MATH 480 Assignments Spring, 2011


Back to Martin Flashman's Home Page :)   Last updated: 1/24/2011
Software: Wingeometry,  The Geometer's Sketchpad®, and GeoGebra

TEXTS for Math 371: 


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.]