TEXTS for Math 371:
| Week | Class Topic |
Class Tasks |
|---|---|---|
| 1 1-27 |
Introduction to geometry technology. Points,
lines, circles, intersections, figures, labels, and text. |
Introduction to GeoGebra. |
| 2 2-3 |
More on points, lines, and using GeoGebra on-line.
|
Download File from GeoGebra Tube Examine File. Construct a sketch with technology of 1. Euclid's Proposition 1 in Book I. |
| 3 2-10 |
|
2. Euclid's Proposition 2 in Book I. 3. One "proof" of the Pythagorean Theorem. 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. |
| 4 2-17 |
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 |
| 5 2-24 |
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. |
| 6 3-2 |
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 3-9 |
Draw sketches for each of
the following triangle
coincidences: 1. Medians. 2. Angle Bisectors. 3. Altitudes. 4. Perpendicular Bisectors |
|
| Spring break | ||
| 8 3-23 | 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. |
|
| 9 3-30 |
NO Meeting |
|
10 4-6 |
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). | |
| 11 4-13 |
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). |
| 12 4-20 |
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. |
|
| 13 4-27 |
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. |
|
| 14 5-4 |
A. Draw a figure in space that illustrates
the "conic sections". B. Draw a spatial sketch for Desargues' Theorem |
|
| ??? | 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.] |
|