Math 3181
Name:
Dr. Franz Rothe
February 9, 2015
All3181\3181_spr15hs1.tex
Homework has to be turned in this handout.
For extra space, use the back pages, or blank pages between.
The homework can be done in groups up to four students
due January 27/28
1
S
Math 3181
Name:
Dr. Franz Rothe
September 16, 2015
All3181\3181_fall15h2.tex
2
Solution of Homework
(Alhazens Problem). Given is a circular mirror, and two points inside its disk. A
light ray is emanated from one of these points, and has to be directed to
Math 3181
Dr. Franz Rothe
January 11, 2016
Name:
All3181\3181_spr16h1.tex
1
Solution of Homework
Neutral geometry
Problem 1.1. Encircle the statements below which are valid for any arbitrary incidence
plane; and scratch through the statements which are no
Math 3181
Dr. Franz Rothe
February 10, 2016
Name:
All3181\3181_spr16h2.tex
2
Solution of Homework
Neutral geometry
Problem 2.1. As far as two-dimensional geometry is concerned, Hilberts Proposition 1 reduces to one simple statement: any two different line
Math 3181
Dr. Franz Rothe
February 24, 2016
Name:
All3181\3181_spr16h3.tex
Homework has to be turned in this handout.
For extra space, use the back pages, or put blank pages between.
The homework can be done in groups up to three students
due Wednesday Ma
Math 3181
Name:
Dr. Franz Rothe
May 13, 2016
All3181\3181_spr16f.tex
Solution of Final
10 Problem 1 (Building up geometry). For an axiomatically built-up geometry, six groups of axioms needed:
I. Axioms of incidence
II. Axioms of order
III. Axioms of cong
Math 3181
Dr. Franz Rothe
October 30, 2015
Name:
All3181\3181_fall15t2.tex
2
Solution of Test
Figure 1: Central and circumference angle of a circular arc, both obtained as differences
Problem 2.1. Complete the following proof of Euclid III.20, referring t
Math 3181
Name:
Dr. Franz Rothe
May 14, 2014
All3181\3181_spr14hs5.tex
Homework has to be turned in this handout.
The homework can be done in groups up to three
due April 15
5
Solution of Homework
Construction 1 (Construct the midpoint of a segment with H
Math 3181
Name:
Dr. Franz Rothe
May 14, 2014
All3181\3181_spr14h5.tex
Homework has to be turned in this handout.
The homework can be done in groups up to three
due April 15
5
10
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10
70
Homework
Construction 1 (Construct the midpoint of a seg
Math 3181
Dr. Franz Rothe
August 27, 2015
Name:
All3181\3181_fall15h1.tex
1
Solution of Homework
Problem 1.1 (A special triangle). Use the equilateral triangle and Thales Theorem
to construct a triangle with angles of 30 , 60 and 90 . Describe your constr
Math 3181
Name:
Dr. Franz Rothe
March 27, 2012
All3181\3181_spr12h1.tex
Use the back pages for extra space
due date: January 20
1
Solution of Homework
10 Problem 1.1 (A special triangle). Use the equilateral triangle and Thales
Theorem to construct a tria
Math 3181
Dr. Franz Rothe
April 23, 2012
Name:
All3181\3181_spr12h3.tex
Use the back pages for extra space
due date: April 19
3
Solution of Homework
10 Problem 3.1. Given is a triangle ABC. Construct with straightedge and
compass a square inside this tria
Math 3181
Dr. Franz Rothe
February 23, 2015
Name:
All3181\3181_spr15ts1.tex
1
Solution of Test
Problem 1.1. The second part of Hilberts Proposition 1 states: Any two dierent
planes have either no point in common, or they have one line and no further point
Math 3181
Dr. Franz Rothe
February 7, 2015
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Name:
All3181\3181_spr15t1.tex
1
Test
Problem 1.1. The second part of Hilberts Proposition 1 states: Any two dierent
planes have either no point in common, or they have one line
Math 3181
Dr. Franz Rothe
Name:
All3181\3181_spr13h3.tex
3
Solution of Homework III
One line of information about Hippocrates of Chios comes from Alexander of Aphrodisias. Alexander was the teacher of Simplicius, the most learned and reliable among
the co
Math 3181
Dr. Franz Rothe
Name:
All3181\3181_spr13t2.tex
2
Solution of Test II
20 Problem 2.1. Given is a quadrilateral with two pairs of congruent opposite
sides. Prove in neutral geometry that the two pairs of opposite sides are parallel. Provide
a draw
Math 3181
Dr. Franz Rothe
Name:
All3181\3181_spr13h1.tex
1
Solution of Homework I
10 Problem 1.1. As far as two-dimensional geometry is concerned, Hilberts
Proposition 1 reduces to one simple statement: any two dierent lines either intersect
in one point,
Math 3181
Dr. Franz Rothe
Name:
All3181\3181_spr13h2.tex
2
Solution of Homework II
10 Problem 2.1. Prove the Four-point Theorem directly from the Three-point
Theorem and the Plane separation Theorem.
Answer. Given are four dierent points on a line l. By t
Math 3181
Dr. Franz Rothe
March 10, 2012
Name:
All3181\3181_spr12h2.tex
Use the back pages for extra space
due date: March 1
2
Solution of Homework
Proposition 1 (Hilberts Proposition 2).
.
(a) Given a line and a point not lying on it, there exists a uniq
Math 3181
Dr. Franz Rothe
September 24, 2014
Name:
All3181\3181_fall14t1.tex
1
Solution of Test
Problem 1.1. Encircle the statements below which are valid for any arbitrary incidence
plane; and scratch through the statements which are not always valid.
T
Math 3181
Name:
Dr. Franz Rothe
February 25, 2014
All3181\3181_spr14h3.tex
Homework has to be turned in this handout.
The homework can be done in groups up to three
due March 11/12
3
Solution of Homework
10 Problem 3.1. Give a detailed denition what is me
Math 3181
Name:
Dr. Franz Rothe
March 12, 2014
All3181\3181_spr14h4.tex
Homework has to be turned in this handout.
The homework can be done in groups up to three
due March 20
4
10
10
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80
Homework
Denition 1 (Reection across a Line). Given
Math 3181
Name:
Dr. Franz Rothe
January 24, 2014
All3181\3181_spr14h1.tex
Homework has to be turned in this handout.
For extra space, use the back pages, or blank pages between.
due January 22/23
1
Solution of Homework
10 Problem 1.1. As far as two-dimens
Figure 1: What are the angles of
Math 3181
Dr. Franz Rothe
ABC ?
Name:
All3181\3181_fall12h1.tex
Use the back pages for extra space
due September 7
1
Solution of Homework
These exercises deal with some interesting questions from Euclidean geometry on the
Math 3181
Dr. Franz Rothe
December 25, 2012
Name:
All3181\3181_fall12f.tex
Use the back pages for extra space
Final
Figure 1: Dissection proof of the Pythagorean theorem in a special case
10 Problem 1. Given is a right triangle ABC with angle = 60 . Squar
Math 3181
Dr. Franz Rothe
Name:
All3181\3181_fall12h4.tex
Use the back pages for extra space, attach blank pages if necessary
You may submit the solution in groups up to four students
due in two weeks
4
Solution of Homework
4.1
Two runners
Figure 1: Where
Math 3181
Dr. Franz Rothe
May 9, 2012
Name:
All3181\3181_spr12f.tex
Use the back pages for extra space
10 Problem 1 (Another triangle). Construct a triangle with angles of 30 , 45
and 105 , using only compass and straightedge, but no protractor. Describe
Math 3181
Dr. Franz Rothe
20
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20
20
80
Name:
All3181\3181_fall12t1.tex
Use the back pages for extra space
1
Test
20 Problem 1.1. Given is a line l and a point not lying on the line. Provide a
drawing and explain how the perpendicular is dropped with tra
Math 3181
Dr. Franz Rothe
20
20
20
20
80
Name:
All3181\3181_fall12t1.tex
Use the back pages for extra space
1
Part of Solution for Test
20 Problem 1.1. Given is a line l and a point not lying on the line. Provide a
drawing and explain how the perpendicula
Math 3181
Dr. Franz Rothe
April 25, 2012
Name:
All3181\3181_spr12t3.tex
Use the back pages for extra space
10 Problem 2.1. Given is a triangle ABC . Construct, with straightedge and
compass, a rectangle inside this triangle with width twice of its height.