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20.1 Taxicab Geometry

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The student will learn about:

other geometric figures in Taxicab Geometry.

1

1

Introduction

We are going to examine a variety of geometric figures that use distance in their definitions.

A

Let A (0, 0). Graph all the points P so that PA = 6.

What is the name given to this set of points?

Just as a circle is all the points equidistant from a fixed point the other conics may be defined with respect to distance.

A parabola is all the points equidistant from a fixed point (focus) and a fixed line (directrix).

Consider the line that is the x-axis and the point F(0, 2). Find the set of points P so that the taxicab distance from the line is equal to the distance PF.

Find all the points equidistant from the point and line given below.

6

6

Given two points A and B (foci), an ellipse is all the points P so that │PA + PB│ = d where d is some fixed positive constant.

After view the examples given be able to make and observation about d.

Consider the two points A(0, 0) and B(6, 0). Find the set of points P so that the │AP + BP│= 10

A

B

Consider the two points A(0, 0) and B(5, 5). Find the set of points P so that the │AP + BP│= 14

B

A

Consider the two points A(0, 0) and B(4, 2). Find the set of points P so that the │AP + BP│= 12

B

A

Given two points A and B (foci), a hyperbola is all the points P so that │PA - PB│ = d where d is some fixed positive constant.

Consider the two points A(0, 0) and B(6, 6). Find the set of points P so that the │AP - BP│ = 4

Consider the two points A(0, 0) and B(6, 2). Find the set of points P so that the │AP - BP│ = 4

- We learned about taxicab ellipses.

- We learned about taxicab hyperbolas.

With the remaining class time lets work on our homework assignment 20.1.

Assignment: §20.1

and Ideal City