conics

Resources on Conics for H2 Further Maths

In Service Course Oct 2017

Date	Topic	Resources
3 Oct 2017	Introduction and Parabola	Introduction to Conics (Powerpoint slides)pdf Handout for Session 1 (with details). pdf Come Together: Discover Science Episode on the Parabola. 3 minute preview on youtube but does not get to the point about parabola youtube Link to buy the video but with IP restrictions. National Film Board, Canada Demo on drawing the locus of conics Real life demo of drawing a parabola with T-bar youtube One of many youtube videos: Introduction to conics youtube Generating Conics (animated gif, right click to save). Source : http://www.mathdemos.org/mathdemos/family_of_functions/conic_gallery.html
10 Oct 2017	Ellipse	Handout for Session 2 (with details) pdf Folding a circle to create an ellipse youtube Geometric proof of the reflection property of an ellipse Elliptic Billards youtube Ripple Effect youtube Try out the reflection property at the Singapore Science Centre. (Photo taken on 25 Aug 2017) Ellipsoidal Reflector Spotlight youtube Whispering Gallery in the US Capitol Building, the interesting part begins at about 1:10 youtube
17 Oct 2017	Hyperbola	Handout for Session 3 (with details) pdf Animated gif demonstrating how to generate a hyperbola. (Created with GeoGebra.) Generating a hyperbola by throwing two stones Wikipedia entry on the Cassegrain Reflector
24 Oct 2017	Classification Applications	Handout for Session 4 (with details) pdf Localizer Sound Dome youtube If you go to browninnovations.com, you can find photos and specfications of the various types of sound domes that they are marketing Wikipedia entry on the Catenary

Lecture Notes for Conics

Lecture notes for the course. Updated 24 Oct 2017 pdf

References for Conics

The following are some books that I had used. My comments in italics pertain to the specific edition of the books that I had access to.

College Trigonometry - Richard Aufmann, Vernon Barker and Richard Nation Amazon link
A comprehensive reference I could find. I believe other books by the same authors contain similar material if you cannot find this title.
College Algebra: Concepts through functions - Sullivan and Sullivan Amazon link
More elementary, D-E-F is relegated to exercises.
Calulus - James Stewart Amazon link
Two short sections but contains the polar form and applications.
Explorations in Geometry - Bruce Shawyer publisher site
Only one short chapter on conics but well written.
Conics and Cubics - Robert Bix publisher site
Too advanced for A levels, but useful to view conics using projective plane. Proves that five points (no three of which collinear) lie on exactly one conic.
Practical Conic Sections - J. W. Downs publisher site
Available at a reasonable price from BookDepository. This book really emphasizes the practical aspects. There are no proofs but lots of examples of how to actually draw conics and practical applications.
Pure Mathematics for Advanced Level - B.D. Bunday and H. Mulholland
Chapter 20 is on Conics. Lots of problems and examples related to tangents and normals.
Analytical Geometry (Two and Three Dimensions) - D. Chatterjee
Chapters 4 and 5 are on Conics. Contains many useful examples/problems that are quite appropriate for A-Levels, including the clever proof of the director circle for ellipses and hyperbolas.
An Imaginary Tale, The Story of Sqrt(-1) - Paul J. Nahin
This is a book about complex numbers, not conics. But Section 5.3 (pp 109-120) is about Kepler's Laws and contains a very nice and understandable proof of the laws via complex differentiation. This section is highly recommended.

The following is a list of articles from the College Mathematics Journal that are related to conics.

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Updated Oct 2017