Archimedes' Quadrature of the Parabola

65 Pages·2013·0.61 MB·English

by  John B. Little

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