In geometry, a Steinmetz solid is the solid body obtained as the intersection of two or three cylinders of equal radius at right angles. Each of the curves of the intersection of two cylinders is an ellipse. The intersection of two cylinders is called a bicylinder. Topologically, it is equivalent to a square hosohedron. The intersection of three cylinders is called a tricylinder. A bisected bicylinder is called a vault, and a cloister vault in architecture has this shape. Steinmetz solids are named after mathematician Charles Proteus Steinmetz, who solved the problem of determining the volume of the intersection. However, the same problem had been solved earlier, by Archimedes in the ancient Greek world, Zu Chongzhi in ancient China, and Piero della Francesca in the early Italian Renaissance. (Wikipedia).
Andrew Putman - The Steinberg representation is irreducible
The Steinberg representation is a topologically-defined representation of groups like GL_n(k) that plays a fundamental role in the cohomology of arithmetic groups. The main theorem I will discuss says that for infinite fields k, the Steinberg representation is irreducible. For finite field
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Incredible Rolling Objects which aren't Spheres!
These strange solids roll in interesting and unexpected ways! Join me as we explore these curious geometries the Wobbler, Oloid and Steinmetz Solid. 3D Print your own with the files here - https://makersmuse.podia.com/oloidsandwobblers Get your own stainless steel Oloid! https://amzn.to/
From playlist Engineering
Albert Einstein, Holograms and Quantum Gravity
In the latest campaign to reconcile Einstein’s theory of gravity with quantum mechanics, many physicists are studying how a higher dimensional space that includes gravity arises like a hologram from a lower dimensional particle theory. Read about the second episode of the new season here:
From playlist In Theory
Parametric Excitation of Electric Oscillations
#SoME2 #electricity #ericdollard This video gives an introduction into parametric resonance in a series resonant electric circuit. This is my first attempt at making a lecture style video and my first time coding math animations, two things I've always wanted to do. It was so fun to l
From playlist Summer of Math Exposition 2 videos
How Steinmetz became the "Wizard of Schenectady"
Charles Proteus Steinmetz was known as the "Wizard of Schenectady." This video is on his wild and influential life and how he more than earned that moniker. For the script: My mailing list: https://kathylovesphysics.ck.page/welcome My Patreon Page: https://www.patreon.com/user?u=15291200
From playlist "The Lightning Tamers": A History of Electricity
Intersection of 2 cylinders volume
I use multivariable calculus (double/triple integrals) to calculate the volume of the famous Steinmetz solid that is obtained by intersecting two cylinders. One could do it using single variables, but the multivariable approach is more systematic. Enjoy! Note: The thumbnail is taken from
From playlist Double and Triple Integrals
Charles Proteus Steinmetz: A Fun Scientific Biography (Part 1: 1865-1894)
How and why Charles Proteus Steinmetz came to America, created his theory of hysteresis, the first 3-phase system in the US, and phasors, all before he became the "Wizard of Schenectady." Links: My mailing list: https://kathylovesphysics.ck.page/welcome My Patreon Page: https://www.p
From playlist "The Lightning Tamers": A History of Electricity
Harold Steinacker - Covariant Cosmological Quantum Space-Time
Covariant Cosmological Quantum Space-Time: Higher-spin and Gravity in the IKKT Matrix Model https://indico.math.cnrs.fr/event/4272/attachments/2260/2717/IHESConference_Harold_STEINACKER.pdf
From playlist Space Time Matrices
C. P. Steinmetz The Man Who Made Lighting
Pioneer of AC power Charles Proteus Steinmetz - a short film on him. Rescued from archives of degraded video and film this rare film examines one of North America's greatest scientists. Charles Steinmetz was an immigrant from Prussia who carried German expertise with him. He further dev
From playlist GE History
How and Why We Write the History of the Social Sciences - George Steinmetz
https://www.ias.edu/events/friends-talk-steinmetz More videos on http://video.ias.edu
From playlist Friends of the Institute
AWESOME SUPERCONDUCTOR LEVITATION!!!
A quantum levitator it's a circular track of magnets above which a razor-thin disc magically levitates, seeming to defy the laws of physics. The key to the levitator is the disc, which is made of superconducting material sandwiched between layers of gold and sapphire crystal. A piece of fo
From playlist THERMODYNAMICS
What's in Peanut Butter? | Ingredients With George Zaidan (Episode 7)
Crunchy versus creamy, runny versus solid ... there’s a lot more to peanut butter than just peanuts and salt. ➡ Subscribe: http://bit.ly/NatGeoSubscribe ➡ Watch all episodes of Ingredients here: http://bit.ly/WatchIngredients ➡ Get updates and tweet episode ideas @georgezaidan About Ingre
From playlist Newest Clips | National Geographic
Geometric Algebra - Rotors and Quaternions
In this video, we will take note of the even subalgebra of G(3), see that it is isomorphic to the quaternions and, in particular, the set of rotors, themselves in the even subalgebra, correspond to the set of unit quaternions. This brings the entire subject of quaternions under the heading
From playlist Math
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From playlist Science Unplugged: Quantum Mechanics
This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for
From playlist Quaternions
Toothpaste | Ingredients With George Zaidan (Episode 1)
Ancient toothpaste used stuff like rocks and bones -- and modern toothpaste isn’t all that different. Watch as chemist George Zaidan tries to create his own homemade toothpaste. ➡ Subscribe: http://bit.ly/NatGeoSubscribe ➡ Watch all episodes of Ingredients here: http://bit.ly/WatchIngredie
From playlist Newest Clips | National Geographic
This Mandelbulb fractal is real!
A fractal just grew from my desk! Testing my Shadertoy plugin for After Effects ^_^
From playlist Shorts
Intersection of 3 cylinders volume
In this video, I calculate the volume of the Steinmetz 3-solid obtained by intersecting three cylinders, using a symmetry argument and cylindrical coordinates. It’s actually not as bad as you think! Note: The thumbnail was taken from https://commons.m.wikimedia.org/wiki/File:Steinmetz-ccc
From playlist Double and Triple Integrals
Schrödinger Equation : its impact on the electron and the atom
The Schrödinger Equation is fundamental to the quantum behaviour of the atom, and quantum mechanics in general. But what is it all about? In this video I discuss what it means, without delving too deeply in the mathematics, and how it helps understand the nature of the electron in the atom
From playlist New here? A selection of what I do