF patterns such as the power perimeter crossovers, the consecutive spirals (not the Silver MIF spirals), brackets in the field, three-turns in the field, and many more have the lobes placed perpendicular to the long axis, meaning that at the beginning of each lobe, you are stepping along the short axis. (In many cases, stepping diagonally instead of perpendicular to the long axis would negatively affect your marks for that move, plus it messes up the placement of the edges in that pattern.)

[flo]

Also if you can get a photo of a scribe, it acted as a compass. As skaters we do have to be aware of such things as the long and short axis, bisecting a circle and so on. Think about how we need to step into the circle, or jump out of the circle perpendicular to the circle. Counters, rockers and three turns are all differentiated on the basis of turns inside and outside the circle.

[Isk8NYC]

If you think about spinning, the curve of the blade meets the ice at one point. (OK, it's an back inside edge, but it's not a full edge, it's partial)

You could make a case for tangents or arcs.

[flo]

Also look at the blades themselves, lots of geometry there.

[xofivebyfive]

Wow lots of replies.. cool. Thanks everybody :bow:

[dbny]

Also look at the blades themselves, lots of geometry there.

Hollow and Rocker are two of the most important properties of blades which are measured as an arc of a circle with a particular radius.

[techskater]

How about for an Axel, you step on a tangent to the back outside edge on the take off?

[Perry]

IIRC, there's actually a book just about the geometry of figures. No idea what it was called, but maybe someone else remembers the same thing?

[mikawendy]

Also, the general principle of symmetry applies in some things in skating, especially some moves in the field and figures, in which the judges are looking for a person to execute the steps equally well on each foot. (You can probably find examples of the different kinds of symmetry in different moves/turns/figures.)

[flo]

What level is this? After you finish it for school, it might be a good thing to tweak a bit and submit it to the Skating magazine. It would be fun (and good) for the kids to see geometry in action.

[xofivebyfive]

^This is for my Geometry Honors class in 9th grade. Ooh, that would be cool to submit it to the magazine. Maybe I'll do that.

Thank you so much everyone for all your help. I appreciate it so so much.