EMAT 6690 Instructional Unit Ideas

1. Circumcenter/ Perp Bis of Sides

2. Incenter/ Angle Bisectors
(and excenters)

3. Centroid/Medians

4. Orthocenter/Altitudes

5. Other Cevians

6. Euler line

7. Loci problems

8. Nine-Point Circle

9. Pythagorean Relations

1. Center of Similarity; projections

2. Similarity coefficient

3. 3-D

4. 2-D

5. Dilations

. . . . . see Video Tape from Project Mathematics . . .

1. Polygons

2. Polyhedra

3.

4.

5.

6.

. . .

1. Arcs

2. Central angle relationships

3. Chords, Secants, Tangents

4. Intersecting circles

5. Great circles

6.

7.

8.

9.

. . .

1. Concepts

2. Formulas

3. Applications

4. Maximization (Minimization) Probs

5. Isoperimetric inequalities and relationships 2-D and 3-D

6. Heron's Formula

7. Brahmagupta's formula

8. Visualization of 4 dimensions

9.

1. Basic isometries

2. Coordinatization

3. 3-D translations, rotations

4.

5.

1. Cross Ratio

2. Desargue's Theorem

3. Pappus's Theorem

4. Pascal's Theorem
Pascal Line of a hexagon inscribed in a circle.

5. Menelaus's Theorem

6. Duality
. . . principle
. . . examples

7. Dual point/line for conics

.............. and maybe ...........

8. Perspective drawings

... see Serra's book


9. Drafting basics

... e.g. Mechanical Drawing

1. 3-D models; 3-D images

. . . Intersection of Plane and double cone

2. Projection of a ring

. . . circle
. . . ellipse See Nicollett Films
. . . parabola
. . . hyperbola

3. Animation: directrix and focus

4. Other animations

5. Paper folding

6. Eccentricity coefficient

and
7. Analytic geometry

. . . Formulas
. . . xy coordinates
... graphs with center at origin
... other
. . . polar equations
. . . parametric equations

1. Quadrilaterals

2. Polygons and Regular Polygons

3. Euler's Formulas

4. Platonic Solids

5. Archimedian Solids

6. Model building; nets

7. Projections

8. Stellated Polyhedra

1. Basic concepts

2. Graphs

3. Polar coordinates

4. Complex numbers

5. Applications

6.

7.

8.

9.

1. 2-D

2. 3-D

3.

4.

5.

6.

. . . . .


n. Non-linear systems

1. Iteration of pattern

2. Iteration of function

3. Use of iterations to find roots

4. Recursive functions

5. Fractals

6.

7.
. . .

1. Functions

2. Relations

3. Discontinuities

4. Composite graphs
f(x) + g(x)
f(x) g(x)
f(g(x))
x = g(x) obtained from f(x) = 0

5. Explorations with Polar equations

6. What if? with equations such as

x2 + y2 = 1

when it is changed to x3 + y3 = 1