Definitions in Mathematics

Introduction

Definitions per se are not something specific to the field of mathematics, but are rather prevalent in almost all subjects (for example English Grammar). An obvious need for definitions is to express a new term using already existing vocabulary. In mathematics however they have much more importance than in any other subject. Definitions in mathematics are rather precise and clearly express what a thing is or is not. From now on we will restrict ourselves to the form of definition used in mathematics.

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Conics and the Cone: Part 3

After having dealt with the case of circular sections of an oblique cone in previous post, let's now focus on the conics. We will first treat the case of a parabola as this is the simplest case after the case of a circular section.

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Conics and the Cone: Part 2

In the previous post we established that sections of a right circular cone are the familiar curves (ellipse, parabola, hyperbola) having the focus directrix property. Now we will have a look at the more general case when the cone is not right but oblique. Our approach will be identical to the one followed by the great Greek geometer Apollonius. However we will not be developing a systematic theory of conics as described by Apollonius, but rather focus on the interesting results which will help us to connect them with the modern definition of conics. In doing so we will observe that the main tool used by Apollonius is the similarity of triangles.

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