Can You Feel Gravity?
What you feel is not explainable just by the gravity at your own
location; what you feel is due to the difference between gravity at
your location and gravity in distant parts of the world.
A discussion of linear
least-squares fitting, using a spreadsheet or otherwise, including
the case of multiple fitted parameters, and including the case where
the basis functions are nonlinear (even though the fitted function
remains a linear combination of the basis functions). Examples
include using the linest(...) spreadsheet function to fit a quadratic, or to fit a
If you know about complex numbers, and a little bit about
vectors, you can use that to jump-start your understanding of Clifford
Algebra. So here is a side-by-side comparison of complex numbers and Clifford
There is a mathematical theorem that says vortex lines are
endless. They either go on forever, or form closed loops. If
something looks like half a vortex loop, it cannot possibly be what it
seems, and it's almost certainly worth your trouble to figure out
what's actually happening.
A careful derivation (actually two derivations) of
Bernoulli's theorem. In particular,
we find that the equation directly describes the enthalpy (not energy)
of the fluid parcel. The equation applies just fine
to compressible fluids, which is good thing, because
there are no incompressible fluids.
A puzzle about the inertia of a
cube, illustrating qualitative reasoning, and illustrating the
geometrical and physical significance of a tensor, with applications
to the Wigner-Eckart theorem.
The famous Twelve Coins Puzzle
with a discussion involving Design-of-Experiment, Information Theory,
and Communication Theory.
An analysis of the famous Twenty Questions
game, including a method for winning 100% of the time.
The analysis is a good illustration of information theory.
A discussion of why atomic physics says that electrons hate each
other and pair up only as a last resort (Hund's rule #1) whereas
high-school chemistry deals almost exclusively with molecules that
have all their valence electrons paired up. Why pairs -- Or not?