﻿ Math 480 Assignments

## MATH 480 Assignments Spring, 2011

Software: Wingeometry,  The Geometer's Sketchpad®, and GeoGebra

TEXTS for Math 371:

•  Fundamentals of Geometry by B.Meserve and J. Izzo, A.W. (1969) - ON LINE  through Moodle.
• The Elements by Euclid, Volume 1, edited by T.L. Heath, Dover (1926)
• The Elements (David Joyce's on-line version)
The First Six Books of The Elements of Euclid (Comprehensive connections with Oliver Byrne's on-line version)
• Proof in Geometry by A.I Fetisov, Mir (1978)
• Flatland, (one of many on-line versions available) by Edwin A. Abbott, Dover.

Tentative assignments and topics for classes.
Week Class Topic
Math 480 Assignments: Subject to Change.
Assignments are not made until a due date is established.

1 Introduction to geometry technology. Points, lines, circles, intersections, figures, labels, and text.
Introduction to Technology for Geometry: Wingeometry,  The Geometer's Sketchpad®, and GeoGebra.
2 Lab Exercises 1:
Due:8 pm 1/25
More on points, lines, and circles.
• Special points.
• Special Lines.
• How to determine circles and arcs.
• Determining points and lines.
Construct a sketch with technology of
1. Euclid's Proposition 1 in Book I.
2. Euclid's Proposition 2 in Book I.
3. One "proof" of the Pythagorean Theorem.
3 Lab Exercises 2:
Due 8 pm 2/1
Constructions: Points, lines, circles.
Do Construction 3, 4, 6, 7, and 8 from Meserve and Izzo Section 1.2.
BONUS:Show how to "add" two arbitrary triangles to create a single square.
4Lab Exercises 3:
Due 8 pm 2/8
Transformations that preserve distance:
Translations, Rotations, Reflections, Glide Reflections.
1. Construct a scalene triangle . Illustrate how to do i) a translation by a given "vector", ii) a rotation by a given angle measure, and iii) reflections across a given line..
2. Create a sketch that shows that the product of two reflections is either a translation or a rotation
5Lab Exercises 4:
Due 8pm 2/15
Measurements.
Central Similarities. Other Magnifications.
Parameters(?) / Slider
Problem 1 now due 2/22
1. Draw a figure showing the product of three planar reflections as a glide reflection.
2. Draw a figure illustrating the effects of a central similarity on a triangle using magnification or dilation that is a) positive number >1, b) a positive number <1, and c) a negative number.
6Lab Exercises 5:
Due 8 pm 2/22
Rotations of lines about the point of intersection.
More on use of angle measurements and perpendicular lines.
1. Construct the inverse of a point with respect to a circle a) when the point is inside the circle; b) when the point is outside the circle.
2.  Given a circle O and two interior points A and B, construct an orthogonal circle O' through A and B.
3. Draw two intersecting circles O and O' and measure the angle between them.
7 Lab Exercise 6: Due 3/1

Draw sketches for each of the following triangle coincidences:
1. Medians. 2. Angle Bisectors. 3. Altitudes. 4. Perpendicular Bisectors
8Lab Exercise 7: Due 3/8
1. Inversion: Investigate and sketch the result of inversion on lines and circles in the plane with a given circle for inversion.
When does a line invert to a line? When does a line invert to a circle? When does a circle invert to a line? when does a circle invert to a circle?  Show sketches where each case occurs. [ Remember the inverse of the inverse is the original figure.]
2. Use inversion with respect to the circle OP to invert <BAC to <B'A'C'. Discuss briefly the effects of inversion on angles.
9Lab Exercise 8:
Due 3/22

Draw a sketch of the affine plane showing the horizon line and label the lines X=1,2,-1, Y= 1,2,-1 and points (1,2) and (2,-1).
Spring break

10Lab Exercise 9:
Due 3/29
Traces?
1. Using trace features, draw a parabola, ellipse and hyperbola from focus (and directrix).
2. Use built in features of software to draw a parabola, ellipse and hyperbola from focus (and directrix).

11Lab Exercise 10:Due 4/5
A.1. Construct a sketch showing ABC on a line perspectively related to A'B'C' on a second line with center O.
2. Construct a sketch of  ABC on a line projectively (but not perspectively) related to A'B'C' on a second line. Show two centers and an intermediate line that gives the projectivity.
B.1'. Draw a dual sketch for the figure in problem 1.  2'. Draw a dual sketch for the figure in problem 2.
C. Draw a sketch for Desargues' theorem in the plane.
12Lab Exercise 11:Due 4/12
Pascal's configuration: Hexagons inscribed in conics. Points of intersections of opposite sides lie on a single line.
Construct a figure for Pascal's configuration  with  a) an ellipse , b)a parabola,  and c) an hyperbola.
13Lab Exercise 12: Due 4/19
A. Draw a figure in space that illustrates the "conic sections".
B. Draw a spatial sketch for Desargues' Theorem
14Lab Exercise 13: Due 5/12
1.Draw a sketch showing H(AB,CD) and H(CD, AB) are equivalent. [Proof.]
2. Draw a sketch that shows that if H(AB,CD) and H(AB,CD*) then D= D*.[Proof.]