The Mathematics of Archimedes (287-212 B.C.) (Greek). Why look at Archimedes?. He is considered the greatest mathematician of ancient times. . He was also a great scientist and had many inventions credited to his name. Archimedes Activities. Approximating Pi. Drawing an Archimedean Spiral.
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He is considered the greatest mathematician of ancient times.
He was also a great scientist and had many inventions credited to his name
Drawing an Archimedean Spiral
Creating a Stomachion game
He found the volume and surface area of a sphere.
Archimedes proved, among many other geometrical results, that the volume of a sphere is two-thirds the volume of a circumscribed cylinder. This he considered his most significant accomplishments, requesting that a representation of a cylinder circumscribing a sphere be inscribed on his tomb.
He computed the area of an ellipse by essentially "squashing" a circle.
He approximated Pi (π)
Between 3 10/71 and 3 1/7
Use long division to calculate the value of 3 10/71
Use long division to calculate the value of 3 1/7
Archimedes estimate Pi to be between 3 10/71 and 3 1/7
Find Pi (π) on your calculator: how far off was he?
What’s the difference between an Archimedean spiral and an Equiangular Spiral?
How would you draw the spiral?
Draw a series of concentric rings (6 rings).
Cut the circle into 6 equal angles (pie-shaped pieces).
Connect successive intersections of ring and radius to produce a spiral.
His invention of the water-screw, still in use in Egypt, for irrigation, draining marshy land and pumping out water from the bilges of ships
According to legend, when Archimedes got into his bath and saw it overflow, he suddenly realised he could use water displacement to work out the volume and density of the king's crown. Archimedes not only shouted "Eureka" - I have found it - he supposedly ran home naked in his excitement.
His invention of various devices used in defending Syracuse when it was besieged by the Romans.
Any ideas what this is?
Archimedes used mirrors and sunlight to blind invading ships
Archimedes also invented a jigsaw game consisting of 14 ivory pieces that were to be used to create pictures and shapes
Start with a 12 by 12 grid (144 squares)
Draw lines through the indicated lattice points.
The lines divide the square into 14 three-, four-, and five-sided polygons. These polygons are called lattice polygons because their vertices are at lattice points. The lattice polygons form the 14 pieces of the Stomachion.
Here are 12 of the 13 Archimedean solids. Can you find the missing one?