Math. 467: Modern Geometry
c
S. A. Fulling 2009
First day
Introduce yourself:
Name, major, class
Future plans (career, etc.)
Why are you here? What do you expect to get out of the course?
Content and objectives of the course
[Refer to handout, top half p.
Math. 467
10 December 2010
(Fulling)
Final Examination
Name:
1. (20 pts.) Rearrange these names into historical order, earliest to latest:
Thales,
Klein,
Euclid,
Lambert,
Lobachevsky
Thales, Euclid, Lambert, Lobachevsky, Klein
2. (30 pts.) State the conve
Math. 467
3 March 2011
(Fulling)
Midterm Test Solutions
Name:
1. (Multiple choice each 5 pts.) (Circle the correct capital letter.)
(a) Which of these statements is false? A right angle
(A)
(B)
(C)
(D)
(E)
is congruent to its supplement.
has angle measure
Math. 467
13 October 2010
(Fulling)
Midterm Test Solutions
Name:
1. (Multiple choice each 5 pts.) (Circle the correct capital letter.)
(a) Euclid lived before
(A)
(B)
(C)
(D)
C
Thales
Plato
Proclus
Pythagoras
(the last of the famous ancient Greek geometer
Math. 467
16 October 2009
(Fulling)
Midterm Test Solutions
Name:
1. (10 pts.) All but two of the following propositions are theorems of Hilbert geometry (that
is, they can be proved from the I, B, and C axioms without additional assumptions).
Identify the
Quyen Dang
October 4, 2016
Projective Plan
Using basic mathematical propositions and axiom proved in Modern Geometry course, a
proof will be formulated in order to solve the problem given. The problem given from the
Modern Geometry textbook in chapter two
Quyen Dang
September 17, 2016
Homework 1 W Revision
Prove that the following are definition of a rectangle:
i.
ii.
iii.
A quadrilateral with four right angles
A quadrilateral with all angles congruent to one another
A parallelogram with at least one right
Quyen Dang
October 1, 2016
Major Exercise
Chapter 2: Major Exercise 3:
Let P be a finite projective plane so that, according to Exercise 14(c), all lines in P have the same
number of points lying on them; call this number n+1, with n 2. Show the following
Koki Hara
15.) Imagine three distinct points A,B,C in which A B C. If B is the
midpoint of AC, then A,B,C are three distinct collinear points.(satisfies B-1)
Given points B and D, we can find C as the midpoint of BD. We can also find
A, such that d(A,B) =
Assignment 1!
a.)!
Mean 78.275, Median 81, Std Dev 9.527!
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b.)!
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Bin width 1!
The distribution of data shown by this histogram is
generally well represented even w
Professor Decker
2305 US GOVT
STUDENT NAME_Koki Hara_
Date Due: Day of Exam 4
Homework Exercise 4
Assignment worth 100 points
!
Part 1: Fill in the Blanks (Worth 40 Points)
1) During Reconstruction two black senators and fourteen representatives were elec
Math. 467
6 March 2009
(Fulling)
Midterm Test
Name:
1. (20 pts.) Pronounce each of the following assertions true or false.
(a) In Euclids geometry, by denition, a line m is parallel to a line l if for any two points
P, Q on m, the perpendicular distance f
Math. 467
13 October 2010
(Fulling)
Midterm Test Solutions
Name:
1. (Multiple choice each 5 pts.) (Circle the correct capital letter.)
(a) Euclid lived before
(A)
(B)
(C)
(D)
C
Thales
Plato
Proclus
Pythagoras
(the last of the famous ancient Greek geometer
Math. 467: Modern Geometry
c
S. A. Fulling 2009
First day
Introduce yourself:
Name, major, class
Future plans (career, etc.)
Why are you here? What do you expect to get out of the course?
Content and objectives of the course
[Refer to handout, top half p.
Math. 467
11 May 2009
(Fulling)
Final Examination
Name:
1. (40 pts.) was the take-home essay.
2. (30 pts.) Rearrange these names into historical order, earliest to latest:
Saccheri,
Euclid,
Bolyai (the son),
Klein,
Thales,
Proclus
3. (30 pts.) State and p
Math. 467
11 May 2011
(Fulling)
Final Examination Solutions
Name:
1. (50 pts.) was the take-home essay.
2. (20 pts.)
(a) In the Klein disk, draw a sketch showing how the parallel postulate (HE) can be
violated.
(b) In the Klein disk, draw a sketch showing
Math. 467
10 December 2010
(Fulling)
Final Examination
Name:
1. (20 pts.) Rearrange these names into historical order, earliest to latest:
Thales,
Klein,
Euclid,
Lambert,
Lobachevsky
Thales, Euclid, Lambert, Lobachevsky, Klein
2. (30 pts.) State the conve
Math. 467
May 2011
(Fulling)
Final Examination Take-Home Part
We have taken it more or less for granted that the real Cartesian plane, R2 , is a model
for all the Hilbert axioms. Your task is to write a good essay proving that it does satisfy four
of the
Math. 467
(Fulling)
December 2009
Final Examination Take-Home Part
Carefully verify that the Klein disk model satises all the Hilbert incidence and betweenness
axioms and the hyperbolic parallel property (in the form stated on p. 75 of Greenberg).
You may
Math. 467
(Fulling)
May 2009
Final Examination Take-Home Part
Carefully verify that the Klein disk model satises all the Hilbert incidence and betweenness
axioms and Hilberts hyperbolic axiom of parallels.
You may assume that the underlying Euclidean plan
Koki Hara
1.)a.) By Axiom B-1, A, B, and C are three distinct collinear points, and
A, C, and D are three distinct collinear points. (RAA) Suppose B=D. Then by
Axiom B-3, if A, B, and C are three distinct collinear points, only one of hte
points is betwee