Partial differential equations | Spectral theory
To hear the shape of a drum is to infer information about the shape of the drumhead from the sound it makes, i.e., from the list of overtones, via the use of mathematical theory. "Can One Hear the Shape of a Drum?" is the title of a 1966 article by Mark Kac in the American Mathematical Monthly which made the question famous, though this particular phrasing originates with Lipman Bers. Similar questions can be traced back all the way to physicist Arthur Schuster in 1882. For his paper, Kac was given the Lester R. Ford Award in 1967 and the Chauvenet Prize in 1968. The frequencies at which a drumhead can vibrate depend on its shape. The Helmholtz equation calculates the frequencies if the shape is known. These frequencies are the eigenvalues of the Laplacian in the space. A central question is whether the shape can be predicted if the frequencies are known; for example, whether a Reuleaux triangle can be recognized in this way. Kac admitted that he did not know whether it was possible for two different shapes to yield the same set of frequencies. The question of whether the frequencies determine the shape was finally answered in the negative in the early 1990s by Gordon, Webb and Wolpert. (Wikipedia).
One cannot (always) hear the shape of a drum
The question "Can One Hear the Shape of a Drum?" was asked by Marc Kac in a 1966 article in the American Mathematical Monthly. The vibrations of a drum are governed by its resonant frequencies, which are related to what mathematicians call the "eigenvalues of the Laplace operator with Diri
From playlist Billiards in polygons
One cannot always hear the shape of a drum: Isospectral billiards in 3D
This is a remake of the video https://youtu.be/RaQZ11ydBZo showing isospectral drums, this time in 3D. The question "Can One Hear the Shape of a Drum?" was asked by Marc Kac in a 1966 article in the American Mathematical Monthly. The vibrations of a drum are governed by its resonant frequ
From playlist Wave equation
Wave amplitude in two isospectral drums
Like the video https://youtu.be/RaQZ11ydBZo this simulation shows two drums that have exactly the same resonant frequencies. It is based on the same construction involving 7 triangles obtained by reflecting an initial triangle. The initial triangle has a different shape than before, and th
From playlist Billiards in polygons
How do we hear sound? License: Creative Commons BY-NC-SA More information at http://k12videos.mit.edu/terms-conditions
From playlist Physics
Why does your voice sound different on a recording? Greg Foot Answers Your Questions | Head Squeeze
Greg Foot tells us exactly why we hate the sound of our own voice on answering machines and such like in this Headsqueeze single question science video. When we make a recording of our own voice then play it back, we are hearing it more or less as other people do. The sound waves travel
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Can you hear the shape of a drum?
Bach, the Universe & Everything - Can you hear the shape of a drum? In Bach the Universe & Everything, mathematics and music share the stage. A partnership between Orchestra of the Age of Enlightenment and Oxford Mathematics, these secular services aim to reflect the community atmosphere
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If you listen closely, the drumbeats of Amazonian tribes sound like human speech. Now the first in-depth study of how the drummers do it: Tiny variations in the time between beats match how words in the spoken language are vocalized. Read more: https://scim.ag/2I0Vpck About Science Snippe
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Homophonic drums: two different drums that should sound the same
Like the video https://youtu.be/RaQZ11ydBZo this simulation shows two drums that have exactly the same resonant frequencies. In addition, their resonant modes (eigenfunctions) have the same value at two specific points, namely the inner points where 6 triangles meet. Therefore, the drums m
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How do we HEAR Where Things Are? I Sci Guide with Jonathan Webb I Head Squeeze
How do we hear where things are? Sounds are concentric ripples in the air. If a sound starts over on your left, it will be louder in your left ear than your right and that's because your head is in the way. There is a sound shadow which means there is a level difference between your two ea
From playlist Sci Guide - the latest science and tech news
Can We Hear Shapes? | Infinite Series | PBS Digital Studios
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Mathematician Mark Kac asked the question “Can we hear the shape of a drum?” It was a question that took over 20 years to answer. Sine waves, fundamental frequencies, e
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Rodrigo Bañuelos: "Events of Small Probabilities Do Happen"
Latinx in the Mathematical Sciences Conference 2018 "Events of Small Probabilities Do Happen" Rodrigo Bañuelos, Purdue University Institute for Pure and Applied Mathematics, UCLA March 9, 2018 For more information: http://www.ipam.ucla.edu/programs/special-events-and-conferences/latinx-
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Recitation 11 - Fourier Analysis in Action
Fourier Series: Example and Connections. Basel Problem and the Guitar String; Can we hear the Shape of a Drum? Recitation 11 of Caltech's Ph2a Course on Vibrations and Waves by Prof. Frank Porter and Dr. Ashmeet Singh. View course materials on the course website http://waves.caltech.edu
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James Arthur: The Langlands program: arithmetic, geometry and analysis
Abstract: As the Abel Prize citation points out, the Langlands program represents a grand unified theory of mathematics. We shall try to explain in elementary terms what this means. We shall describe an age old question concerning the arithmetic prime numbers, together with a profound gene
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Open Days 2019 Part 3: Applied Mathematics at Oxford
Our Open Days are intended to give an insight in to Maths at Oxford, whether you are a potential applicant or are just curious. In this talk to an audience of sixth-formers (High School students) and their families, about the Applied Maths that our undergraduates study at Oxford, Dominic V
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Black Spirituals | Resonance | Interview | Exploratorium
Join us as Resonance kicks off its second season with Oakland-based sound-making duo Black Spirituals. Sarah Cahill interviews electronic artist and guitarist Zachary James Watkins and percussionist Marshall Tramell.
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The Concept Of Sound Waves And Frequency Explained In ONE Minute!! #Physics #Theory #Mechanics #Science #NicholasGKK #Shorts
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Walter van Suijlekom: Non-commutative geometry and spectral triples - Lecture 1
Mini course of the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: Our starting point is a spectral approach to geometry, starting with the simple ques tion ’can one hear the shape of a drum’. This was phrased by Mark Kac in t
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