## The Parabola

Parabola definition: locus of such that . Cartesian Equations: with gradient: Parametric Equation: with gradient: tangent: normal:

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## The Parabola

## Sale Prices: Fifty Seven Point Five Percent Off on Streets of Canterbury!

## Transformations of Sine

## Parallelograms generalise Pythagoras to any triangle

## The Ghosts of Departed Quantities and the difficulties of teaching and learning caculus

## support for school mathematics exams

## depression near Greenland – logarithmic spirals in nature

Parabola definition: locus of such that . Cartesian Equations: with gradient: Parametric Equation: with gradient: tangent: normal:

Whilst wandering through the streets of Canterbury this sign caught my eye. With the mathematics department’s favourite coffee shop in the back-ground, the sign promises a further drop of prices for outdoor enthusiasts. ‘Half price’ and ‘15%’ are both eye catching figures which are immediately understandable to the shopper, but the sign promises something else. …

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Functional notation and transformations is always tricky to teach and understand. GCSE students will meet this in Year 11. In general, transformations applied after the function are more easily understood: or Something very un-intuitive happens when the transformation is applied to the argument of the function: or with things stretching when they …

There’s always space on the inter-web for another proof of Pythagoras’s Theorem. Here’s one that uses the following equal areas property of parallelograms. This kind of area chopping and shape translation is a feature of Euclidean geometry and our senses support it’s veracity at the order of size of the classroom. The squares on the …

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Bishop Berkeley writes this attack on the apparent supernatural reasoning involved in calculus. The infidel was probably Halley (of comet fame) or Newton. If pupils find the subject difficult to understand at school, and teachers find it difficult to teach, then the reason may be articulated in this book by the great man. Quotes include: …

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I have developed a database driven website which shares past papers, markschemes and my own ‘write outs’ for most Edexcel modules in mathematics and further mathematics: jped Exam Bucket I use this mostly as a resource for my own teaching; using it I can lay my hands of exam questions and solutions of different types …

Logarithmic spirals frequently occur in nature. Is this such a manifestation? The general equation for a logarithmic spiral is as follows. Changing the variables and produces spirals of different qualities. The is really an enlargement scale factor but the controls how the spiral grows per revolution. If is more representative of an ammonite then seems …

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