Math 348 (2006): Assignment #1
due Monday, July 10, 2006
1. Let ABC be a triangle. Suppose that B C. Prove that AB = = AC, so the triangle is isosceles. Hint: Mimic the proof of Pappuss Theorem but us
MATH 348: Solved Emergency Problems, Week 1
Leonid Chindelevitch
July 13, 2008
1
Tuesday, July 8, 2008
1. Problem: Given a circle , construct its center O using only a compass.
Solution: Let r be the
MATH 348: Solved Emergency Problems, Week 2
Leonid Chindelevitch
August 25, 2008
1
Monday, July 14, 2008
1. Problem: ABCD is a cyclic quadrilateral with extended sides AD, BC
meeting at Q and extended
MATH 348: Solved Emergency Problems, Week 3
Leonid Chindelevitch
August 24, 2008
1
Monday, July 21, 2008
1. Problem: Let ABC be an equilateral triangle inscribed in a circle , and
let P be a point on
MATH 348: Solved Emergency Problems, Week 4
Leonid Chindelevitch
August 26, 2008
1
Monday, July 28, 2008
1. Problem: From each of the centers O1 , O2 of two circles 1 , 2 tangents
are drawn to the oth
GEOMETRY #1
DYLAN CANT
Problem 1. Let A, B, C, D be distinct points in the plane and suppose that the lines AC
and BD intersect in a point E. Prove that the following two conditions are equivalent:
(i
MATH 348 TOPICS IN GEOMETRY
Course Outline (2017)
Instructor: Tom Fox, Burnside Hall 1243, [email protected]
Office Hours: Tuesday 11:00-14:00 (provisional) or by appointment
Textbook: None. Notes an
Let ABC be a triangle.
I t is required to prove that the
= cfw_we fig/2,23 angles.
time LEABC, BOA, CAB together ' n'l' MF- . [1- : m w 35-h]; L'- .- ., 11 :' . _ . -. 2%.: I':' u'._'l_-|.'_:'-.-_'\-n
76 SOLIDS FOR WHICH V = (mean 13)]: [CHAR V
Properties
1. The altitude of a prismatoid is the perpendicular distance
between the planes of the bases. '
2. The midsection of a prismatoid is the section
BOOK I.
DEFINITIONS.
I. A point is that "which has no part.
2. A line is breadthless length.
3. The extremities of a line are points.
4. A straight line is a line which lies evenly with the
8. A plane
MATH 348: Assignment 5 (nal version)
Leonid Chindelevitch
July 29, 2008
1. Suppose that A, B, C, D are 4 distinct points in the plane, with AB CD
and AC BD. Prove that AD BC . Hint: Consider several c
MATH 348: Assignment 4 (nal version)
Leonid Chindelevitch
August 2, 2008
1. Two circles, 1 and 2 , and a line l are given. Locate a line, parallel to
l, so that the distance between the points at whic
Math 348 (2006): Assignment #1: Solutions
1. Consider the correspondence of vertices A A, B C, C B. Under this correspondence, we have that B C (by hypothesis) and also C B. Finally, = = the sides con
Math 348 (2006): Assignment #2
due Monday, July 17, 2006
1. Let f be an isometry of the plane. Show that f takes a pair of parallel lines to a pair of parallel lines. (You can use the fact that we kno
Math 348 (2006): Assignment #2: Solutions
1. Let and be a pair of parallel lines. Suppose the line m intersects and at points P and P , respectively. Since , the alternate interior angles are congruen
Math 348 (2006): Assignment #3
due Monday, July 24, 2006
For problems 1, 2, and 3, let be a circle with centre O and radius k. 1. Show directly, using the denition of inversion, that if is a circle pa
Math 348 (2006): Assignment #3: Solutions
1. Let be a circle passing through O. Let A be the point on diametrically opposite from O. Let A be the inverse of A. Now consider any point P on other than O
Math 348 (2006): Assignment #4
due Monday, July 31, 2006
1. Show that any orientation reversing isometry of E 3 can be written as the composition of a reection and a half-turn. 2. Consider a dilative
Math 348 (2006): Assignment #4: Solutions
1. We know that there are three types of orientation-reversing isometries of E 3 : reflection, glide, and rotatary reflection. We also know that a half-turn H
MATH 348: Assignment 1 (nal version)
Leonid Chindelevitch
July 11, 2008
1. Choose a geometer you are interested in and write a brief biography explaining their contribution to the geometry of their ti
MATH 348: Assignment 2 (nal version)
Leonid Chindelevitch
July 15, 2008
1. Let the triangle ABC have circumradius R. Prove that its area is given
by
abc
.
S=
4R
Comment: This is an ordinary proof, so
MATH 348: Assignment 3 (nal version)
Leonid Chindelevitch
July 22, 2008
1. Show that if a regular n-gon can be constructed with a ruler and compass,
then a regular 2n-gon can also be constructed with