Computer-assisted proofs | Conjectures that have been proved | Discrete geometry | Spheres | Packing problems
The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements. The density of these arrangements is around 74.05%. In 1998, Thomas Hales, following an approach suggested by , announced that he had a proof of the Kepler conjecture. Hales' proof is a proof by exhaustion involving the checking of many individual cases using complex computer calculations. Referees said that they were "99% certain" of the correctness of Hales' proof, and the Kepler conjecture was accepted as a theorem. In 2014, the Flyspeck project team, headed by Hales, announced the completion of a formal proof of the Kepler conjecture using a combination of the Isabelle and HOL Light proof assistants. In 2017, the formal proof was accepted by the journal Forum of Mathematics, Pi. (Wikipedia).
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Science Bulletins: Kepler Discovers Dozens of Worlds
Kepler is the first NASA mission able to discover planets the size of Earth—and smaller—that are orbiting other stars. Kepler has discovered 11 solar systems and 26 planets, ranging from the size of Earth to larger than Jupiter. By searching for planets that lie within a star's habitable z
From playlist Science Bulletins
Generalized Kepler Problems - Guowu Meng
Generalized Kepler Problems Guowu Meng Hong Kong University of Science & Technology; Joint Member, School of Mathematics & Natural Sciences February 4, 2011 ANALYSIS/MATHEMATICAL PHYSICS SEMINAR For many elegant mathematical examples, one can 1) find theories behind them, 2) understand wh
From playlist Mathematics
Geometric Algebra Applications - Kepler Problem (Part 1)
In this video, we will begin our study of the Kepler problem, in which two masses move under an inverse-square law, namely the law of universal gravitation. We will derive the equation that needs to be solved and also talk about two conservation laws: angular momentum (geometric algebra pe
From playlist Math
3 - Kick-off afternoon : Thomas Hales, Formalizing the proof of the Kepler Conjecture
Thomas Hales (University of Pittsburgh): Formalizing the proof of the Kepler Conjecture
From playlist T2-2014 : Semantics of proofs and certified mathematics
The Gravity of Kepler Systems - Eric Agol
Joint IAS/Princeton University Astrophysics Colloquium Tuesday, September 15, 2015 http://www.sns.ias.edu/~seminar/colloquia.shtml More videos on http://video.ias.edu
From playlist Joint IAS/PU Astrophysics Colloquium
Kepler’s First Law of Motion - Elliptical Orbits (Astronomy)
Our Socratica Astronomy series is back! Bookmark the playlist here: ✷ https://socratica.link/Astro_Playlist We also ask you join our STELLAR email list so we can notify you when new videos go live: ✷ https://snu.socratica.com/astronomy (Don’t rely on the YT algorithm to show you what
From playlist Kepler's Laws
Geometric Algebra Applications - Kepler Problem (Part 3)
In this video, we will finish our discussion of the Kepler problem by deriving Kepler's 3rd Law, total energy, the Vis-Viva equation, and the Virial Theorem. Along the way, we'll review some facts about the ellipse and observe the total energies for the different conic sections. Reference
From playlist Math
Anisotropic Kepler Problem with Mathematica
For the latest information, please visit: http://www.wolfram.com Speaker: Keita Sumiya This talk covers how Mathematica is used to explore the periodic orbit theory in the Anisotropic Kepler Problem and Devil's Staircase surface faceting.
From playlist Wolfram Technology Conference 2014
Structured Regularization Summer School - A.Hansen - 4/4 - 20/06/2017
Anders Hansen (Cambridge) Lectures 1 and 2: Compressed Sensing: Structure and Imaging Abstract: The above heading is the title of a new book to be published by Cambridge University Press. In these lectures I will cover some of the main issues discussed in this monograph/textbook. In par
From playlist Structured Regularization Summer School - 19-22/06/2017
Astrophysics: Binary Star System (15 of 40) Kepler's Law M is (MUCH, MUCH) Larger Than m
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the period of s planet orbiting around a sun using Kepler's law. Next video in this series can be found at: https://youtu.be/3swag0ftxSQ
From playlist ASTROPHYSICS 1 BINARY SYSTEMS & KEPLER'S LAWS
Weak Stability Boundary and Capture in the Three-Body Problem - Edward Belbruno
Edward Belbruno NASA/AISR & IOD, Inc. January 19, 2011 GEOMETRY/DYNAMICAL SYSTEMS The problem of capture in the planar restricted three-body problem is addressed. In particular, weak capture is described, which occurs at a complicated region called the weak stability boundary, where the m
From playlist Mathematics
Thomas Fernique - Maximally Dense Sphere Packings
It is well known that to cover the greatest proportion of the Euclidean plane with identical disks, we have to center these disks in a triangular grid. This problem can be generalized in two directions: in higher dimensions or with different sizes of disks. The first direction has been the
From playlist Combinatorics and Arithmetic for Physics: special days
Lakatos on Science & Pseudoscience (1973)
Imre Lakatos's most succinct public summary of his philosophy of science. In this talk, he outlines his distinctive view of the importance of 'the demarcation problem' in the philosophy and history of science, namely the normative methodological problem of distinguishing between science an
From playlist Shorter Clips & Videos - Philosophy Overdose
Astrophysics: Binary Star System (24 of 40) Kepler's 1st Law: Elliptical Orbits - Part 2 of 3
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn about Kepler’s 1st Law of planetary motion: Elliptical Orbits. Kepler realized and proved that planets orbit around the
From playlist ASTROPHYSICS 1 BINARY SYSTEMS & KEPLER'S LAWS
Marjorie Wikler Senechal - Unwrapping a Gem - CoM Apr 2021
If the celebrated Scottish zoologist D’Arcy W. Thompson (1860 – 1948) could have met the near-legendary German astronomer Johannes Kepler (1571 – 1630), what would they talk about? Snowflakes, maybe? It is true that both men wrote about their hexagonal shapes. But they both wrote about Arc
From playlist Celebration of Mind 2021
IMS Public Lecture: Mathematics in the Solar System
William A. Casselman, The University of British Columbia, Canada
From playlist Public Lectures
The Search for a Theory of Everything – with Yang-Hui He
The search for a theory of everything spans centuries, from Kepler, Galileo and Newton, to Faraday and Maxwell, to Einstein, Bohr, Dirac, and C.N.Yang, to recent advances in superstring theory. Watch the Q&A: https://youtu.be/FB7aeEevo3g This event is in collaboration with the London Inst
From playlist Ri Talks
Astrophysics: Binary Star System (14 of 40) Kepler's Law
Visit http://ilectureonline.com for more math and science lectures! In this video I will review Kepler's 3 laws of planetary orbits. Next video in this series can be found at: https://youtu.be/hd6yNilLEh0
From playlist ASTROPHYSICS 1 BINARY SYSTEMS & KEPLER'S LAWS
The Best Way to Pack Spheres - Numberphile
Featuring James Grime... Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Sphere trilogy: http://bit.ly/Sphere_Trilogy Strange Spheres in Higher Dimensions: https://youtu.be/mceaM2_zQ
From playlist Sphere Trilogy on Numberphile