Advanced Euclidean
Geometry
What is the center of a triangle?
But what if the triangle is not equilateral?
?
Circumcenter
Equally far from the vertices?
P
A
P
I
Points are on the
perpendicular
bisecto
Geometric
Transformations
Definitions
Def: f is a mapping (function) of a set A into a set B if for every
element a of A there exists a unique element b of B that is paired
with a; this pairing is den
A Communications Network
?
A Communications Network
What are the desirable properties of the switching box?
1. Every two users must be connected at a switch.
2. Every switch must "look alike".
3. The
Geometric Constructions
Philosophy of Constructions
Constructions using compass and straightedge have
a long history in Euclidean geometry. Their use
reflects the basic axioms of this system. However,
The
Inversion
Transformation
A non-linear transformation
The transformations of the Euclidean plane that we
have studied so far have all had the property that
lines have been mapped to lines. Transfor
Non-Euclidean
Geometry
The Parallel Postulate
Non-Euclidean Geometry is not not Euclidean
Geometry. The term is usually applied only to the
special geometries that are obtained by negating the
paralle
Arithmetic and Geometry:
Uncomfortable Allies?
Bill Cherowitzo
University of Colorado Denver
MAA Rocky Mountain Sectional Meeting
April 25, 2008
In the beginning.
Only
there was Geometry
^
Euclid XII.
What is a proof?
Proofing as a social process, a communication art.
Theoretically, a proof of a mathematical
statement is no different than a logically valid
argument starting with some premises and e