The concept of Analytical Geometry was given by Mr. Percey F. Smith and Mr. Arthur Sullivan Gale. Mr. Percey F. Smith was a professor of mathematics in Sheffield scientific school, Yale University and Arthur Sullivan Gale was an assistant professor of mathematics in the University of Rochester. Now, we will see introduction to analytical geometry.
Define Inclination of a LineBack to Top
The inclination of an angle helps us to find the Slope of any line which is represented by tan Ө. By the angle of inclination we mean the measure of angle Ө, that the line or the part of the line forms with the positive direction of the x – axis and it is measured in anti clock wise direction. So, we say that the value of Ө is always a positive quantity. Thus, it is clear that the value of Ө is always between 0 degrees to 180 degrees.
We must look at the following observations about the Slope or inclination of the line:
1. The inclination of the line which is parallel to x – axis, or the x – axis itself is always 0 degrees and 180 degrees.
2. The inclination of the line which is parallel to y – axis or y – axis itself is 90 degrees.
Thus we come to the conclusion that any line parallel to the x axis or the x axis itself is called a horizontal line and the line which is parallel to y axis, or the y- axis itself is called the perpendicular of the vertical line. Another type of line is oblique line, which we say is neither a parallel line nor a horizontal line. If we know the inclination of any given line then we can easily find the slope of that line.
Analytical Geometry DefinitionBack to Top
Before we define analytical geometry we should mention that the analytical geometry possesses two distinct types of the meanings in the context of the math. One of those two meanings of the analytical geometry is the modern meaning and the other meaning refers to the classical meaning of the analytical geometry. The definition of analytical geometry in two of its forms can be given as follows.
The definition of analytical geometry in its modern form or we can say that the advanced understanding of the term analytical geometry generally emphasizes on the geometry of such type of the varieties which are analytic.
Now we will define analytical geometry in its classical form but before we do that we should first mention that the meaning of analytical geometry in its classical form is same as the definition of the coordinate geometry or the definition of the Cartesian geometry. In context to classical math, the analytical geometry is defined as the study of the geometry with the help of the system of a coordinate and also by the use of various principles of the analysis and the principles of the Algebra. The analytical geometry has got many applications in the fields of engineering and Physics.
History of Analytical GeometryBack to Top
The analytical geometry history starts from the Period when a great mathematician of Greece whose name was Menaechmus started solving some of the problems. With this he start proving some of the theorems by utilizing a method which was very similar to the utilization of the coordinates and even it is sometimes realized that he was the one who was greatly responsible for the introduction of the analytical geometry.
The history of analytical geometry, also includes the contribution of the Apollonius belonging to the Perga who also solved some of the problems in a way that can be referred as the analytical geometry of kind of the one dimension and the question which they used to solve normally was determining the points which exist on a line and that happened to be in the form of a Ratio with the others.
The further development of the analytical geometry was also credited to the Apollonius who in the Conics again gave a process to solve the problems which was very much like the analytical geometry. He gave his contribution in the fields of the lines of the reference also gave the uses of Tangent and Diameter which we very normally use in the modern math in the system of coordinate in which we find the distance along any diameter starting from the Point which is called the Point of Tangency.