Author Archives: 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. … Continue reading →
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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 … Continue reading →
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In quantum electrodynamics, the bare charge of an electron is infinite, but the 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 [latex display=”true”] \infty … Continue reading →
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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 … Continue reading →
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I just bought a new calculator. New to me, that is, and 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 … Continue reading →
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A focussed 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 … Continue reading →
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Edwin Aldrin obtained 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, … Continue reading →
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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 planets Mars, Mercury, Jupiter, Venus, and Saturn. In many languages, these wanderers became … Continue reading →
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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 … Continue reading →
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The Shape In dimensionless coordinates, with the [latex]z[/latex]-axis pointing down, Norton’s dome has the shape [latex display=”true”] z = \frac{2}{3}s^{3/2},[/latex] where [latex]s[/latex] is the arc length along the dome. If [latex]ds^2 = dx^2 + dz^2[/latex], then [latex display=”true”] x = \int dx … Continue reading →
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