Some notes on trigonometry.
Surely you
already know trig (and you won't learn it from this page,
anyway). But if you don't know why it's called a cosine
or an arctan you might find this interesting.  Some Trigonometry 
On this page, we find the value of π directly from its definition, using nothing more sophisticated than Pythagoras's theorem.  Pi from Pythagoras 
Continuing
in the same vein, we find the area of a circle, the volume of a sphere,
and the surface area of a sphere using simple geometric arguments.  Volume of a Sphere 
The common proof that the square root of 2
is irrational works by contradiction, and is unsatisfying (to me,
anyway). On this page we present what I think is a more intuitive
proof that the square root of 2, along with all noninteger roots of
integers, is irrational.

Irrational Roots

Calculus
of a single variable. In this collection of pages, I present
visual arguments to motivate a number of the basic facts about
calculus, which are often presented only with "symbol pushing"
arguments and little actual explanation.  Calculus 
Some
basic facts about the
hyperbolic functions, and what they mean for special relativity.  Hyperbolic Rotations 
The
edge of a slice through a cone forms a circle, ellipse, parabola, or
hyperbola. This page contains a proof of that assertion.  Conic
Sections 
Solid angles: Definition of steradians, and derivation of the formula to find the solid angle subtended by a cone.  Solid Angles 
Integers,
rational numbers, and real numbers. The axioms for all of them
are presented and we develop models for all of them. (This is not really "basic" material but it fits better here than anywhere else on the website.)  Numbers 
A
general discussion of ideal lenses and mirrors, some aspects of real
lenses and mirrors, the brightness of an image in a camera, in your
eye, and when viewed through a telescope, and, possibly, some other
items as they come up.  Simple Optics 
This includes a handful of results which I think are really kind of cool which can be derived just
from the second law of thermodynamics. In order to get to the
results we also include a very brief introduction of the first two laws
of thermodynamics and a brief introduction to the concept of a blackbody. This page uses almost no mathematics; the results are derived by simple arguments and a few diagrams.

Blackbodies

A very
brief introduction to Lagrangian mechanics  Lagrangians 
A
very brief essay on the dangers of "rigid
rods" and similar nearlyphysical connectors.  Rigid
Rods 
Do you find the fact that the traveling twin
ages more than the stayathome twin paradoxical, since from the point
of view of the traveler, the stayathome twin is the one who
moved? Simple explanations of time dilation obscure more than
they explain.  Against
Gamma 