Monday, February 10, 2014

Class #6

• Example: Numbers for counting and measuring...
• numeral: a symbol for representing a number
• Number: a form of universal language to describe anything/ physical things/ concepts related to measurement
• Numerals : 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 5"
• Is 3 smaller than 5?
• Numerals are symbols (visual or linguistic) that we use to represent numbers.
• Numbers are concepts. They are not physical objects but are used to describe a quality of an object or a collection of objects. Some regard numbers as abstract entities that "exist" in a non-physical world - sometimes described a "platonic" after the Greek philosopher Plato.
• 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 associated with points, so "the points visualize the corresponding numbers."

Geometric Puzzle Foundations
• Measuring angles, lengths and areas.
• Triangles  : add to 180 degrees- straight angle [Illustrate physically and with Wingeometry andGeoGebra]
• Squares, rectangles  : 90 degree/ right angle

More on measurements of angles of polygons with n sides. .
When n = 3 this is a triangle, n=4, a quadrilateral, or when n= 5, a pentagon.

The sum of the measures of the interior angles of a triangle is 180 degrees.
What about a quadrilateral? and a pentagon?  or an n sided polygon  ( an "n -gon")?