## The Nephoid – a caustic in a coffee cup

The Nephoid is the curve formed by the envelope of rays reflected on a circular surface from a set of initial parallel rays.  In other words, the curve which owns all the rays as tangents. The geomtery of each ray path is relatively straight forward, involving properties of parallel lines and isocelels triangles. It is …

## The Cardioid as the Envelope of Pencil Curves

Draw a circle and divide the circumference into and even number of equally spaced points.  In this example I have used 44: Draw following chords between numbers in such a way that when viewed as a sequemce, the second point of each pair moves twice as fast around the circle.: and and on completion, sketch …

## The Parabola

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

## t-Formulae and parameterisation of the circle

t-Formulae are used in integration to tackle rational expressions of tigonometric functions.  After a spell in the cold, when they were not included in some A level specifications, they are now back in sixth form lessons. It all starts with the subsitution, from which the following functions can be derived, ,  ,  . These derivations …

## Sum of Odd Numbers

Latex (Tikz) graphic I made, inspired by Weissman’s An Illustrated Theory of Numbers. There could be so many more …

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

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. …

## Edexcel Practice Paper G – Statistics and Mechanics

This paper felt a little rough around the edges as a finished product but good revision practice nevertheless. Only Word versions available with the parsing of symbols and format presenting small problems. Notes:– Statistics section seemed very chatty, had to write a lot for the marks on offer.-Q4, not sure whether ‘p-value’ is defined anywhere …

## Edexcel Mathematics Practice Paper A

Practice Paper A – Questions Practice Paper A – Mark Scheme Practice Paper A – JPED Write Out My write out included to show students how I would have answered the questions using the style of mathematics taught in my lessons. This paper was one of a number of revision and preparation resources published by …

## Counting Pennies, Generating Functions and STEP

STEP I 1997, Question 1 Show that you can make up 10 pence in eleven ways using 10p, 5p, 2p and 1p coins. In how many ways can you make up 20 pence using 20p,10p 5p, 2p and 1p coins? There is an interesting way of approaching this question using generating functions. A generating function …