Hyperbola – locus of points in which ratio of distance from a focus point to the perpendicular distance to a line (directrix) is constant and greater than 1. Staple diet of school Further Mathematics.

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# Tag: maths

## Hyperbola – Focus Directrix

## The Angle in a Semi-Circle, Euclid Book III, Proposition 31

## Algebraic Form of the Modulus Function

## Functional Transfromations – Core Maths into STEP

## Transformations for IGCSE – Enlargement

## IGCSE Transformations – Rotation

## Great Circles and Spherical Triangles

stuff that arises in my teaching of mathematics at the King's School Canterbury

Hyperbola – locus of points in which ratio of distance from a focus point to the perpendicular distance to a line (directrix) is constant and greater than 1. Staple diet of school Further Mathematics.

Ancient theorem of Euclid (Book III, Proposition 31) still a fundamental part of school maths. The angle in a semi-circle is a right angle.

Sneaky play with algebraic notation and function definition lays traps for scholarship students in school maths.

Linking core maths 3 functional transformations to Step algebra and solutions of equations.

Enlargement.

Rotations in space make good Saturday morning maths at the King’s School.

In the geometry of mariners, where straight lines are Great Circles, the angle sum of a triangle is more than 180 degrees.

This method for finding the centre, and by extension the equation, of a circle given three non-colinear points, brings the ancient textbook master Euclid onto Descartes’ coordinate plane and right into the 21 century classroom.

The sine function starts life in a triangle (year 9?) then becomes intimate with a circle at A level, as y-coord of a point rotating on a unit circle. Later it is about infinite series or, even, differential equations.

Have got absorbed by the National Cipher Challenge. Not sure what this animation varying the multiplier in an ‘Affine Shift’ add 5. Functional grid shows transition from Caesar Shift 5, multiply by 1, through to multiply by 13, which is a useless cipher. In fact any multiplier not co-prime with 26 can be seen to be not one-one, and therefore useless too. Modular arithmetic, straight line graphs, ciphers, dotty patterns, ….