Geogebra  "4th hour"

Wednesdays 12:00-12:50 BSS 313

Assignments Spring, 2016

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Software:   GeoGebra.

TEXTS for Math 371:

Tentative topics for classes.
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.
  • Special points.
  • Special Lines.
Download File from GeoGebra Tube
Examine File.
Construct a sketch with technology of 
1. Euclid's Proposition 1 in Book I. 

3 2-10
  • How to determine circles and arcs.
  • Determining points and lines.
Constructions: Points, lines, circles.
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

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.]