Math 532: Quiz 3
Name KEY
Axiom 1. There exist exactly 3 points. Axiom 2. Given any 2 distinct points, there exists exactly one line passing through the 2 points. Axiom 3. Given any line, there is a point not on the line. Axiom 4. Any two lines intersect
Math 532: Quiz 2
Name
Axiom P1: There exist at least 4 points no 3 of which are collinear.
Axiom P2: There exists at least 1 line with exactly n + 1 (distinct) points on it.
Axiom P3: Given 2 distinct points, there is exactly 1 line that they both lie on.
M ATH 532/736I, L ECTURE 2
1. Finish Previous Notes 2. Assignment: Problems 1, 2, 8, 9 and 10 from Homework 1. 3. Components of an Axiomatic Systems: (i) Undened Terms (points, lines) (ii) Dened Terms (parallel) (iii) Axioms (iv) A system of logic (if A o
Axioms for a Finite Projective Plane of Order n
Axiom P1. There exist at least 4 distinct points no 3 of which are collinear. Axiom P2. There exists at least 1 line with exactly n + 1 points on it. Axiom P3. Given any 2 distinct points, there exists exact
M ATH 532/736I, L ECTURE N OTES 8
Theorem 1. Let A and B be distinct points. Then C is on AB if and only if there is a real number
t such that C = (1 t)A + tB.
Theorem 3. If A, B and C are points and there exist real numbers x, y, and z not all 0 such tha
A T HEOREM C ONCERNING A FFINE P LANES
Theorem: In an afne plane of order n, each point has exactly n + 1 lines passing through it.
Lemma. If is a line with exactly n points on it (in a nite afne plane of order n) and A is a point
not on , then there are
M ATH 532/736I, L ECTURE 1
1. Hand out and go over syllabus. 2. Class photos. 3. No homework (today). 4. Logic in the Last Century: Are there statements that can be made in mathematics which are true but which we cannot prove? Remark 1: The answer cannot
M ATH 532, 736I: M ODERN G EOMETRY
Test 1 Solutions
Test 1 (1992):
Part I:
(1) Axiom P1:
Axiom P2:
Axiom P3:
Axiom P4:
There exist at least 4 distinct points no 3 of which are collinear.
There exists at least 1 line with exactly n + 1 (distinct) points on
MATH 532, 736I: R EVIEW I NFORMATION FOR T EST 1
What to Memorize:
Know the axioms for a nite projective plane of order n:
Axiom P1. There exist at least 4 distinct points no 3 of which are collinear.
Axiom P2. There exists at least 1 line with exactly n
M ATH 532, 736I: M ODERN G EOMETRY
Name Practice Test #1 (1) State the axioms for a finite affine plane of order n. (Number or name the axioms so you can refer to them.)
(2) Two points have been circled in the 7 7 array of points below. Using the model fo
Math 532: Quiz 2
ANSWERS
Name
Axiom P1: There exist at least 4 points no 3 of which are collinear.
Axiom P2: There exists at least 1 line with exactly n + 1 (distinct) points on it.
Axiom P3: Given 2 distinct points, there is exactly 1 line that they both
Math 532: Homework 1
The rst 7 problems deal with an axiomatic system consisting of the following axioms: Axiom 1. There exist exactly 3 points. Axiom 2. Given any 2 distinct points, there exists exactly one line passing through the 2 points. Axiom 3. Giv
=
Name _ Period _
Activity Sheet 3-3
Solving System of Equations Using Addition With Pictures
Directions: Build and Draw each variable using the following key and combine like terms. In the other set of
boxes Draw different algebraic form(s) of the proble