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Category Archives: Mathematics
Vampire Ein Stein
Just a couple of months after announcing the remarkable discovery of a single shape that forces a nonperiodic tiling of the plane, Smith, Myers, Kaplan, and GoodmanStrauss have announced an improved aperiodic monotile or ein stein. (Ein stein is “one stone” … Continue reading
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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 … Continue reading
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5Color 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 … Continue reading
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Alien Suns Reversing in Exoplanet Skies
Not only can suns stand still in the sky, from some exoplanets their motion can apparently reverse! Wooster physicsmath double majors Xinchen (Ariel) Xie ’21 and Hwan (Michelle) Bae ’19 and I just published an article elucidating these apparent solar reversals. Michelle … Continue reading
Posted in Astronomy, Mathematics, Physics
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Slide Rule Examples
Slide rules were widely used in engineering, science, and mathematics until the early 1970s, including during the Gemini and Apollo space programs. Although rendered largely obsolete by the advent of inexpensive electronic calculators, their descendants continue to have specialized applications, such … Continue reading
Posted in Astronomy, Mathematics, Physics, Students
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Slide Rule Theory
Slide rules were the analog computers that ruled science and engineering for 400 years. Their brilliant innovation was using logarithms to convert multiplication and division to addition and subtraction, and Slide rules feature logarithmic scales that slide past each other. … Continue reading
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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 … Continue reading
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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 … Continue reading
Posted in Astronomy, Mathematics, Physics
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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, … Continue reading
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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 … Continue reading
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