Author: John F. Lindner

  • 720° untangles 360° tangles

    John F. Lindner

    Despite growing up in three dimensions, as a kid I did not recognize one of 3D’s deep and subtle properties: full rotations tangle, but double rotations untangle! Following physicist Paul Dirac, twist a belt one full turn about its length. The 360° single twist cannot be undone without changing the belt buckles’ orientations, although the twist…

  • Luna’s Convex Orbit

    John F. Lindner

    Luna orbits Earth and Earth orbits Sol (where Luna is Earth’s moon and Sol is Earth’s star, the sun). As a kid, I thought Luna’s solar orbit formed a loopy spirograph pattern. Instead, Luna’s orbit is convex! Neglecting the eccentricity and tilts of the orbits and the incommensurability of the periods, Luna’s counterclockwise path around…

  • 1+2+3+… = -1/12?

    John F. Lindner

    In quantum electrodynamics, the bare charge of an electron is infinite, but the renormalized dressed charge is finite. The bare electron shields itself by polarizing the virtual electron-positron pairs of the nearby quantum vacuum to reduce its coupling at large distances to in natural units, where the “I” decorating the equals sign denotes an informal relationship. Renormalization techniques help…

  • A Better Table

    John F. Lindner

    The periodic table of the elements is almost as old as The College of Wooster, and I am a big fan. As we approach next year’s sesquicentennial of Dmitri Mendeleev‘s 1869 periodic table, I present a modest addition to the over 600 known periodic tables, which include , , and even designs! I wanted the…

  • Math Grenade

    John F. Lindner

    I just bought a new calculator. New to me, that is, but older than me. Inspired by the 1600s Gottfried Leibniz stepped cylinder and the 1800s Thomas de Colmar arithmometer, the Curta mechanical calculator design was developed by Curt Herzstark while imprisoned in the Buchenwald concentration camp during World War II. Curta calculators were manufactured between…

  • Optical Tweezers

    John F. Lindner

    A focused light beam can trap a small particle, such as a micron-sized latex sphere (or biological cell). If the sphere is much larger than the light’s wavelength, ray optics suffices to explain the trapping. Light bends as it passes through the sphere, as in Fig. A. The piconewton forces (red and blue arrows) on…

  • Dr. Rendezvous

    John F. Lindner

    Edwin Aldrin earned his PhD from MIT in 1963 with a thesis titled, “Line-of-sight guidance techniques for manned orbital rendezvous”. Just three years later in 1966, Aldrin was the pilot of Gemini XII, the last flight of the Gemini program, a critical precursor to the Apollo moon program. Aldrin and his commander James Lovell were…

  • Saturnday

    John F. Lindner

    Ancient cultures everywhere observed seven “wanderers” move against the apparently fixed stars of the night sky: our star the sun, our natural satellite the moon, and the brightest planets Mars, Mercury, Jupiter, Venus, and Saturn. In many languages, these wanderers became the basis for the names of the seven days of the week; for example,…

  • Anholonomy

    John F. Lindner

    A falling cat’s twisting returns its shape to normal but rotates its body to land feet down. Earth’s spin returns a Foucault pendulum to its initial position in one day but rotates its oscillation plane. Parallel parking cyclically rotates a car’s front wheels but shifts the car sideways. These are examples of nonholonomic motions or…

  • Norton’s Dome

    John F. Lindner

    Norton’s Dome is a fascinating counterexample in classical mechanics: A frictionless mass balanced at the dome’s top can remain there forever — but can also spontaneously slide down! A mass slides down Norton’s dome from rest and then is kicked back up to rest. The Shape Norton’s dome has a cubed square root profile: if…

Recent Comments

Recent Posts

Categories

Archives

Meta

Log in