Plane Analytical Geometry
By M Bourne
An interesting application from nature:
The Nautilus Shell
See: Equiangular spiral.
(Image from Tree of Life)
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The curves that we learn about in this chapter are called conic sections. They arise naturally in many situations and are the result of slicing a cone at various angles.
Depending on where we slice our cone, and at what angle, we will either have a straight line, a circle, a parabola, an ellipse or a hyperbola. Of course, we could also get a single point, too.
Why study analytic geometry?
Science and engineering involves the study of quantities that change relative to each other (for example, distance-time, velocity-time, population-time, force-distance, etc).
It is much easier to understand what is going on in these problems if we draw graphs showing the relationship between the quantities involved.
The study of calculus depends heavily on a clear understanding of functions, graphs, slopes of curves and shapes of curves. For example, in the Differentiation chapter we use graphs to demonstrate relationships between varying quantities.
In this Chapter
- 1. Distance Formula
- Gradient (Slope) of a Line, and Inclination
- Parallel Lines
- Perpendicular Lines
- 2. The Straight Line
- Perpendicular Distance from a Point to a Line
- 3. The Circle
- 4. The Parabola
- 5. The Ellipse
- 6. The Hyperbola
- 7. Polar Coordinates
- 8. Curves in Polar Coordinates
- Equi-angular Spiral
We begin with the Distance Formula »