This preview shows page 1. Sign up to view the full content.
Modern Geometries
General
•
Why was there renewed interest in geometry in the 1600s?
◦
Why was there a Renaissance?
◦
Mathematical tools like algebra now available.
Analytic or “Algebraic” Geometry
•
What is it?
◦
“Analytic” is not correctly descriptive.
◦
Ancient Greeks did geometric algebra.
◦
Ancient mapmakers used coordinates (latitude and longitude).
◦
In the 14th century, Nicole Oresme had been graphing dependent versus independent
variables.
◦
Eves: Real essence is the transference of a geometric investigation to an algebraic inves
tigation.
◦
By this deFnition, Descartes and ±ermat have claim as the originators.
•
How has it been appraised?
◦
Cooke: “Everyone who has studied analytic geometry in school must have been struck at
the beginning by how much clearer and easier it was to use than the synthetic geometry
of Euclid.”
◦
John Stuart Mill: “[T]he greatest single step ever made in the progress of the exact
sciences.”
◦
Paul Valéry: “[T]he most brilliant victory ever achieved by a man whose genius was
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.
 Fall '10
 wen
 Algebra, Geometry

Click to edit the document details