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Part Science, Part Art, Part Luck
Launched just last month, Lucy will be the first spacecraft to visit Jupiter’s trojan asteroids, rocky swarms that orbit about 60 degrees ahead and behind Jupiter in its orbit. Hal Levison, Lucy’s Principal Investigator, has described Lucy’s complicated trajectory, which includes an Earth gravity-assist and visits to both trojan swarms, as “part science, part art, and part luck”.…
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4D Unknot
In four dimensions, you can’t tie your shoelaces — because 4D knots don’t work. Any 1D curve in 4D space can be continuously deformed to the unit circle, which is an unknot. The looping animation below demonstrates how to undo a trefoil knot in 4D, where rainbow colors code the 4th dimension. The animation pauses when…
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Punch it, SpaceX
She’s not looking up at the sky; she’s looking down at it. I am excitedly following the Inspiration4 spaceflight and its diverse all-private crew of Jared Isaacman, Sian Proctor, Christopher Sembroski, and Hayley Arceneaux. Orbiting higher than any humans this millennium and carrying the largest window ever flown in space, their Crew Dragon Resilience is providing unprecedented and…
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Dandelin Spheres
In 1609, Johannes Kepler first described how planets orbit the sun in ellipses. Kepler understood an ellipse as both the locus of points whose distances from two foci sum to a constant and as the intersection of a cone and a plane. But how are these familiar definitions equivalent? In 1822, Germinal Dandelin discovered a beautiful construction that proves this…
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Grad Schools
Wooster physics graduates do many things after Wooster, including graduate work. Below is a map of some of the graduate schools they have attended, one dimension of the influence of our department. If you are a recent Wooster physics graduate and don’t see your graduate schools on the map, please contact us, and we will…
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For Teague
Sadly and unexpectedly Wooster physics senior Teague Curless ’22 died yesterday. I was fortunate to teach Teague some physics, especially in my Nonlinear Dynamics class last spring. Teague’s semester project beautifully illustrated chaos in a double pendulum — a pendulum swinging from another pendulum, like The Swinging Sticks® kinetic sculpture that silently rotates and librates beside…
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21st Century Skyscraper
Recently at its Boca Chica launch site, SpaceX stacked a Starship on a Superheavy booster to briefly form history’s largest rocket, dwarfing the Apollo Saturn V. Both a fit-check and a statement, SpaceX released the photograph below in black & white, which evokes classic mid-20th century skyscraper construction. But this 21st-century skyscraper is designed to…
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Spinors
Fermions like electrons, protons, and neutrons inhabit a 720° world: 360° rotations negate their quantum states, but 720° rotations restore them. A simple macroscopic model of such spinors is an arrow translating on a Möbius strip: as the center circle rotates, the attached arrow flips after 360° but flips back after 720°. As the circle rotates,…
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Squares & Cubes
Marvelously, the square of the sum of natural numbers is the sum of their cubes! Equivalently, the sum of their cubes is the square of their sum. This mathematical gem is attributed to Nicomachus of Gerasa who lived almost 2000 years ago. For example, More generally, or The accompanying animation illustrates the identity, where the cubes…
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Transition
As I transition to emeritus status tomorrow, I reflect on 33 years at Wooster. I am thankful for the freedom I’ve had to design my own courses, including eight first-year seminars; for the flexibility to explore a wide range of research topics, from celestial mechanics to biophysics to dancing in reduced gravity; and for six…
Author: John F. Lindner
Recent Comments
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.