Elliptic Functions Lay the Foundations for Modern Physics
Overview
Elliptic functions are considered a special class of analytic mathematical functions that are used to analyze and solve problems in physics, astronomy, chemistry, and engineering. More specifically, elliptic functions (known to modern mathematicians as elliptic integrals) are a large class of integrals related to, and containing among them, the expression for the arc of an ellipse. The advancement of elliptic functions during the nineteenth century provided mathematical precision in calculations required for discoveries in astronomy, physics, algebraic geometry, and topology. In addition to their use in applied mathematics, the development of the theory of elliptic functions also spurred the study of functions of complex variables and provided a bridge between pure and applied mathematics.
Background
Although not called elliptical functions until the nineteenth century, modern study of elliptical functions began in the middle of the seventeenth century. Several mathematicians published works examining the arc length of an elliptical path and Sir Isaac Newton (1642-1727) published works regarding the mathematics of elliptical orbits. As a particular consequence of Newton's work, the mathematical development of the elliptic functions and integrals emerged from centuries of struggle to accurately (i.e., mathematically) explain themechanics of motion, including the motions of the Sun and planets.
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