Some Pysics Insights

Some Basic Math and Physics

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Just a few pages on relatively basic material here.  For the most part, these discuss general principles, rather than specific problems.

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 non-integer 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 mechanicsLagrangians
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


Page created on 11/16/06, from pieces extracted from the old front page.  Last updated 9/25/2013