# Month: March 2016

## Before the beginning – Euclid’s Common Notions

This preamble from Euclid’s Elements is where mathematics education still goes wrong, even after 2000 years or so. Sound notions of what equality is are required as a bedrock of algebra.  Dynamic approaches of teaching equation solving, in which terms and numbers move and change sign, seem to work at first but lack the simplicity …

## Conic sections in the sand give shipwrecked philosophers good hope

Conic sections in the sand give shipwrecked Socratic philosopher, Aristippus, good hope. I wonder if this ancient tale, in which the mathematics of planetary motion some 2000 years prior to it’s application in space travel, is used to signify the presence of intelligent life and therefore hope of salvation has some echo in our …

## First Definition of Triangles

First definition of triangles from Euclid’s Elements Book I (Fundamentals of Plane Geometry Involving Straight Lines), Definition 20.

## Further Maths Conic Section Locus Problem

Intersection of perpendicular normals on one parabola makes another. Another A level further maths conic sections locus problem.

## Conic Sections Tangent/Normal Locus

A level further mathematics question animated.  Mid point of Normal x-intercept and Tangent y-intercept traces out another curve as original point moves round an ellipse.

## Hyperbola – Focus Directrix

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.