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One reason I’ll still use pi

Every so often, someone brings up the thing with tau (τ) versus pi (π) as the fundamental circle constant. In general I find the discussion wearisome because it usually focuses on telling people they are stupid or wrong for choosing to use one constant or the other. There are more productive uses of your time, […]

Posted in Being a good teacher, How people learn (or don't) | Tagged , |

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The right order for the fundamental trig identity

If you google “fundamental trig identity” you will get many many images and handouts which all list the fundamental trig identity as:
sin2 t + cos2 t = 1
This is, of course in the wrong order and it should really have cos first then sin, like this:
(cos t)2 + (sin t)2 = 1
“But David,” you say, “it’s addition, […]

Posted in How people learn (or don't), Thoughts about maths thinking | Tagged , |

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The trig functions are about multiplication

When I was taught trigonometry for the first time, I learned it as ratios of sides of right-angled triangles. Like this:

Most students coming into a Science degree at the University of Adelaide are at least vaguely familiar with this, and it’s their first instinct when using trigonometry. However, the lecturers in Physics and Engineering don’t […]

Posted in Isn't maths cool?, Thoughts about maths thinking | Tagged , |

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