Conjectures that have been proved | Discrete geometry | Euclidean plane geometry

Honeycomb conjecture

The honeycomb conjecture states that a regular hexagonal grid or honeycomb has the least total perimeter of any subdivision of the plane into regions of equal area. The conjecture was proven in 1999 by mathematician Thomas C. Hales. (Wikipedia).

Honeycomb conjecture
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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

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The Pattern to Prime Numbers?

In this video, we explore the "pattern" to prime numbers. I go over the Euler product formula, the prime number theorem and the connection between the Riemann zeta function and primes. Here's a video on a similar topic by Numberphile if you're interested: https://youtu.be/uvMGZb0Suyc The

From playlist Other Math Videos

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A (compelling?) reason for the Riemann Hypothesis to be true #SOME2

A visual walkthrough of the Riemann Zeta function and a claim of a good reason for the truth of the Riemann Hypothesis. This is not a formal proof but I believe the line of argument could lead to a formal proof.

From playlist Summer of Math Exposition 2 videos

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Mertens Conjecture Disproof and the Riemann Hypothesis | MegaFavNumbers

#MegaFavNumbers The Mertens conjecture is a conjecture is a conjecture about the distribution of the prime numbers. It can be seen as a stronger version of the Riemann hypothesis. It says that the Mertens function is bounded by sqrt(n). The Riemann hypothesis on the other hand only require

From playlist MegaFavNumbers

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Weil conjectures 4 Fermat hypersurfaces

This talk is part of a series on the Weil conjectures. We give a summary of Weil's paper where he introduced the Weil conjectures by calculating the zeta function of a Fermat hypersurface. We give an overview of how Weil expressed the number of points of a variety in terms of Gauss sums. T

From playlist Algebraic geometry: extra topics

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The Most Difficult Math Problem You've Never Heard Of - Birch and Swinnerton-Dyer Conjecture

The Birch and Swinnerton-Dyer Conjecture is a millennium prize problem, one of the famed seven placed by the Clay Mathematical Institute in the year 2000. As the only number-theoretic problem in the list apart from the Riemann Hypothesis, the BSD Conjecture has been haunting mathematicians

From playlist Math

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Understanding and computing the Riemann zeta function

In this video I explain Riemann's zeta function and the Riemann hypothesis. I also implement and algorithm to compute the return values - here's the Python script:https://gist.github.com/Nikolaj-K/996dba1ff1045d767b10d4d07b1b032f

From playlist Programming

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The Honeycombs of 4-Dimensional Bees ft. Joe Hanson | Infinite Series

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Be sure to check out It's OK to be Smart's video on nature's love of hexagons https://youtu.be/Pypd_yKGYpA And try CuriosityStream today: http://curiositystream.com/inf

From playlist Higher Dimensions

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Nikos Frantzikinakis: Ergodicity of the Liouville system implies the Chowla conjecture

Abstract: The Chowla conjecture asserts that the signs of the Liouville function are distributed randomly on the integers. Reinterpreted in the language of ergodic theory this conjecture asserts that the Liouville dynamical system is a Bernoulli system. We prove that ergodicity of the Liou

From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi

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Why do Bees build Hexagons? Honeycomb Conjecture explained by Thomas Hales

Mathematician Thomas Hales explains the Honeycomb Conjecture in the context of bees. Hales proved that the hexagon tiling (hexagonal honeycomb) is the most efficient way to maximise area whilst minimising perimeter. Interview with Oxford Mathematician Dr Tom Crawford. Produced by Tom Roc

From playlist Mathstars

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Why do bees build hexagonal honeycombs? - Forces of Nature with Brian Cox: Episode 1 - BBC One

Subscribe and 🔔 to the BBC 👉 https://bit.ly/BBCYouTubeSub Watch the BBC first on iPlayer 👉 https://bbc.in/iPlayer-Home Programme website: http://bbc.in/29kGs3z Honeybees around the world build perfectly hexagonal honeycombs, but why? Professor Brian Cox reveals the hidden mathematical rule

From playlist Forces Of Nature

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Two-dimensional Self Avoiding Walks - Mireille Bousquet-Melou (2014)

Slides for this talk: https://docs.google.com/viewer?url=http://www.msri.org/workshops/616/schedules/14374/documents/1552/assets/17052 Abstract: Exactly solvable classes of self-avoiding walks Mireille Bousquet-Mélou Université Bordeaux 1 A walk on a lattice is self-avoiding if it never

From playlist Mathematics

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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

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Hilbert's 15th Problem: Schubert Calculus | Infinite Series

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Get 2 months of Curiosity Stream free by going to www.curiositystream.com/infinite and signing up with the promo code "infinite." It's said that Hermann Schubert perfor

From playlist An Infinite Playlist

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Number Theory 1.1 : Product Formula for the Zeta Function

In this video, I prove Euler's product formula for the Riemann Zeta function. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Number Theory

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Michael Weinstein: Dispersive waves in novel 2d media; Honeycomb structures, Edge States ...

Abstract: We discuss the 2D Schrödinger equation for periodic potentials with the symmetry of a hexagonal tiling of the plane. We first review joint work with CL Fefferman on the existence of Dirac points, conical singularities in the band structure, and the resulting effective 2D Dirac dy

From playlist Partial Differential Equations

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Large deviations for random hives and the spectrum of the sum of two random...- Hariharan Narayanan

Probability Seminar 11:15am|Simonyi 101 and Remote Access Large deviations for random hives and the spectrum of the sum of two random matrices Hariharan Narayanan Affiliation: Cambridge University Date: April 07, 2023  Hives, as defined by Knutson and Tao, are discrete concave functions

From playlist Mathematics

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Michael Weinstein - Discrete honeycombs, rational edges and edge states - IPAM at UCLA

Recorded 30 March 2022. Michael Weinstein of Columbia University, Applied Physics and Applied Mathematics, presents "Discrete honeycombs, rational edges and edge states" at IPAM's Multiscale Approaches in Quantum Mechanics Workshop. Abstract: We first discuss the derivation of tight bindin

From playlist 2022 Multiscale Approaches in Quantum Mechanics Workshop

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The Quasi-Polynomial Freiman-Ruzsa Theorem of Sanders - Shachar Lovett

Shachar Lovett Institute for Advanced Study March 20, 2012 The polynomial Freiman-Ruzsa conjecture is one of the important open problems in additive combinatorics. In computer science, it already has several diverse applications: explicit constructions of two-source extractors; improved bo

From playlist Mathematics

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Randomness and topology in correlated insulators by Itamar Kimchi

PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS: Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In

From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)

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