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Math 103 Contemporary Math

Math 103 Contemporary Math. Thursday, January 20, 2005. More Introduction to Course Organization. Web Materials What is Visual Mathematics? Mathematics that studies topics related to visual experience. [Geometry, Topology, Motion]

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Math 103 Contemporary Math

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  1. Math 103 Contemporary Math Thursday, January 20, 2005

  2. More Introduction to Course Organization • Web Materials • What is Visual Mathematics? • Mathematics that studies topics related to visual experience. [Geometry, Topology, Motion] • Visualization of mathematics that is not inherently visual. [Visualizing Counting, numbers] 

  3. Example: Numbers... • numeral: a symbol for representing a number  • such as V, 5, five, cinq, chamesh, cinco • Number: a form of universal language to describe anything/ physical things/ concepts related to measurement • Frege distinguished numerals from numbers in the late 19th century. • We can compare numbers... for instance we say" 3 is less than 5" • Is 3 smaller than 5? • Numerals are symbols (visual or linguistic) that we use to represent numbers. • We use numbers to measure (lengths) and put things in order (which was first). • Another common visual representation of numbers uses the number line. ___.___.___.___.___.___.___.___ 1     2     3     4     5     6     7 • Here the numerals are connected to points, so the points are considered to visualize the corresponding numbers. Use Wingeometry? • 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? or Winplot?

  4. Another example of "visual Math": • My Name: Martin Flashman • How to start a letter to me:  Hello ___ ________________ • How many different openings are possible?

  5. Tree for counting • We can visualize this problem with a "tree" • This visualization allows us to count the possibilities easily... • seeing there are 8 possibilities for each of 4 title branches so that the total is 8*4 = 32 possibilities. • This is an example of a visualization used to understand and solve a problem that initially is not connected to anything visual .

  6. Miscellaneous: Some topics we will study • The film lists as a guide to the course topics. • The color problem. • The motion problem. • The Sphere  and the Torus. Who first showed the earth was a sphere?

  7. Measurement and the Pythagorean Theorem (PT) • Measuring angles, lengths and areas. • Squares, rectangles, parallelograms and triangles. • Dissections, cut and paste methods of measurement. • Cutting and reassembling polygons. • The Square Me Puzzle. • Do Pythagorean Activity Sheet • Virtual Manipulative for PT. • Discuss Pythagorean Theorem and proofs. • Over 30 proofs of the Pythagorean theorem! • Many Java Applets that visualize proofs of the Pythagorean Theorem a2 + b2 = c2

  8. Next Time? • Show video on PT • Puzzles and Polygons • Flatland and the plane • The triangle, quadrilateral, pentagon, and hexagon. • More on measurements of angles and areas of polyons. • Activity: Measuring angles in regular polygons.

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