Approximations that lie
The pendulum, and the small lie that makes it simple
A pendulum's period does not depend on how far it swings. This is one of the most useful false statements in physics, and it is worth knowing exactly how false.
MechanicsThe angle that throws furthest, and why nobody notices
Forty-five degrees is the answer, and the maximum is so flat that a throw ten degrees off loses almost nothing. Both halves of that are worth drawing.
MechanicsThe slope, and the two directions that make it easy
An inclined plane looks like a harder problem than a flat one. Split the weight into two components chosen to suit the slope and it becomes an easier one.
OpticsWhat a lens is doing, and why three rays are enough
A lens bends every ray that reaches it. The construction uses three, because three are all that can be drawn without calculation — and any three that meet prove all the rest do.
RelativityThe clock that has to slow, and why no clock can refuse
One constant speed and one right-angled triangle force a moving clock to tick slower. The argument is Pythagoras, which is what makes it inescapable rather than merely surprising.