CI 499 Fall 2004

	Last Updated: Thursday, December 16, 2004 9:44 AM

Assignments:

Michael Eiland & I Developed a Flatland Activity: [Web format | PDF format | Word Format]
My Excel version of Dan Brown's initial exercise
My Excel version of Dan Brown's second exercise
Tetrahedral Volume Excel Sheet | Document
Pointy Fences [Web] [Word] [Excel]
My take on Phil's Dance Project (illustrated in LoggerPro - notice, that I used a cosine wave due to the fact I started at the top of the circle. You will need loggerPro 3.2 and a digital camera to do it yourself) [The Actual Movie]
Sierpinksi Gasket Information (Ala Michael E.'s project)
October 28, Assignment [Web] [Word] [PDF]
Emily [Quilting] and Brennan's [Origami] were done in class. Rosa's [Mira] and Lindsay's [Knots] are on paper and here- and done.
Greg's Assignment [GSP] [Java Sketch]
Knots & More Knots
Michael M's Assignment [Spherical Easel Files - Need Spherical Easel to open this file]
My Project [MainProject in GSP]

TaxiCab Geometry:

Response to Exercise 2, page 6. and some selected exercises from the book.
GSP File

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Report on Bruce Hannon's Topic (Michael E., Michael M., and I met to congeal what we had learned from Bruce Hannon's presentation) Here is what we came up with (so far) [quadratics.doc]:
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MidTerm: Paper
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Final Project: Perspective & Projective Geometry:

A Two-point Perspective Sketch [GSP] [Java]
A One-point Perspective Sketch [GSP] [Java]
Desargues' Theorem [GSP] [Word] [Java]
A Presentation about Perspective Geometry [Acrobat] [PowerPoint]
Artisitic Examples [Image Slide Show] - Durer, Alberti, DaVinci

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Final: Paper [A Vision for the Future of Perspective/Projective Geometry]
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Software for my fellow Geometers and examples of each:

Geometer's Sketchpad [Here is a fine dynamic geometry example]: [INTERACTIVE]
Sorry, this page requires a Java-compatible web browser.

Cabri, Located at www.ti.com/cabri
[An example using Cabri]

A very simple example illustrating Triangle Angle Sums:[INTERACTIVE]

Cinderella, Located at www.cinderella.de
[An example of lines in a plane compared with the same lines on a sphere]
https://mste.illinois.edu/dildine/cinderella/parallellines.html [INTERACTIVE]

This Java Sketch from Cinderella represents Two-views of parallel lines. One view is in the "typical" Euclidean Plane. The parallel lines here NEVER meet. The definition of parallel lines is: lines that extend in the same direction and are the same distance apart at every point. While on a sphere (as in our world) parallel lines will intersect at exactly two points.

Please enable Java for an interactive construction (with Cinderella). Please enable Java for an interactive construction (with Cinderella).
NonEuclid, Located at cs.unm.edu/~joel/NonEuclid/
[Several examples using NonEuclid]

First, a triangle and its circumcenter.

Next, the basic set-up for creating an evelope of a parabola.

Spherical Easel: A very cool Java Applet simulating Spherical Geometry
Located at: http://merganser.math.gvsu.edu/easel

A few screenshots that I created for Michael M's. Activity:

Two perpendicular lines in Spherical Geometry:

Comparing Three Triangles:

Euclidean Geometry - Triangle Sum = 180 degrees [INTERACTIVE]

Spherical Geometry - Triangle Sum >= 180 degrees

Hyperbolic Geometry - Triangle Sum <= 180 degrees

Interesting (to me) JavaSketches:

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Cool Graphing Calculator Projects: [most located at https://mste.illinois.edu/dildine/times/tiprograms.html] [others are mostly images of what I have done: located at https://mste.illinois.edu/dildine/classes/ci499fall04/ti.html]

Graphing a pseudo-Sine wave with the TI-83+ and a CBR by walking in a circle while facing a wall:
This is me walking in a circle trying to create a sine wave over several attempts.
as opposed to a real Sine wave

https://mste.illinois.edu/dildine/times/primfac2.8xp (Screen Shots Below)

The concept of factoring down to a number’s prime factors is a crucial concept in pre-algebra and algebra. This program may help students understand and build factor trees for integers that they enter when prompted. Students should be familiar with the following table prior to using the program. Students should also create a factor tree of several numbers that they wish to factor.

Divisible By:	Divisibility Test:	Example:
2	Number ends in an even digit (0, 2, 4, 6, 8)	9,458 (ends in 8)
3	Sum of the digits are divisible by 3	8,751 (8+7+5+1 = 21, divisible by 3)
4	Last two digits form a number divisible by 4	3,432 (32 is divisible by 4)
5	Number ends in 0 or 5	890 and 7,345 are both divisible by 5
6	Number is divisible by both 2 & 3	342 is divisible by both 3 and 2
8	Last three digits for a number divisible by 8	27,816 is divisible by 8 since 816 is divisible by 8
9	Sum of the digits is divisible by 9	76, 104 is divisible by 9 since the sum of the digits is 18 which is divisible by 9
10	Last digit is 0	Any number that ends in 0
12	Number is divisible by both 4 & 3	4,032 is divisible by 12 since it is divisible by both 3 and 4

Second, Pythagorean Triples:

https://mste.illinois.edu/dildine/times/ptrips.8xp (Screen Shots Below)

The Pythagorean Theorem (a^2 + b^2 = c^2) is an important concept in Algebra and Geometry. Knowing this relationship is very important throughout additional Mathematics areas as well. Pythagorean triples are the collection of an infinite many numbers that satisfy the Pythagorean Theorem. The user can use this program to examine a specific number of these triples. The user is prompted for an “UPPER bound”, that is the value that the program will use as the largest value for the largest of the legs. Students should be asked to discover relationships within these sets of triples. For example: (3, 4, 5) produces multiples (6, 8, 10) and (12, 16, 20) etc… Students should also realize that developing a list of Pythagorean Triples does not soely rely on multiples but on a more comprehensive formula.

Third, Heron’s Formula for the Area of a Triangle:

https://mste.illinois.edu/dildine/times/heron2.8xp (Screen Shots Below)

This program can be used in any math class that presents the formula for finding the area of a triangle. Typically students are given the standard triangle area formula Area = ½ Base x Height. This formula is a bit more complex but it allows the user to calculate the area of any triangle, given the lengths of its sides. Three examples are shown above: One that could have been calculated using the standard area formula, one that would have been a bit more difficult with the standard form but Heron’s Formula solves it for us, and one that determines that the given values do not fulfill the triangle inequality theorem which is an extension which may be explored.
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Other Links:

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References:

Abbott, E. A. (1992). Flatland: A Romance of Many Dimensions. New York: Dover Publications, Inc.
Hauptman, H., Posamentier, A. (2001). 101 Great Ideas for Introducing Key Concepts in Mathematics . Thousand Oaks , CA : Corwin Press, Inc.
Kaplan, R. & Kaplan, E. (2003). The Art of the Infinite: The Pleasures of Mathematics . New York : Oxford University Press.
Key Curriculum Press (2004). The Geometer's Sketchpad. V. 4.06. Emeryville , CA : Key Curriculum Press.
Krause, E. F. (1986). TAXICAB GEOMETRY: An Adventure in Non-Euclidean Geometry . New York : Dover Publications, Inc.
Miller, C (1997). Mathematical Ideas. Reading , Mass: Addison-Wesley.
Murdock, J. (1998). Advanced Algebra Through Data Exploration : Key Curriculum Press.
National Council of Teachers of Mathematics (NCTM). (1997). Curriculum and Evaluation Standards for School Mathematics: Addenda Series Grades 5 - 8, Geometry in the Middle Grades . Reston , VA : The National Council of Teachers of Mathematics, Inc.
National Council of Teachers of Mathematics (NCTM). (2000). Pinciples and Standards for School
Mathematics . Reston , VA : The National Council of Teachers of Mathematics, Inc.
Serra, M. (1997). Discovering Geometry: Emeryville, Ca: Key Curriculum Press.
Tondeur, P. (1993). Vectors and Transformations in Plane Geometry . Houston : Publish or Persish, Inc.
Travers, K. (1985). Using Statistics . Reading , Mass: Addison-Wesley.
Wallace, E., West, S. (1992). Roads to Geometry . Englewood Cliffs, NJ: Prentice Hall.
Ward, P. & Brownlee, D. (2000). Rare Earth: Why Complex Life is Uncommon in the Universe. New York: Copernicus, Springer-Verlag.
Youden, W. J. (1998). Experimentation and Measurement . Mineola , NY : Dover Publications, Inc.