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