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 of mathematical logic and create all sorts of problems when randomly, but apparently sensibly, applied.
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 modern era.
What obscure and impenetrable modern theorems could be left on a 21st century beach to do the same job?
First definition of triangles from Euclid’s Elements Book I (Fundamentals of Plane Geometry Involving Straight Lines), Definition 20.
Intersection of perpendicular normals on one parabola makes another. Another A level further maths conic sections locus problem.
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 – 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.