Ellipsoid Wall Thickness

Here's the front of our 2010-Family-Reunion T-Shirt.

It's the last thing I did before retiring about 1995.
Because of it, my 86-year-old wife gets lots of attention at the grocery store.

Here is the derivation:
 https://ethicsblackhole.blogspot.com/2013/08/blog-post.html

Transmitter Antenna

  *  Over several months, I've searched for a convincing description of transmitter-antenna function, unsuccessfully; so I decided to attempt my own.  A valid description must explain why or predict that the optimal length of a dipole transmitter antenna is half a carrier-wave length, each limb being 1/4 as long as the carrier wave.  An axiom of my theory is that photons are emitted as electrons are accelerated by a passing EMF pulse.  A postulate is that all photons share essential properties, so the radio wave is like Alice's looking glass, where classic deterministic physics might illustrate quantum probabilistic mechanics.
  *  The figure below shows a dipole antenna at ten evenly spaced moments.  The plus (+) and minus (-) show the input polarities at each moment.  The up and down arrows show the directions of electron acceleration in an antenna limb at those moments, black for a primary pulse, red for a reflected pulse (each arrow representing 1/4 of a pulse's duration).  Note that the negative input to a branch repels electons; positive input to a branch attracts electrons -- both branches therefore experiencing EMFs in same direction and analogous locations at any moment hence emitting photons of the same orientation at any moment.  In progressing from one moment to the next in the upper branch, the lower black arrow moves up, the upper black arrow becomes the upper red arrow with reversed direction, the upper red arrow moves down, and a new lower black arrow is  generated from the input voltage.  In the lower branch, the progress of arrows (EMFs) is inverted, the electron accelerations agreeing with those of the upper branch.
  *  This diagram is a crude way to see whether the mixture of primary pulses and reflected pulses would cooperate or cancel at various moments of the carrier-wave cycle in various segments of the antenna.  It turns out that the pulses in an antenna branch oscillate between cancelling (moments 2, 6 & 10) when the second half of a pulse meets the reflected first half of itself) and maximal coopertion (moments 4 & 8 when the first half of a pulse meets the reflected second half of the previous pusle) with weaker combinations in between (transition moments: 1, 3, 5, 7 & 9).
  *  Cooperating pulses crossing in the middle of an antenna branch constitute a standing wave.  Thus, the two antenna branches experience cooperative standing waves simultaneously, thereby maximizing signal output.  The 2 standing waves regenerate as long as the oscillator is active and connected.

  *  Below is an attempt to illustrate the same sequence just in the upper branch.  The black curve is the primary wave generated by an oscillator on the left and progressing rightward (ie upward).  The solid segment is the portion in the 1/4-wave antenna branch, the dashed segment continuing the wave cycle as if the antenna were as long as the carrier wave, so we can see its shape.  The red curve is the reflected wave in the antenna, which is the nearest segment of the dashed line flipped leftward for orientation and inverted for valence.  I believe this picture needs more work.

  *  The best YouTube description of antenna function that I have seen ANT06 Half Wave Dipole by Greg Durgin.  I haven't quite reconciled his and my descriptions, but I hope to.