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Visualizing Mathematics:An Investigation of Random
Visual Mathematical Phenomena and Somewhat
Specifically Using Visual Models in Statistics
Some Random Visual Mathematical Phenomena
• One Triangle to Rule Them All…• Matthew Peterson – Teaching Without Words• Multiplying/Dividing Polynomials Visually• The Sum of Consecutive Integers• Nets• Visual of Pythagorean Theorem• Playing With Parabolas• Visualizing Functions• Other Resources
To describe the space of all triangles, we will consider two triangles to be the same if they are similar.
How much information do you need to know to describe a triangle, under this definition?
How could you represent all the triangles visually?
The space of all triangles
One Triangle to Rule Them All…
The space of all trianglesWhere are: • The degenerate
triangles? • Right triangles?• Acute triangles?• Isosceles triangles?• Equilateral
triangles?
Other questions to consider:• Is every triangle
represented here?
Matthew Peterson – Teaching Without Words
• http://www.youtube.com/watch?v=2VLje8QRrwg (go to 4:41)
Multiplying/Dividing Polynomials Visually
From www.mathrecreation.com
From www.billthelizard.com
Multiplying/Dividing Polynomials Visually
From www.mathrecreation.com
Visualizing Sums of…
• http://www.billthelizard.com/2009/07/six-visual-proofs_25.html
Visual of Pythagorean Theorem
• See Geogebra
Playing With Parabolas
• See Geogebra
Visualizing Functions
Other Resources
• See document
Using Visual Models in Statistics
• Handouts…
