C HINESE R EMAINDER T HEOREM
M ATH C IRCLE AT WASHINGTON U NIVERSITY IN S T. L OUIS , A PRIL 19, 2009
Baili MIN
In a third-centry A. D. Chinese book Sun Tzus Calculation Classic one problem
is recorded which can be translated into English as:
Suppose we h
Math 266
Lecture Notes on Euclidean Geometry
Baili Min
March 18, 2010
1
Axiom Sets
Measuring Segments
In the Euclidean geometry, measurement is granted by some axioms:
Axioms for segment measurement:
S1 To every pair of points A and B there corresponds a
Math 266
Lecture Notes on Euclidean Geometry
Baili Min
March 25, 2010
1
Euclidean Plane Geometry
Fifth Postulate
Euclids fth postulate If two lines are cut by a transversal in such a way that the sum of the two
interior angles on one side of the transvers
Math 266
Lecture Notes on Euclidean Geometry
Baili Min
February 25, 2010
1
Axiom Sets
Review
Axioms of incidence:
I1 Given two distinct points P , Q there exists a unique line incident with P and Q. This line
will be denoted by P Q.
I2 For every line l th
Math 266
Lecture Notes on Euclidean Geometry
Baili Min
February 18, 2010
1
Axiom Sets
Euclids Five Postulates
Key words: Euclid, The Elements, fth postulates, Euclidean and Non-Euclidean Geometries
I A line may be drawn between any two points.
II Any line
Counting: Dene 0, 1, 2, 3, . . .
When we build a house, we always start with foundations. For this subject, we do in a similar way.
We will learn the mathematics of counting, but right now, we have no idea what is 0, what is 4,
what is the idea of how man