Archimedes' Quadrature of the Parabola PDF
Preview Archimedes' Quadrature of the Parabola
Introduction TheproblemandArchimedes’discovery Someconclusions Archimedes’ Quadrature of the Parabola John B. Little DepartmentofMathematicsandComputerScience CollegeoftheHolyCross June 12, 2013 JohnB.Little Archimedes’QuadratureoftheParabola Introduction TheproblemandArchimedes’discovery Someconclusions Outline 1 Introduction 2 The problem and Archimedes’ discovery 3 Some conclusions JohnB.Little Archimedes’QuadratureoftheParabola Studied many topics in what we would call mathematics, physics, engineering (less distinction between them at the time) We don’t know much about his actual life; much of his later reputation was based on somewhat dubious anecdotes, e.g. the “eureka moment,” inventions he was said to have produced to aid in defense of Syracuse during Roman siege in which he was killed, etc. Perhaps most telling: we do know he designed a tombstone for himself illustrating the discovery he wanted mosttoberememberedfor(discussedbyPlutarch,Cicero) Introduction TheproblemandArchimedes’discovery Someconclusions Who was Archimedes? Lived ca. 287 - 212 BCE, mostly in Greek city of Syracuse in Sicily JohnB.Little Archimedes’QuadratureoftheParabola We don’t know much about his actual life; much of his later reputation was based on somewhat dubious anecdotes, e.g. the “eureka moment,” inventions he was said to have produced to aid in defense of Syracuse during Roman siege in which he was killed, etc. Perhaps most telling: we do know he designed a tombstone for himself illustrating the discovery he wanted mosttoberememberedfor(discussedbyPlutarch,Cicero) Introduction TheproblemandArchimedes’discovery Someconclusions Who was Archimedes? Lived ca. 287 - 212 BCE, mostly in Greek city of Syracuse in Sicily Studied many topics in what we would call mathematics, physics, engineering (less distinction between them at the time) JohnB.Little Archimedes’QuadratureoftheParabola Perhaps most telling: we do know he designed a tombstone for himself illustrating the discovery he wanted mosttoberememberedfor(discussedbyPlutarch,Cicero) Introduction TheproblemandArchimedes’discovery Someconclusions Who was Archimedes? Lived ca. 287 - 212 BCE, mostly in Greek city of Syracuse in Sicily Studied many topics in what we would call mathematics, physics, engineering (less distinction between them at the time) We don’t know much about his actual life; much of his later reputation was based on somewhat dubious anecdotes, e.g. the “eureka moment,” inventions he was said to have produced to aid in defense of Syracuse during Roman siege in which he was killed, etc. JohnB.Little Archimedes’QuadratureoftheParabola Introduction TheproblemandArchimedes’discovery Someconclusions Who was Archimedes? Lived ca. 287 - 212 BCE, mostly in Greek city of Syracuse in Sicily Studied many topics in what we would call mathematics, physics, engineering (less distinction between them at the time) We don’t know much about his actual life; much of his later reputation was based on somewhat dubious anecdotes, e.g. the “eureka moment,” inventions he was said to have produced to aid in defense of Syracuse during Roman siege in which he was killed, etc. Perhaps most telling: we do know he designed a tombstone for himself illustrating the discovery he wanted mosttoberememberedfor(discussedbyPlutarch,Cicero) JohnB.Little Archimedes’QuadratureoftheParabola Introduction TheproblemandArchimedes’discovery Someconclusions Figure: Sphereinscribedincylinderofequalradius 3V = 2V and A = A (lateral area) sphere cyl sphere cyl JohnB.Little Archimedes’QuadratureoftheParabola On Floating Bodies (2 books) Measurement of a Circle On Conoids and Spheroids On Spirals On the Sphere and Cylinder (2 books) Introduction TheproblemandArchimedes’discovery Someconclusions Surviving works On the Equilibrium of Planes (2 books) JohnB.Little Archimedes’QuadratureoftheParabola Measurement of a Circle On Conoids and Spheroids On Spirals On the Sphere and Cylinder (2 books) Introduction TheproblemandArchimedes’discovery Someconclusions Surviving works On the Equilibrium of Planes (2 books) On Floating Bodies (2 books) JohnB.Little Archimedes’QuadratureoftheParabola On Conoids and Spheroids On Spirals On the Sphere and Cylinder (2 books) Introduction TheproblemandArchimedes’discovery Someconclusions Surviving works On the Equilibrium of Planes (2 books) On Floating Bodies (2 books) Measurement of a Circle JohnB.Little Archimedes’QuadratureoftheParabola
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