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Vampire Ein Stein
Just a couple of months after announcing the remarkable discovery of a single shape that forces a non-periodic tiling of the plane, Smith, Myers, Kaplan, and Goodman-Strauss have announced an improved aperiodic monotile or ein stein. (Ein stein is “one stone” in German.) The hat and turtle shapes tile the plane only non-periodically, but with their…
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The Temperature of the Vacuum
Quantum field theory predicts that the temperature of empty space should depend on the observer’s motion, increasing proportionally with acceleration. Here I attempt an accessible introduction to this striking effect, related to Hawking radiation and discovered independently by Fulling, Davies, and Unruh, assuming only sophomore-level physics (including hyperbolic functions) with some assistance from Mathematica. Hyperbolic…
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A Century of Compton Scattering
One hundred years ago today the Physical Review published research on light scattering electrons that would earn its author, Wooster graduate Arthur Compton, a Physics Nobel Prize. By relativistically conserving spacetime momentum, as in the diagram below, and treating light as particles now called photons, Compton discovered that deflecting an electron through an angle stretches…
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We Are Going
After half a century confined to low-Earth orbit, and as soon as late next year, humans will once again leave Earth and voyage to Moon. The reality of this exciting adventure crystallized earlier this month when NASA announced the diverse and inspiring Artemis II crew: Clockwise from left in the photo below are Christina Koch,…
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Behold, an Ein Stein!
This academic year has been thrilling: first nuclear fusion breakeven, now an ein stein! Last week, a preprint at arxiv.org by David Smith et al. announced an “ein stein”, or one stone, a shape that forces a non periodic tiling of the plane, ending a half-century quest by many researchers, including me. A retiree and…
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Generalizing Coulomb’s Law
The forces between two electric charges in arbitrary motion are complicated by velocity, acceleration, and time-delay effects. The forces need not even lie along the line joining the two charges! Suppose a source charge is at position with velocity and acceleration , and a test charge is at position with velocity and acceleration . Let…
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Triple EVA
Since the mid 1960s, all space walks or extra-vehicular activities (EVAs) have involved just one or two astronauts — except once. In May 1992, on the STS-49 mission, the crew of the space shuttle Endeavour was attempting to rescue a stranded communications satellite, Intelsat 603. After repeated two-person EVAs failed to capture the satellite, NASA and the…
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5-Color Theorem
On 1852 October 23, Francis Guthrie noticed that he needed only 4 colors to color the counties of England so no two bordering counties shared the same color. This works for any map, but only in 1976, and with the aid of a computer, did Kenneth Appel and Wolfgang Haken finally prove the 4-color theorem. Here I outline…
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Compton Generator
Long before he won the Nobel Prize in Physics, and while still a Wooster undergraduate, Arthur Compton realized a third way to demonstrate Earth’s spin (after pendulums and gyroscopes). Compton reported his results in a manuscript submitted to the journal Science on 1913 January 13 and published as “A Laboratory Method of Demonstrating the Earth’s Rotation”,…
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Analemma
Photograph the sky at the same time each day for a year and Sun will appear to execute a figure-8 path called an analemma, which is often inscribed on Earth globes and can be used as an almanac, as by Tom Hanks‘ character Chuck Nolan in the movie Cast Away. The 2D animation below illustrates…
Author: John F. Lindner
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Nice post, John! Thanks for writing these. I always enjoy them.
David Smith’s ein stein is an awesome shape!
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Thanks, Mark! I enjoy reading your posts as well.