Tuesday, September 6
- More Introduction to course organization.
- What is Visual Mathematics?
- Mathematics that studies topics related to visual experience. [Geometry,
- Visualization of mathematics that is not inherently visual.
- Example: Numbers...
- numeral: a symbol for representing a number
- Number: a form of universal language to describe anything/
physical things/ concepts related to measurement
- such as V, 5, five, cinq, chamesh, cinco
- Frege distinguished numerals from numbers in the late 19th century.
- We can compare numbers... for instance we say" 3 is less than
- Is 3 smaller than 5?
- Numerals are symbols (visual or linguistic) that we use to
- We use numbers to measure (lengths) and put things in order
(which was first).
- Another common visual representaion of numbers uses the number line.
2 3 4
5 6 7
Here the numerals are associated with points, so the points are considered
to visualize the corresponding numbers.
[Use Wingeometry to illustrate numbers
used for measurement.]
- We visualize equations that give relations between numbers with graphs
in the coordinate plane.
3x + 2y = 6 is visualized by the graph of a line.
Use Wingeometry to visualize coordinates, points, and lines.
- Miscellaneous: Some topics we will study.
- The film lists as a guide to the
- Symmetry.(Chapter 5)
- Tiling. (Chapter 5)
- Similarity and Projection. (Chapter 4)
- The color problem. (Chapter 6)
- The motion problem.(Chapter 3)
- The Sphere and the Torus. Surfaces (Chapter 6)
Theme Question:Who first showed the earth
was a sphere?
- Measurement and the Pythagorean
a2 + b2 = c2
Show video on PT.
Area of triangles = 1/2
Area of parallelogram= bh
Scaling: a linear scale change of r gives area change
of factor r2.
3 questions: running, moat, wind power...
Proof of the PT: Similar right triangles: c= a2 /c + b2 /c .
applications and other proofs.
Prop. 47 of Euclid.
Prop 31 Book VI Similar shapes.
Simple proof of PT using similar triangles of the
Use in 3 dimensional space