Mathematics 3052 Assignment 6 Due February 4, 2015
The dropbox contains a sheet with 4 distinct possible parallel postulates .
Short names for each of these are: Triangle Sum, Parallel Transport, Euclids Fifth
Postulate, and Playfairs Postulate.
You task

Name 1
Name 2
3050 Projections from the Sphere to the Plane
1. Gnomic projection is projection from the center of the sphere onto a plane
(tangent to the south pole). In responding to the following questions, include a
sketch, if possible, where the proje

Chapter 2
STRAIGHTNESS ON SPHERES
. [I]t will readily be seen how much space lies between the two
places themselves on the circumference of the large circle which is
drawn through them around the earth. . [W]e grant that it has been
demonstrated by mathem

Name _ Name
1
_
Math 3052 Lab tasks February 11, 2015
Wewillexplorefurthersomepropertiesofplanetransformations.Intheusual3050folderyouwillfind
aGSPDocuments'SecretTransformations'.
Eachpageofsecretisometrycontainsapairoftriangles(labeled)whichillustratewh

Geometry Autobiography.
Walter Whiteley Updated September 2014
I took my last 'formal' geometry course back in high school. (In my case,
Ontario Grade 13, Analytic Geometry in the early 60's. If you did your high
school in Ontario, it is possible that you

Chapter 1
WHAT IS STRAIGHT?
Straight is that of which the middle is in front of both extremities.
Plato, Parmenides, 137 E [AT: Plato]
A straight line is a line that lies symmetrically with the points
on itself.
Euclid, Elements, Definition 4 [Appendix

Math 3050 End of Term Assignments, 2015
The dates are for students who have chosen to follow the revised schedule.
Contact me if you have specific needs that should be accommodated.
Revised Marking Scheme:
Autobiography:
5 Regular assignments (2-6), inclu

Name 1
Name 2
Parabola Analysis:
(0,1/4)
y = -1/4
Consider this construction of a parabola.
(1) Write the equation for all points equal distant from the focus (0,1/4) and the
directrix (line) y= - 1/4. Simplify the equation to a standard form.
(2) Show th

Chapter 0
HISTORICAL STRANDS
OF GEOMETRY
All people by nature desire knowledge.
Aristotle (384 B.C.322 B.C.), Metaphysics
History is the witness that testifies to the passing of time; it
illumines reality, vitalizes memory, provides guidance in daily
lif

Woori Kim
210 874 998
MATH 3052
A possible definition of an angle can be the measured value between two straight
lines that share an endpoint. This definition can apply to both sphere and plane. However,
not all the definitions or statements about an angl

Name 1
Name 2
3050 Projections from the Sphere to the Plane
1. Gnomic projection is projection from the center of the sphere onto a plane
(tangent to the south pole). In responding to the following questions, include a
sketch, if possible, where the proje

1
To appear in the Proceedings of the 1999 CMESG Conference
The Decline and Rise of Geometry in 20th Century North America.
Walter Whiteley, Mathematics and Statistics, York University, Toronto Ontario
Introduction
While I will begin with my own evidence

Math 3050 Assignment 2. Due September 24 2014 (third class)
Write your solutions to Problems 1.1 and 2.1 from Henderson.
It might help to think about how you would explain straightness to a 5-year-old (or how
the 5-year-old might explain it to you!). If y

MATH 3050 Assignment 1 Due September 17, 2014
Write a brief 'geometry autobiography' that indicates your own experiences, reflections and
questions about geometry, the learning of geometry, and the teaching of geometry. Recall mine
is on the Moodle Site.

Your Name:
Math 3052 Peer Feedback (one for each of 10 project presentations)
What was the title of the presentation and who presented?
What was the question they were answering?
What did you learn from the presentation? Please be as detailed and explicit

Assignment 4, 2014 Due November 5
From Chapter 6:
Problem 6.2 C (the converse of ITT) If a triangle has two angles congruent, then two sides
are congruent
plus the following corollary to this proof : In an isosceles traingle, the right bisector of the
bas

Graduate Peer Mentors/Junior Fellows
Vision: Peer-based, Bethune College academic service, in
which upper-year students are paired with GPMs to
explore future career opportunities in graduate and/or
professional schools
Current Bethune-affiliated graduate

Math 3052 Assignment 5, with Bonus Problem
The due date for this assignment is December 3.
Question 1: Problem 7.1 The area of a small triangle on the sphere. Write a full
proof of the formula for the area of a triangle on the sphere.
There are resources

A proof of Eulers Formula
ve+f=0
Draft Walter Whiteley
November 23, 2011
The formula
Given a connected planar graph, with v
vertices, e edges, and f faces:
v-e+f = 2
Proof is by induction on the number of edges
Inductive Proof
Start with a vertex. If th

Versions of this paper appeared in the Ontario Mathematics Gazette, and the
St. Louis Convergence (magazines for teachers).
Why you should learn geometry.
Walter Whiteley, Professor of Mathematics and Statistics,
Graduate Programs in Mathematics, in Educa

Woori Kim
210 874 998
MATH 3052
Assignment 4
According to Isosceles Triangle Theorem, it states that if two sides of a
triangle are congruent, then two angles are congruent. Assume there is a triangle
with two congruent sides as below.
Then, if one draws