There is much more to the arabesque, grand jeté, and fouetté than just hours of practice and strong toes. Dancers do not often understand the physics and mathematics describing their movements, but they know how to execute them with grace. If ballerinas were not able to feel physics, they would fall over. Legs, arms and head are oscillating as they turn– moving back and forth in seemingly separate patterns. For dancers, everything must move in separate patterns, yet at the same time, move at the same rhythm. This presentation introduces the history, mathematics, and physics behind ballet. Ballet originated in the Italian Renaissance courts during the 15th century. Noblemen and women attended special events, such as wedding celebrations, where dancing and music were considered an elaborate spectacle. Dancing masters taught the steps to the nobility and the court participated in the performances. In the 16th century, Catherine de Medici, an Italian noblewoman and the wife of King Henry II of France, funded ballet within the French Court. A century later, King Louis XIV helped to popularize and standardize ballet. In 1661, the first dance academy opened in Paris and ballet moved from the courts to the stage. The French opera created the opera-ballet tradition in France. During the mid-1700s, a French ballet master, Georges Noverre, rebelled against the opera-ballet because he believed that ballet could stand as its own art form. This led to the establishment of a dramatic style of ballet that conveys a narrative story. In the late 18th century, the popularity of ballet increased in Russia, where classical ballet was represented in its most classical form: Marius Petipa’s The Nutcracker, Swan Lake, and Sleeping Beauty, were composed. The main purpose of classical ballet was to display technique to its fullest— pointe work, high extensions, precision of movement, and turn-out (the outward rotation of the legs from the hip) are included. Demanding leaps, steps, and turns were choreographed into the story. During the Romantic Movement in the start of the 19th century, ballet was influenced by spirits, magic, and fragility; henceforth, the romantic ballets were established. During the Romantic Era, en pointe, dancing on the tips of toes, became the norm for ballerinas, and the “tutu,” a skirt made of tulle, was introduced. Later on in the 19th century, New York City Ballet founder, George Balanchine, a Russian who immigrated to America, introduced what is now known as the neo-classical ballet. This is a form that expands the classical form. Balanchine is considered to be one of the greatest innovators of the “plot-less” contemporary ballet: without a definite story line, its purpose is to use movement to express the music, and to illuminate human emotion and endeavor. Today, ballet is multi-faceted: classical forms, traditional stories, and contemporary innovations intertwine to produce the character of a modern ballet. Physics and mathematics are found in every aspect of dance. First, it is important to understand that the net force (Fnet) involves the addition of applied forces. The net force causes a change in an object’s momentum. For example, the net force on a dancer is the force of gravity acting down, the force from the support of the floor acting upon, and the sideways force of the friction from the floor. A torque in physics is an off-center force that causes something to spin. Also, the torque can change angular momentum of an object. In dance, it should be understood that the greater the force, the more quickly a dancer can spin. Torques are further generated from the spin-axis, which causes the dancer to spin more quickly. The longer a torque is activated, the greater the total change in angular momentum. This is expressed through the equation: ΔL=τΔt. If a torque is not applied to a rigid object, or a solid body of finite size, it spins at a constant rate. Its spin-axis does not wobble. Non-rigid objects, like...
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