Statement of Purpose for Part III

An Approach to Mathematic Functions Basics

Section VIII - A Statement of Purpose for Part III

In this Part III of the paper :
- we shall take a close look at the Hyperbola .
The reason for doing so here is rather simple :
- Since Logarithm is expressed as an intergral of the [ area under the Hyperbola ] ,
  - understanding the Hyperbola properly does contribute to the understanding of Logarithms .

In Section IX , coming up next :
- We shall look at the Hyperbola in conventional { Cartesian Co-ordinates } .
In Section X :
- We shall spell out the Geometric Definition for the Hyperbola .
In Section XI :
- We shall derive the equation for the Hyperbola in { U-V Co-ordinates } .
In Section XII :
- We shall derive the equation for the Hyperbola in { Cylindrical Co-ordinates } ,
  - using the [ Point-of-Origin ] as the Base-Point for the [ Position Vector ] .
In Section XIII :
- We shall derive the equation for the Hyperbola in { Cylindrical Co-ordinates } ,
  - using the [ 1st Focal-Point ] as the Base-Point for the [ Position Vector ] .
In Section XIV :
- We shall derive the equation for the Hyperbola in { Cylindrical Co-ordinates } ,
  - using the [ 2nd Focal-Point ] as the Base-Point for the [ Position Vector ] .
In Section XV :
- We shall look at the Asymptotes using the conventional approach .
In Section XVI :
- We shall further comment on the Asymptotes .