As I move through my Maahd Najd (Uppercuts)and Kao Loi (Flying knee) in a quiet corner of thetraining room, the thought of my Trigonometry homework pops up in my head. Instead of feelingexhausted,Isort of feel exhilarated (Yes, I’ve already received multiple friendly death threats frommyclassmatesfor expressing my love forsine, cosine and tangent). As a person with an overactiveimagination and a tendency to ask the most random ‘’alien” questions, I think about howmathematics, trigonometry, can be applied to martial arts. I reached home to find millions of articles alreadypublished on the topic. After following the thread connecting these two gloriousforms of art, here’smy two pence.

Most people see martial arts as a package deal to get their physical exercise done as well aslearnself-defence techniques. Mathematics on the other hand, is a threat to the report cards ofsome studentsoran extraordinary game of mental exercise and hobby forsome. Martial arts and mathematics areseemingly unrelated concepts. But you must have thought (at least once in your life) that thereis some practical use of high school mathematics.

Martial arts are more than just kicks, punches, and strikes as much as math is more than just theorems, axioms, and formulas. Martial artsrequire flexibility of mind and body. We’ve all heard of the phrase‘’Practice makes perfect’’. See where I’m going with this? Both these forms of art require practiceandprecision for perfect execution.

I’ve done Karate for 2 years(Brown belt) and I’m currently 7 monthsinto Muay Thai (Kickboxing) classes. Being a science student to top that off, I think I can articulate how the beauty of martial artsisexecuted by mathematical concepts. For instance, the proper execution of a roundhouse kickrequires stepping out with your pivoting foot at 45-degree angle to maintain your balance (Youdonot want to lose your balance and land on the floor). Stepping out at this angle also reducesthe distance from the target and increasesthe power of the kick. We can calculate the appropriate angleof elevation and depression necessary to reach the target effectively by using trigonometric ratios. Thissame principle can also be applied to elbow and knee strikes. Itsoundstedious but once youstart practising long enough, it becomes muscle memory.

After years ofsearching for complex real-life applications of the infamous a2+b 2=c2, I foundout that to execute kicks or punches with maximum impact, the optimal distance should be calculatedbyusing ……. (Dramatic pause) …….

YES, by using the Pythagoras Theorem. It involves understanding the relationship between thedistance from the opponent(base), the height of the kick (height) , and the imaginary line connectingthe practitioner and the opponent (hypotenuse).

Not more than a stone’s throw away from this concept, is physics. Yes, physics is part of thewide spectrum of factorsthat influence the perfect execution of those 360° kicksin Taekwondoor the superman punch in Muay Thai.

Undeniably, there are real life scenarios where we might need Newton’s Laws of motion. Perhapsthisis one of them. Contrary to popular belief, muscle mass is not the only factor that affects theimpact of your punch. A harder punch doesn’t involve a greater force but a greater kinetic energy.

Remember thisformula we derived from Newton’s 2 nd law in 9 th grade?

Kinetic Energy = (mass × velocity 2) / 2

This relationship emphasizes that velocity plays a more significant role than mass in determining the punch's power. According to the kinetic energy formula, doubling the velocityof the punch quadruples its kinetic energy, thereby increasing the impact force. This highlightsthe importance of speed and technique over sheer muscle mass in martial arts, where efficient energy transfer is key to effective strikes.

Now, the impact force of the punch, depends on kinetic energy as well asthe time taken to deliver the blow.

Impact Force = (mass · velocity) / impact duration

Other principles of physics like the centre of mass and centre of gravity for balance and stabilityinstancesis also useful. The application of the concept of projectile motion works wonders (I oncetriedit while playing basketball. It works!)

In conclusion, the graceful arcs of Teep Mea Yun (Angle Kick) and the precise angles of awell-executed throw reveal a beautiful dance between martial arts and the laws of mathematics and physics. This harmonious integration not only elevates the artistry of combat but also showcases the profound connection between abstract concepts and tangiblereality. Every move is a choreography of calculated finesse, creating an unparalleled expressionof skill and strategy in the realm of combat.

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Fatema

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