| Interesting how a fighting technique using the | | | | nunchuks as a weapon. When executing these |
| nunchaku weapon, the octagonal oak sticks | | | | katas, Lee, or any expert nunchakudoka (martial |
| connected by a short chain or string, which were | | | | artist who is expert at the nunchuks), would |
| immortalized by Bruce Lee in his famous martial | | | | wave these curious sticks in wave patterns and |
| arts film, "Enter the Dragon," and | | | | swirls which are described by some beautiful |
| mathematics---particularly parametric | | | | mathematical curves called Lissajous, |
| equations---could be so nicely entwined. It is as | | | | eponymously named after the French |
| though mathematics has no favoritism when | | | | mathematician who studied them in detail. |
| popping its head up in all kinds of seemingly | | | | The Lissajous are given parametrically by x = |
| unrelated fields. Read on and you will see how the | | | | A[sin(at) + d], y = B[sin(bt)]. The curves range |
| nunchaku and math are so related. | | | | from the simple sideways figure eight, as when A |
| In a previous article titled, "Why Study Math? - | | | | = 1, B = 2, and d = pi/2 (pi is approximately 3.14), |
| Parametric Equations," I talked about how these | | | | to intricate opposite-facing boomerang figures. |
| nifty equations can describe some exotic curves | | | | Now relating these curves back to nunchakudo, it |
| which, using only the variables x and y, could not | | | | turns out that when practicing with these sticks, |
| be so easily expressed. Thus we talked about the | | | | the expert will swing them in patterns that trace |
| cycloid and how it is easily described by the two | | | | out the various Lissajous curves. As the |
| parametric equations x = a(t - sint) and y = a(1 - | | | | practitioner becomes more and more expert, he |
| cost). If you tried to eliminate the parameter and | | | | or she can trace out more intricate Lissajous |
| express this curve only in terms of x and y, I | | | | curves and do this with poise, artistry, and |
| think you will find this to be an insurmountable | | | | balance. Now how's that for a real-life example of |
| task. I tried it and quickly found myself mired in | | | | where math comes into play in the world! |
| some deep quicksand. Better to stick to the | | | | The next time you watch a martial arts movie |
| parametric equations. | | | | like "Enter the Dragon" and see the nunchuks |
| Now how would parametric equations and math | | | | being swung in graceful fashion, remember there's |
| get caught up with Bruce Lee and the art of | | | | a set of parametric equations that describes that |
| nunchakudo? Well firstly, as a master of the | | | | beautiful motion and elegant display of the chuks. |
| martial arts and particularly the art of using the | | | | Indeed Bruce Lee would be proud to know that |
| nunchuks, which is called nunchakudo, Bruce Lee | | | | someone understood his art in this way. |
| could produce beautiful katas, or forms, using the | | | | |