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Constructing Pentagons
A highlight of Euclid’s Elements is the exact construction of a regular pentagon using a straight edge and a compass. But I’ve noticed recently that some of the pentagon constructions on YouTube are merely approximations – and are not advertised or understood as such. Furthermore, many of these constructions require non-collapsible compasses, which can “carry”…
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Negative Resistance
I recently coauthored an article in the International Journal of Bifurcation and Chaos that reports efficiently performing logic with a simple nonlinear electronic device that exhibits negative resistance, something I had previously theorized. At the heart of the device is a single p-n junction, which is formed by a silicon semiconductor crystal doped with impurity…
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Stokes’ Drag Law
Introductory physics often assumes without proof that the drag force on an object is proportional to its velocity, at least for smooth or laminar flow. In particular, a sphere of radius falling slowly with velocity in air of viscosity experiences a drag force which was first derived by George Stokes in 1851. Here is a…
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1+2+3+… = -1/12 Revisited
Why is minus-one-twelfth associated with the sum of the natural numbers? It’s the constant term in the series expansion of the corresponding smoothed or regularized sum! Introduce a decay factor, and in the limit of vanishing decay, the finite-non-zero part of the resulting sum is minus-one-twelfth, as one can quickly verify in Mathematica using (for…
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Pythagorean Animations
Known for thousands of years, hundreds of proofs of the Pythagorean theorem have been published, including one by U.S. President James Garfield. Here I animate three of my favorites. Each shows that the sum of the squares of the lengths of the legs of a right triangle equals the square of the length of its…
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Copy, Moon Joy
Carrying the torch from Apollo, through shuttle and station, to a hoped-for new era of space exploration, the Artemis 2 lunar flyby exceeded expectations All last week I monitored the NASA mission coverage livestream. As the flyby approached, the Moon (Luna) waned from gibbous to half to crescent in just a few hours, while its…
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The Dream Is Alive
As a child of the Apollo program and a lifelong dreamer of spaceflight, I am thrilled to follow the Artemis 2 mission, carrying the first humans around the Moon (Luna) in over half a century, with the intent to pick up where we left off, establish a permanent lunar presence, and proceed to Mars and…
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A Method of Reaching Extreme Altitudes
100 years ago, physicist Robert Goddard designed and built the first liquid-fueled rocket. Powered by gasoline and liquid oxygen and launched from his Aunt Effie’s farm in Auburn, Massachusetts on 1926 March 16, the first flight lasted 2.5 seconds and reached an altitude of 12.5 meters. 7 years earlier, in 1919, Goddard published the seminal…
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Guided Flame
Yuhe Ren, Niklas Manz, and I recently published an article Guided flame: reaction-diffusion of fire pulses in narrow channels in the journal Open Transport. Tim Siegenthaler helped machine the channels. This work had been gestating for a long time but has recently became a hot topic. Fortunately, Yuhe was able to acquire all our data…
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Moon Trees
As command module pilot for the 1971 Apollo 14 mission, Stuart Roosa was one of 24 people to travel around the Moon* in the heroic first age of lunar exploration. He was also a former U.S. Forest Service smokejumper, and he carried into lunar orbit about 500 seeds to test the effects of spaceflight on…
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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- Negative Resistance
- Stokes’ Drag Law
- 1+2+3+… = -1/12 Revisited
- Pythagorean Animations
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Thanks, Mark! I enjoy reading your posts as well.