January 7, 2018 - Math Circle 1.0: The number line

The number line

From Gelfand et al 1990 Method of Coordinates:

Introduction to coordinates

The method of coordinates allows us to define where something is
examples
- airplane dropping a package with food in a disaster area
- satellite launch
- cupid --> address
- chess
- lat, lon defines point on earth sfc

Can convert points / lines into numbers

Dimensions: line = 1, plane = 2

The number line

1. origin
2. positive direction
3. unit of measurement

A(5) located on a number line

Defining a point
- ea. point defined by a single number
- the coordinate 5 is 5 units from origin
- notation: A(5) "point A is at coordinate +5"

Correspondence:
- ea. point on line has one and only one number coordinate
- ea. coordinate has one and only one location on the line

Draw A(5) and B(5)
Draw A(2)
    - hint: does not exist

Exercises

draw number line from -5 to 5
place A(5), B(-4), C(1½) on line

- place M(2); which two coordinates are 2 units from M(2)?

Exercise as written in a student's notebook

.

- if B(b) is to the right of A(a), which is greater (a or b)

- Without using a number line, which of the following points is to the right of the other?

•  A(-3), B(-4)
• A(3), B(4)

• A(a), B(-a)

For A(a), B(-a): there are three conditions to consider (a=0, a>0, a<0)

if a=0, A and B are at same point
if a> 0 ...
if a < 0 ...

Homework 

Which of the following is greater:

• M(x) or N(2x)
• A(c) or B(c+2)
• A(x) or B(x²)