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The Fundamentals of Conic Sections

Learn how to draw geometric constructions, and how to use them to construct conic sections in this free online course.

Publisher: NPTEL
In this course, The Fundamentals of Conic Sections, you will learn the key techniques used to draw basic geometric constructions as well as how to use these techniques to draw further, more complicated constructions called Conic Sections. These include Parabolas, Circles, Ellipses, and Hyperbola. This course is for those who have a grounding in technical drawing and would like to expand their current knowledge in technical engineering.

6-10 Hours

47

CPD

Description

In this course, The Fundamentals of Conic Sections, you will learn the technical drawing techniques used in the construction of all forms of conic sections. You will begin the course with the most basic geometric constructions used in engineering drawing. These are; the bisection of a straight line, the bisection of an angle, and how to draw a perpendicular bisector. These all form part of the basis of conic sections and provide you with the necessary knowledge to continue onto more challenging drawing techniques. You will then learn how to construct a circle around three different points and finally, in the last section of geometric constructions, you will tackle tangents. This is the straight-line that "just touches" the curve at a point. You will cover common tangents as well as interior and exterior tangents of a circle. These constructions are slightly more advanced and will need more focus and practice. You will then move onto the next topic of this course, which will focus on Conic Section fundamentals. This is the main focus of the course and will explain the methods used in their different constructions.

A Conic section also called conic, in geometry, is any curve produced by the intersection of a plane and a right circular cone. Depending on the angle of the plane relative to the cone, the intersection is a circle, an ellipse, a hyperbola, or a parabola. These four shapes are the basis for all the construction methods of this course. Alongside this, you will discuss four main methods used to construct the different shapes of a conic section, the main construction being the Focus-Directrix Method. The others are the concentric circle method, oblong method and arcs of the circle method. These four methods are capable of constructing all four of the conics, as well as others. There are different techniques used to construct a tangent and a normal to an ellipse, but the four methods are also capable. You will then continue discovering specific parabola constructions and how to use the rectangle method for this. You will also be taught how to use the tangent method for a parabola construction, as well as for a parabola with a normal. Next, you will move onto special curves.

In the last section of the course, you will examine the different special curves. This includes cycloid curves, involutes, helixes and spirals. You will learn how to construct each of these curves and the different uses for each. You will also realize their daily uses and their importance in our lives. You will determine how to construct a tangent to a spiral, as well as a conical helix. All the constructions in this course provide you with the basis for all engineering drawing construction and allow for the most accurate and disciplined drawing techniques. There is some apparatus used that will be needed to purchase if you are looking at getting the full benefit out of this course, but it will not be needed for the final assessment. This course is for those intending on expanding their already existing knowledge on technical drawing and learning new techniques or those wanting to begin with engineering and would like a basic understanding of a key feature in all engineering professions. So why wait? Start this free online course today and learn the key techniques of engineering and its fundamental technical drawing.

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