Figure skating and mathematics
Figure skating is a competitive winter Olympic sport that combines artistry and athleticism, where skaters glide on ice using metal blades. This sport involves intricate patterns on the ice, which can be described using geometric principles. The shapes formed by skaters, such as the classic figure eight, are a reflection of the curves and arcs created by their movements. Additionally, the physical mechanics of figure skating incorporate mathematical principles; for instance, the execution of jumps and spins involves calculations related to parabolic arcs, velocity, and the skater's center of gravity.
There are four main disciplines in Olympic figure skating: singles (both ladies' and men's), pairs, and ice dance. Skaters are judged based on a combination of technical difficulty and artistic expression, using a scoring system that assigns numerical base values to various elements, such as jumps and spins. The competition requires skaters to showcase a range of skills, including footwork and intricate lifts in pairs skating. Overall, the integration of mathematics and physical principles in figure skating highlights the complexity and precision required to excel in this captivating sport.
Figure skating and mathematics
Summary: The elements, equipment, and scoring system of figure skating all involve a mathematical framework.
Figure skating is a winter Olympic competitive sport, which involves artistically gliding on ice using metal blades. Ice skating rinks are generally shaped in the form of rectangles with rounded corners. The patterns skaters form on the ice can be explained in geometric terms. Physical principles are observed when watching figure skating. The scoring system used to judge figure skating involves algebraic computations.
Patterns
The bottoms of ice skating blades are not flat, but rather slightly curved, like arcs taken from the edge of a circle about seven to nine feet in radius. This enables the skater to angle and tilt to form patterns on the ice. These patterns can be represented geometrically. For instance, the most famous geometric pattern on ice is a figure eight, which can be formed by two circles of equal size tangential to each other. A skater could start the first circle of the figure eight on the right forward outside edge and skate the second circle on the left forward outside edge. The possible edge combinations include using the left or right foot, traveling forward or backwards, and using the inside or outside edges.
Mathematical Principles of Spinning and Jumping
In addition to basic compulsory figures, modern skating requires participants to execute increasingly difficult jumps and spins. In a jump, the skater’s center of gravity follows a parabolic arc with respect to the ice, and a jump is frequently measured in terms of its vertical displacement (the height off the ice) as well as horizontal displacement (the distance). Both are a function of many variables, such as the takeoff angle and velocity immediately prior to the jump.
Spinning, whether in the air as part of a jump or on the ice, is also a complex function of many variables. Factors include the skater’s body mass and speed when entering the spin, as well as the extension of the arms or legs from the body. For example, a spinning skater rotates more slowly with extended arms than when the arms are tucked in because as the radius between the body and the arms decreases, the angular velocity increases.
Judging
Four disciplines of figure skating are competitive at the Olympic level: singles (ladies’ and men’s), pairs, and ice dance. In each of these disciplines, a choreographed program is skated to music in competition and is judged according to the International Skating Union’s International Judging System. The International Judging System awards points for technical difficulty and artistry.
There are many types of skating elements. Jumps vary from their takeoff edges as well as numbers of rotations between one and four. Throw jumps are also performed by the pair teams. A variety of spins are possible, but there are three basic spin positions: upright, camel, and sit. Some spins involve a change of foot, change of position, flying entrance, or difficult variation. Footwork is an element in every program and requires steps and turns that fully cover the ice surface in a circular, straight line, or serpentine pattern. For pairs and ice dance skaters, combination spins, lifts, and other elements requiring two skaters are also scored.
Each of the skating elements performed in a program is assigned a numerical base value, which varies according to difficulty. For example, in the 2010–2011 skating season, the base value of a triple toe loop was 4.1 points, and the base value of the single toe loop was 0.4 points, indicating that the triple toe loop was a much harder jump. Judges add to or subtract from the base value of each element depending upon its execution. For instance, a poorly performed toe loop would receive fewer than 0.4 points. The sum of the values given for each element is called the “technical score.”
In addition to a technical score for performance on the individual elements, overall scores for artistic aspects of the program, such as choreography, interpretations, transitions, and skating skills, are awarded as the program components score, which is added to the technical score for a total overall score. The skaters with the highest scores earn the highest rankings.
Bibliography
Carroll, Maureen, Elyn Rykken, and Jody Sorensen. “The Canadians Should Have Won!?” Math Horizons 10 (February 2003).
Kerrigan, Nancy, and Mary Spencer. Artistry on Ice: Figure Skating Skills and Style. Champaign, IL: Human Kinetics, 2002.
Schulman, Carole. The Complete Book of Figure Skating. Champaign, IL: Human Kinetics, 2002.