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

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20 1 taxicab geometry
20.1 Taxicab Geometry

The student will learn about:

other geometric figures in Taxicab Geometry.

1

1


Introduction

Introduction

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


Definitions
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?


Definitions1
Definitions

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).


Taxicab parabolas
Taxicab Parabolas

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.


Taxicab parabolas1
Taxicab Parabolas

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

6

6


Definition
Definition

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.


Taxicab ellipse
Taxicab Ellipse

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


Taxicab ellipse1
Taxicab Ellipse

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


Taxicab ellipse2
Taxicab Ellipse

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


Definition1
Definition

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.


Taxicab hyperbolas
Taxicab Hyperbolas

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


Taxicab hyperbolas1
Taxicab Hyperbolas

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


Summary
Summary.

  • We learned about taxicab ellipses.

  • We learned about taxicab hyperbolas.



Assignment: §20.1 assignment 20.1.

and Ideal City


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