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TEACHING H2 FURTHER MATHS:CONIC SECTIONS
IME20833, 10, 17, 24 Oct 20172.30 – 5.30 @ AST
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Resources• http://math.nie.edu.sg/pctoh/conics.htm• Feel free to send suggestions to
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H2 F-MathsSyllabus, Extracted Sept 2017
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How Should We Teach Conics?
http://spikedmath.com/517.html
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Discovering Mathematics“Learning mathematics is more than just learning conceptsand skills. Equally important are the cognitive andmetacognitive process skills. These processes are learnedthrough carefully constructed learning experiences. … Forexample, to encourage students to be inquisitive, thelearning experiences include opportunities where studentsdiscover mathematical results on their own.”
- Extracted from 2016 Pre-U H2 Further Mathematics Syllabus
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Polya’s Three Principles of Learning1. For efficient learning, the learner should discover by
himself as large a fraction of the material to be learnt asfeasible under the given circumstances.
2. For efficient learning, the learner should be interested inthe material to be learnt and find pleasure in the activityof learning.
3. Learning begins with action and perception, proceedsfrom thence to words and concepts, and should end indesirable mental habits.
Polya (1963), On Learning, Teaching and Learning Teaching, The American Mathematical Monthly, v70,605-619
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Conics• Menaechmus (380 - 320 BC)• Euclid (325 – 265 BC)• Apollonius of Perga (262 – 190 BC)
• Treatise on Conic Sections• named the various curves
• Pappus of Alexandria (290 – 350 AD)• Focus-Directrix property
Apollonius
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Frontipiece of Treatise on Conic Sections
Socratic philosopher Aristippus, when shipwrecked and cast ashore on the island of Rhodes, said “Let us be hopeful for I see the traces of Man.”
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Generating the conic sections
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Conics (named by Appollonius)• Parabole (Latin) - comparison, to
set alongside, literally to throw alongside
• Hyperbole (Latin) - excess, literally to throw beyond
• Ellipsis (Latin) meaning “omission” or “falling short”
• “…” • The angle between the plane and
the base, when compared to the side of the cone
Photo Credit: Wikipedia
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Parabola
• Double meaning of “to throw”• In Chinese
Photo taken @ Vivocity
Galileo (1564-1642)• Showed that projectiles followed parabolic paths
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Drawing a parabola
Source: http://mathdemos.org/mathdemos/conic_via_locus/
Real life demonstration:https://www.youtube.com/watch?v=BafkJt9KA8I
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Parabolic Pulpits
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Sidney Bandshell (British Columbia)
Creative Commons: Taken by Paul Hamilton
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http://www.flash-lights.com/maglite/maglite-flashlights/Focusability.htmlhttp://www.flashlightuniversity.com/wp-content/uploads/2013/08/spot_vs_flood.jpg
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Straits Times 26 September 2016
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Do not believe Star Wars!