Geometry and extreme sports
Geometry is intricately linked to extreme sports, which encompass high-risk activities like BASE jumping, cliff diving, and skateboarding. These sports appeal to participants for their adrenaline-inducing challenges and to spectators for their unpredictable outcomes. The rise of extreme sports gained momentum in the late 20th century, particularly with the introduction of televised competitions like the X Games, and some events have made their way into the Olympic Games.
Mathematical concepts, particularly geometry and probability, play a crucial role in enhancing both safety and performance in these sports. For example, skateboarders must understand the physics of their tricks, utilizing differential pressure and rotational mechanics to execute complex maneuvers. Snowboarders and BMX riders also rely on geometric principles to optimize their paths and tricks, with competitions highlighting both speed and artistic expression.
The field of sports engineering further integrates mathematics and engineering to improve athletic performance and equipment design, ensuring safety while enhancing the experience for both athletes and spectators. Overall, the synergy between geometry and extreme sports underlines the importance of scientific principles in pushing the boundaries of athletic achievement.
Geometry and extreme sports
Summary: The emphasis on fast motion, tricks, and personal expression in extreme sports makes geometry especially relevant to athletes.
There is no single definition of extreme sports, though they generally include dangerous sporting activities that involve a substantial risk of injury, like Buildings, Antennae, Spans, and Earth (BASE) jumping, cliff diving, street luge, or even the traditional running of the bulls in Pamplona, Spain. Extreme sports are believed to be attractive to participants because of the challenge and adrenaline rush and to spectators because the results are typically unpredictable.
The popularity of extreme sports grew rapidly in the latter part of the twentieth century. The television network ESPN created the Extreme Games, now called the “X Games,” in 1995, making extreme sports more visible to the general public. Other networks have also begun to televise these types of competitions and some extreme sports events have been included in the Olympic Games. Mathematics is important in extreme sports. Knowing and applying concepts from geometry and probability helps participants be safe and successful. Innovative equipment manufacturers use concepts and techniques from many areas, including geometry, statistics, modeling, and simulation, to prototype and refine their designs, resulting in greater safety and effectiveness.
Skateboarding
Skateboarders perform tricks using a wheeled board, either on a flat surface or using equipment like ramps or rails. Many stunts rely on differential pressure applied by the rider’s feet to various parts of the skateboard to tilt or flip it, often rotating both board and rider in one or more axes. Lip tricks require a vertical orientation and transitional edge like the lip of a swimming pool or ramp. In aerial tricks, the rider leaves the ground completely, using counterpressure of hands and feet to maintain control of the board while spinning or flipping.
Tony Hawk is one of the most well-known extreme athletes and a vertical skateboarding pioneer. He was the first person to competitively perform an aerial turn of two and a half rotations, or 900 degrees, at the 1999 X Games. In the past, he has done 720 degree turns. For the 900, he exerted greater takeoff force in the direction of the turn, producing more rotational velocity. Tony Hawk’s Project 8 video game used motion capture technology to smoothly animate professional skaters, while Tony Hawk Ride allowed players to simulate the sport using a skateboard-like controller.
Snowboarding
Snowboarding is similar to skateboarding and involves standing on a board and sliding down a snow-covered hill. Snowboarding became an Olympic sport in 1998, with giant slalom and half pipe competitions taking place. The giant slalom is a speed race in which athletes speed down a steep hill with gates that require them to zigzag between. Determining an optimal path from one gate to another without crashing or wasting time requires mathematics, especially geometry. A half-pipe consists of two quarter-cylinders connected by a flat space and topped by a small lip. The competition is a more artistic event, with athletes generating enough speed using the curves of the pipe to become airborne and do tricks. These may include multiple rotations, both twisting and somersaulting. At the 2010 Olympics, Shaun White executed a record-setting 1260-degree trick consisting of two flips and three and a half spins.
BMX Biking
In bicycle motocross (BMX), athletes ride specially designed smaller bicycles that enable them to shift their center of mass to make precision movements. BMX courses often use steep hills to launch the rider into the air to perform tricks. Other tricks and spins may be done on flat ground. The sport was added to the list of events for the 2012 Summer Olympic Games. Billy Gawrych is a professional BMX competitor who performs intricate routines, often set to music, with tricks linked together in a series of connected, flowing patterns.
Sports Engineering and Equipment
Sports engineering is a growing interdisciplinary field that draws from mathematics, engineering, biology, physics, materials science, and many other disciplines to study characteristics of athletes and equipment, as well as their interaction. The focus is on performance and safety. For example, engineer Mont Hubbard described the motion of skateboards with riders using two mathematical models, and mathematicians develop new models using techniques and theories from areas like trigonometry, physics, differential equations, and probability. Quality function deployment is a method of quality control that attempts to translate often subjective customer requirements into mathematical engineering specifications. One research group studied the subjective perception of the “feel” of snowboards. They used field evaluations and laboratory data to create matrices of parameters. Snowboards for freeride and freestyle, the two primary types of snowboarding, have somewhat different designs; however, issues of flexibility, torsional stiffness, and curvature were the important factors affecting feel and performance for both styles. Equipment for sports of all kinds is subjected to statistically designed tests to evaluate safety, and data from accidents and failures helps fuel further research.
Bibliography
Clemson, Wendy, David Clemson, Oli Cundale, Laura Berry, and Matt King. Using Math to Conquer Extreme Sports. New York: Gareth Stevens Publishing, 2004.
Estivalet, Margaret, and Pierre Brisson. The Engineering of Sport 7. Vol. 1 New York: Springer, 2008.
Gutman, Bill. Being Extreme: Thrills and Dangers in the World of High-Risk Sports. New York: Citadel Press, 2003.
Sagert, Kelly Boyer. Encyclopedia of Extreme Sports. Westport, CT: Greenwood Press, 2008.
Thorpe, Holly. Snowboarding Bodies in Theory and Practice (Global Culture and Sport). New York: Palgrave Macmillan, 2011.
Tyler, M., and K. Tyler. Extreme Math: Real Math, Real People, Real Sports. Waco, TX: Prufrock Press, 2003.