Circles | Euclidean plane geometry | Elementary geometry
In geometry, Apollonian circles are two families (pencils) of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa. These circles form the basis for bipolar coordinates. They were discovered by Apollonius of Perga, a renowned Greek geometer. (Wikipedia).
Studying Apollonian Circle Packings using Group Theory
This video is in response to a colleague who asked for short videos about how we use group theory in our research. One of my interests is Apollonian circle packings. Some links: Wikipedia: https://en.wikipedia.org/wiki/Apollonian_gasket An article in New Scientist by Dana Mackenzie: ht
From playlist Joy of Mathematics
Apollonian packings and the quintessential thin group - Elena Fuchs
Speaker: Elena Fuchs (UIUC) Title: Apollonian packings and the quintessential thin group Abstract: In this talk we introduce the Apollonian group, sometimes coined the “quintessential” thin group, which is the underlying symmetry group of Apollonian circle packings. We review some of the e
From playlist My Collaborators
Apollo 12 on the Ocean of Storms
Ultra high-resolution photos of this historic second manned mission to the moon, including breathtaking photos of the lunar surface. Credit NASA.
From playlist Earth And Its Moon
Apollonian circle packings via spectral methods - Hee Oh (Yale University)
notes for this talk: https://docs.google.com/viewer?url=http://www.msri.org/workshops/652/schedules/14556/documents/1680/assets/17222 Effective circle count for Apollonian circle packings, via spectral methods Hee Oh Brown University We will describe a recent effective counting result f
From playlist Number Theory
Apollonius' circle construction problems | Famous Math Problems 3 | NJ Wildberger
Around 200 B.C., Apollonius of Perga, the greatest geometer of all time, gave a series of related problems; how to construct a circle in the plane touching three objects, where the objects are either a point (P), a line (L) and or a circle (C). Many mathematicians have studied this most fa
From playlist Famous Math Problems
http://www.teachastronomy.com/ Pluto is the outer sentinel of the solar system. With a size of only 2,300 kilometers, it is half the size of Mercury and two-thirds the size of Earth's moon. Its mean distance from the sun is 39 astronomical units, but it has a highly eccentric orbit with
From playlist 10. The Solar System
Apollonius and polarity | Universal Hyperbolic Geometry 1 | NJ Wildberger
This is the start of a new course on hyperbolic geometry that features a revolutionary simplifed approach to the subject, framing it in terms of classical projective geometry and the study of a distinguished circle. This subject will be called Universal Hyperbolic Geometry, as it extends t
From playlist Universal Hyperbolic Geometry
The dynamics of Apollonian circle packings by Sneha Chaubey
PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.
From playlist Smooth And Homogeneous Dynamics
Thin Groups and Applications - Alex Kontorovich
Analysis and Beyond - Celebrating Jean Bourgain's Work and Impact May 21, 2016 More videos on http://video.ias.edu
From playlist Analysis and Beyond
Diophantine analysis in thin orbits - Alex Kontorovich
Special Seminar Topic: Diophantine analysis in thin orbits Speaker: Alex Kontorovich Affiliation: Rutgers University; von Neumann Fellow, School of Mathematics Date: December 8, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Katherine Stange - The Sensual Apollonian Circle Packing
Talk given at the Pacific Northwest Number Theory Conference 2013.
From playlist My Math Talks
The Ramanujan Conjecture and some diophantine equations - Peter Sarnak
Speaker : Peter Sarnak Date and Time : Faculty Hall, IISc, Bangalore Venue : 25 May 12, 16:00 One of Ramanujan's most influential conjectures concerns the magnitude of the Fourier Coefficients of a modular form. These were made on the basis of his calculations as well as a far-reaching in
From playlist Public Lectures
Saturn: Best Rings in the Solar System
I think that nine out of ten people, if you ask them to picture a planet in their minds, will picture Saturn. Why? It's those rings! They are irresistible. Rings are to planets as peanut butter is to chocolate. The perfect complement. But there is much more to Saturn than just its rings. T
From playlist Astronomy/Astrophysics
Geometry and arithmetic of sphere packings - Alex Kontorovich
Members' Seminar Topic: Geometry and arithmetic of sphere packings Speaker: A nearly optimal lower bound on the approximate degree of AC00 Speaker:Alex Kontorovich Affiliation: Rutgers University Date: October 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
STPM - Local to Global Phenomena in Deficient Groups - Elena Fuchs
Elena Fuchs Institute for Advanced Study September 21, 2010 For more videos, visit http://video.ias.edu
From playlist Mathematics
Alex Kontorovich - On the Strong Density Conjecture for Apollonian Circle Packings [2012]
slides for this talk: https://docs.google.com/viewer?url=http://www.msri.org/workshops/652/schedules/14560/documents/1681/assets/17223 Abstract: The Strong Density Conjecture states that for a given primitive integral Apollonian circle packing, every sufficiently large admissible (passing
From playlist Number Theory
Quickly fill in the unit circle by understanding reference angles and quadrants
👉 Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Trigonometric Functions and The Unit Circle
Alex Kontorovich - Diophantine problems in thin orbits
Diophantine problems in thin orbits
From playlist 28ème Journées Arithmétiques 2013
