Fencing and Math

[mrbiggs]

Originally Posted by ra2000a

wow so many ideas. thanks guys! but im gonna after really read through all the ideas and put an outline togehter. yea, its for high school so im gonna need some complicated math .. probably at a precalc level.

Ohhh, well that's not too bad. I had assumed you were in college.

It would be really neat to have graphs of the odds of a hit registering for a given angle or force.

[Larrison]

Originally Posted by PeterGustafsson

Hi!
Every position can be described as a vector with joint angle values as its paramenters. Thus, all movements can be described as quartinions incorporating the joint angles and inter/joint lengths. One can see it as an application of the geomentry needed for a robot with a 3D workspace. That has been studied extensively, but you can apply it to a new use. Should be some math in there.

Dang Peter, that's not bad. Set it up at a 3x3 set of matrixes, each representing the position of the foil (rectangular or spherical coordinates -- spherical would be best). Then after a series of moves, represented by transform matrixes, you can multiply them together and get the final position of the blade... Just have to be able to do the matrix match ... If you can reduce the blade position through a set of equations to another element (such as the fencer's arm) you can then link it to that.. or just use some linear operators to indicate other motions. I'd forgotten you could do that -- I did that (*ahem*) years ago, calculating the field of view of sensors on a spacecraft instrument platform and deriving the local pointing coordinates for ground instruments to point to the same spot in space.

[cfaustus]

The Spanish Circle was a method for teaching the most oportune angels for defense and attack. It is all based upon geometry involving cords in a circle as opposed to attacking along the diameter. Because it uses approximately a 6 foot circle for reference and the fencing strip is so wide, it is quite applicable to modern fencing and it can come in very handy in epee.

[KD5MDK]

Why do you assume foil?

[penguin_2000]

Originally Posted by ra2000a

wow so many ideas. thanks guys! but im gonna after really read through all the ideas and put an outline togehter. yea, its for high school so im gonna need some complicated math .. probably at a precalc level.

I second the suggestion of "RebelFencer" to see if there are statistically significant differences between people who do and don't take lessons. You could track differences in number of bouts/points won/lost in the pools as well as overall finishes. Finding p-values to support/refute statistical significance is pretty easy, but it looks complicated on paper.

One way or another, you could sell the results to your coach. ...course one of those ways is called blackmail...

[Zhi]

hmmm...... You must consider the differences of each players..

[mlr2fence]

Originally Posted by MyrddinsPrecint

how logical reasoning affects fencing, success of math/sci people in fencing as opposed to success of liberal artsy people.......

of course, that's more of a psychology/statistics as it relates to math.........

hrm.
nevermind.

Hmmm....I see a *flawed* poll in here....

[ra2000a]

Originally Posted by KD5MDK

Why do you assume foil?

actually, i was looking more towards sabre just because i am a sabre fencer and understand sabre much better. i like the statistical analysis though.

[mrbiggs]

Oh, there's also something I've been thinking about doing for a long time.


Go to a bunch of tournaments and gather data. Figure out the average time of a foil bout, an epee bout, and a sabre bout. Then figure out the average time to hook up, and the average time lost to equipment problems. Also figure out the average DE time.

You can come up with a formula for the approximate length of a tournament based on the number of fencers and the weapon they fence.

[Epee Scherma]

If you like saber, you could create some trig/geometry in the angle at which the blade hits the opponents mask or part. Like.. you could figure out:

What is theta if the opponent is 6'1'' and your extended arm's palm is 4 feet away. Then you can use pythag to find the hypotenuse and use sin/cos/tan to find the angle at which the blade would have to be to hit the top of that person's helmet.

To make it more complicated? hmm. What if you are lunging at x rate of speed, at what time would the blade connect with the mask?

That's probably the hardest math-fencing problem I could think of.

[PeterGustafsson]

Hi!

Originally Posted by Larrison

Dang Peter, that's not bad. Set it up at a 3x3 set of matrixes, each representing the position of the foil (rectangular or spherical coordinates -- spherical would be best). Then after a series of moves, represented by transform matrixes, you can multiply them together and get the final position of the blade... Just have to be able to do the matrix match ... If you can reduce the blade position through a set of equations to another element (such as the fencer's arm) you can then link it to that.. or just use some linear operators to indicate other motions. I'd forgotten you could do that -- I did that (*ahem*) years ago, calculating the field of view of sensors on a spacecraft instrument platform and deriving the local pointing coordinates for ground instruments to point to the same spot in space.

Note to self: Do not try to outbrain a real rocket scientist.


Have a nice time!

Peter Gustafsson

[Andreas]

Originally Posted by mrbiggs

You can come up with a formula for the approximate length of a tournament based on the number of fencers and the weapon they fence.

It usually also depends on the number of strips!

[oiuyt]

Originally Posted by penguin_2000

I second the suggestion of "RebelFencer" to see if there are statistically significant differences between people who do and don't take lessons.

And you're doing what exactly in order to have a control group?

Massive problems with different populations, hard to establish baselines, etc., etc. on this one. Not to mention just dividing people into groups rationally. Is someone who has taken 4 lessons/week for the past 6 years but, as of 5 months ago stopped completely a lesson or non-lesson fencer?

-B :)

[parrythis]

Fencer A, traveling 2 meters per second, leaves his end of the piste heading toward the other end, 14 meters away. At the same time fencer B, traveling 2.25 meters per second, leaves his end of the piste heading toward the other end. When do the two fencers meet? How far from each end do they meet?

(Sorry, I couldn't resist.)

[Sciurus-Rex]

Explore the false assumption that if A>B and B>C then A>C, where A, B and C are fencers with different skills and styles (or many other sports, for that matter). A>B>C>A is a possible outcome when individual pairings are compared, leading to a situation in which A=B=C in final points. Dress it up and wax philosophically about logic and you've got yourself a doozy.

[Have At You]

Since you're only at a pre-calc level, most of the fun math involved in fencing is beyond you. You need at least derivatives and integrals to get the actions.

I was going to suggest researching ways to map the trigonometry of a whippy foil or sabre blade action, but on thinking it through I realized that the extreme whippiness going back and forth would require complex functions (using the imaginary number i), and the fact of multiple variables of moving through 3 dimensions plus time brought it quickly to the level of college-level math. Geometry plus complex analysis plus partial differential equations sounds ominously like there is a Cauchy-Riemann manifold somewhere down the line, and let's not go there.

However, if you were to ease off your preference for a sabre problem, and permit an epee analysis, I think it's something you could handle. It'd be a more straightforward physics-type bit of research (time, velocity, mass, etc.)

[oiuyt]

Statistical analysis of the reliability of fencers classifications as a means of determining the likely outcome of a tournament bout (DE and pool should likely be separate) in each of the three (or six) weapons. The division posts results from nearly all tournaments including results of pools and DE's. Similarly many tournaments on askFred do so, and likely other divisions, which gives a nice quantity of data from which to work.

How often does a D upset a B? How does that vary across different weapons.

-B :)

[penguin_2000]

Originally Posted by oiuyt

And you're doing what exactly in order to have a control group?

Massive problems with different populations, hard to establish baselines, etc., etc. on this one. Not to mention just dividing people into groups rationally. Is someone who has taken 4 lessons/week for the past 6 years but, as of 5 months ago stopped completely a lesson or non-lesson fencer?

No need to argue about every possible detail. Obviously, you must try to control it as much as possible. Don't compare a kid w/1 month experience with adult w/10 yr experience. But, you could take, say, all kids with 3-4/5-6 years of experience. You may find no diff. between the two groups. Even small sample of 5 kids w/ or w/o coaching may tell you something. You cannot control the motivation of the kids, or if they only take lessons because their parents make them, etc. In scientific experiment, it is impossible to control every variable...
an example, try to compare bone density in old people who do and don't run regularly. You will likely find a difference. But, what if some of the runners never ran when younger or if non-runners used to run when younger? What if some persons are allergic to milk and had reduced calcium? Impossible to control every variable, that is why it a "sample."

[penguin_2000]

Originally Posted by parrythis

Fencer A, traveling 2 meters per second, leaves his end of the piste heading toward the other end, 14 meters away. At the same time fencer B, traveling 2.25 meters per second, leaves his end of the piste heading toward the other end. When do the two fencers meet? How far from each end do they meet?

(Sorry, I couldn't resist.)

... depends. if they're epeeists... they'll just jump around for 3 minutes and never meet.

... we could add a fly to this problem as well

[Sciurus-Rex]

Originally Posted by penguin_2000

... depends. if they're epeeists... they'll just jump around for 3 minutes and never meet.

... we could add a fly to this problem as well

Even better than a fly, add a sabreur or foilist trying to act like a referee. Just about as annoying as a fly.