The context of classical geometry is a domain in which the notions of
straight line

and parallel

do not jar with common intuitions.
Some interesting contexts do not follow rules compatible with those intuitions,
but a broad class of real-world situations are compatible with them to within
close enough tolerances that many honest folk don't care about the difference,
in practice. Contexts in which these intuitions are exactly correct are
formally described as **flat** or **Euclidean**, so I
am effectively describing Euclidean geometry. I'll leave it to other pages to
address matters more formally, in terms which either address deviations from
flatness or formally specify flatness, but I'll here endeavour to set forth some
of the more prominent results of those
intuitions and some of the consequences that follow for any context in which
they hold good enough that *you* don't care about the difference. Many
of the intuitive truths here addressed remain true even in non-Euclidean (or
curved

) geometries, at least if we add some qualifying clauses, typically
confining the points, lines and regions under discussion to some sufficiently
small

portion of the whole context of the curved geometry.

I'll aim to describe geometries verbally, and I'll also use Scalable Vector Graphics (the W3C specification for an XML-based image format) for diagrams: some browsers shall need a plug-in to help them view these, but those that keep up with the times do now support it. Some implementations are still buggy in places: your mileage may vary !

- More pictorial treatments of geometry
- Euclidean geometry
- Why there are only five platonic solids
- The sine and cosine rules and why I measure angles in turns
- The angle bisector theorem.
- The sinusoids and general transcendental functions
- Trigonometry and its application to multiples of an angle.
- How much of a rectangle lies outside its mirror image in one of its diagonals ?
- Measuring (generalised) volume and area of spheres of arbitrary dimension
- The volume left when a cylindrical hole is cut through a sphere's centre only depends on their radii via the length of the cut.