Thinker & Thug Garner The Life of Archimedes The Works of The Thinker and the Thug Archimedes On the Sphere and Cylinder On Conoids and Spheroids The History of Mathematics, Part 9 On Spirals On the Equilibrium of Planes The Sand-Reckoner Quadrature of the Parabola Other Works Chuck Garner, Ph.D. The Archimedes Palimpsest The Legacy of Department of Mathematics Archimedes Rockdale Magnet School for Science and Technology Homework February 22, 2021 1 / 35 Thinker & Thug Outline Garner The Life of The Life of Archimedes Archimedes The Works of The Works of Archimedes Archimedes On the Sphere and Cylinder On the Sphere and Cylinder On Conoids and Spheroids On Spirals On Conoids and Spheroids On the Equilibrium of Planes The Sand-Reckoner On Spirals Quadrature of the Parabola Other Works On the Equilibrium of Planes The Archimedes The Sand-Reckoner Palimpsest The Legacy of Quadrature of the Parabola Archimedes Other Works Homework The Archimedes Palimpsest The Legacy of Archimedes Homework 2 / 35 Thinker & Thug Outline Garner The Life of The Life of Archimedes Archimedes The Works of The Works of Archimedes Archimedes On the Sphere and Cylinder On the Sphere and Cylinder On Conoids and Spheroids On Spirals On Conoids and Spheroids On the Equilibrium of Planes The Sand-Reckoner On Spirals Quadrature of the Parabola Other Works On the Equilibrium of Planes The Archimedes The Sand-Reckoner Palimpsest The Legacy of Quadrature of the Parabola Archimedes Other Works Homework The Archimedes Palimpsest The Legacy of Archimedes Homework 3 / 35 Thinker & Thug Archimedes Garner The Life of Archimedes The Works of Archimedes On the Sphere and Cylinder On Conoids and Spheroids On Spirals On the Equilibrium of Planes The Sand-Reckoner Quadrature of the Parabola Other Works The Archimedes Palimpsest The Legacy of Archimedes Homework Archimedes 287 BC-212 BC “Give me a place to stand and I will move the Earth.” 4 / 35 Thinker & Thug Archimedes of Syracuse Garner The Life of Archimedes The Works of Archimedes On the Sphere and Cylinder On Conoids and Spheroids On Spirals On the Equilibrium of Planes The Sand-Reckoner Quadrature of the Parabola Other Works The Archimedes Palimpsest The Legacy of Archimedes Homework 5 / 35 Thinker & Thug Archimedes Garner The Life of Archimedes The Works of Archimedes On the Sphere and Cylinder On Conoids and Spheroids I Spent youth in Alexandria On Spirals On the Equilibrium of Planes The Sand-Reckoner I Related to King Hieron; advisor to the King Quadrature of the Parabola Other Works I Inventor and mathematician The Archimedes Palimpsest I Unique because he combined pure geometrical The Legacy of analysis and the mechanical/practical (Plato urged Archimedes separation of the two) Homework 6 / 35 Thinker & Thug Archimedes’ Inventions Garner The Life of Archimedes The Works of Archimedes On the Sphere and Cylinder On Conoids and Spheroids On Spirals On the Equilibrium of Planes The Sand-Reckoner Quadrature of the Parabola Other Works The Archimedes Palimpsest The Legacy of Archimedes Homework The Archimedean Screw 7 / 35 Thinker & Thug Archimedes’ Inventions Garner The Life of Archimedes The Works of Archimedes On the Sphere and Cylinder On Conoids and Spheroids On Spirals On the Equilibrium of Planes The Sand-Reckoner Quadrature of the Parabola Other Works The Archimedes Palimpsest The Legacy of Archimedes Homework The Archimedean Screw in use at a water treatment plant in Tennessee 8 / 35 Thinker & Thug Archimedes’ Inventions Garner The Life of Archimedes The Works of Archimedes On the Sphere and Cylinder On Conoids and Spheroids On Spirals On the Equilibrium of Planes The Sand-Reckoner Quadrature of the Parabola Other Works The Archimedes Palimpsest The Legacy of Archimedes Homework The Archimedean Claw 9 / 35 Thinker & Thug Archimedes Garner The Life of Archimedes The Works of Archimedes On the Sphere and Cylinder On Conoids and Spheroids I Discovered the first law of hydrostatics: On Spirals On the Equilibrium of Planes “A body immersed in fluid is buoyed up by a force The Sand-Reckoner Quadrature of the Parabola equal to the weight of the displaced fluid.” Other Works The Archimedes I Invented the pulley Palimpsest The Legacy of I Analyzed the lever Archimedes Homework I Died during the Roman siege of Syracuse 10 / 35 Thinker & Thug Archimedes Garner The Life of Archimedes The Works of Archimedes On the Sphere and Cylinder On Conoids and Spheroids On Spirals On the Equilibrium of Planes The Sand-Reckoner Quadrature of the Parabola Other Works The Archimedes Palimpsest The Legacy of Archimedes Homework “Do not disturb my circles!” 11 / 35 Thinker & Thug Outline Garner The Life of The Life of Archimedes Archimedes The Works of The Works of Archimedes Archimedes On the Sphere and Cylinder On the Sphere and Cylinder On Conoids and Spheroids On Spirals On Conoids and Spheroids On the Equilibrium of Planes The Sand-Reckoner On Spirals Quadrature of the Parabola Other Works On the Equilibrium of Planes The Archimedes The Sand-Reckoner Palimpsest The Legacy of Quadrature of the Parabola Archimedes Other Works Homework The Archimedes Palimpsest The Legacy of Archimedes Homework 12 / 35 Thinker & Thug The Surviving Works of Archimedes Garner The Life of Archimedes I On the Sphere and Cylinder (2 books) The Works of Archimedes On the Sphere and Cylinder I Measurement of a Circle On Conoids and Spheroids On Spirals I On Conoids and Spheroids On the Equilibrium of Planes The Sand-Reckoner Quadrature of the Parabola I On Spirals Other Works On the Equilibrium of Planes (2 books) The Archimedes I Palimpsest I The Sand-Reckoner The Legacy of Archimedes I Quadrature of the Parabola Homework I On Floating Bodies (2 books) I Book of Lemmas I The Cattle-Problem 13 / 35 Thinker & Thug The Surviving Works of Archimedes Garner The Life of Archimedes The Works of Archimedes On the Sphere and Cylinder On Conoids and Spheroids All works come to us with cover letters: On Spirals I On the Equilibrium of Planes The Sand-Reckoner I Many to Dositheus Quadrature of the Parabola Other Works I One to Eratosthenes, librarian at Alexandria The Archimedes I We get insight into mathematical atmosphere of the Palimpsest The Legacy of time Archimedes I We get insight into Archimedes himself Homework 14 / 35 I Propositions 33 and 34 of Book I: The cylinder whose base is equal to a great circle of the sphere and whose altitude is equal to a diameter of the sphere has a total surface exactly 3 equal to 2 the surface of the sphere and a volume 3 exactly equal to 2 the volume of the sphere. Thinker & Thug On the Sphere and Cylinder Garner The Life of Archimedes The Works of Archimedes On the Sphere and Cylinder I Archimedes own favorite work On Conoids and Spheroids On Spirals I 2 books, 60 propositions On the Equilibrium of Planes The Sand-Reckoner Quadrature of the Parabola Other Works The Archimedes Palimpsest The Legacy of Archimedes Homework 15 / 35 Thinker & Thug On the Sphere and Cylinder Garner The Life of Archimedes The Works of Archimedes On the Sphere and Cylinder I Archimedes own favorite work On Conoids and Spheroids On Spirals I 2 books, 60 propositions On the Equilibrium of Planes The Sand-Reckoner Quadrature of the Parabola I Propositions 33 and 34 of Book I: Other Works The cylinder whose base is equal to a great circle of The Archimedes Palimpsest the sphere and whose altitude is equal to a The Legacy of diameter of the sphere has a total surface exactly Archimedes 3 Homework equal to 2 the surface of the sphere and a volume 3 exactly equal to 2 the volume of the sphere. 15 / 35 Thinker & Thug On Conoids and Spheroids Garner The Life of Archimedes The Works of Archimedes On the Sphere and Cylinder On Conoids and Spheroids On Spirals On the Equilibrium of Planes Calculated volumes and areas of paraboloids, cones, The Sand-Reckoner I Quadrature of the Parabola hyperboloids, spheroids Other Works The Archimedes 3 Palimpsest I Proved that the volume of a paraboloid is 2 the The Legacy of volume of a cone with the same base and axis Archimedes Homework 16 / 35 Thinker & Thug On Spirals Garner The Life of Archimedes The Works of Archimedes On the Sphere and Cylinder On Conoids and Spheroids On Spirals On the Equilibrium of Planes The Sand-Reckoner Quadrature of the Parabola Other Works The Archimedes Palimpsest The Legacy of Archimedes Homework I Area of one circuit is one-third the area of the circle with radius equal to the distance of the endpoints 17 / 35 Post. 2, 3 When weights at certain distances are in equilibrium, and something is (added to/subtracted from) one of the weights, they will incline toward the weight (to which the addition was made/from which nothing was taken). Thinker & Thug On the Equilibrium of Planes Garner The Life of Archimedes Represents the first instance of mathematical modeling. The Works of Archimedes Post. 1 Equal weights at equal distances are in On the Sphere and Cylinder On Conoids and Spheroids equilibrium; equal weights at unequal On Spirals On the Equilibrium of Planes distances incline toward the weight at the The Sand-Reckoner Quadrature of the Parabola greater distance. (Principle of Insufficient Other Works Reason) The Archimedes Palimpsest The Legacy of Archimedes Homework 18 / 35 Thinker & Thug On the Equilibrium of Planes Garner The Life of Archimedes Represents the first instance of mathematical modeling. The Works of Archimedes Post. 1 Equal weights at equal distances are in On the Sphere and Cylinder On Conoids and Spheroids equilibrium; equal weights at unequal On Spirals On the Equilibrium of Planes distances incline toward the weight at the The Sand-Reckoner Quadrature of the Parabola greater distance.