Aperiodic tilings | Quasicrystals
Quasicrystals and Geometry is a book on quasicrystals and aperiodic tiling by Marjorie Senechal, published in 1995 by Cambridge University Press (ISBN 0-521-37259-3). One of the main themes of the book is to understand how the mathematical properties of aperiodic tilings such as the Penrose tiling, and in particular the existence of arbitrarily large patches of five-way rotational symmetry throughout these tilings, correspond to the properties of quasicrystals including the five-way symmetry of their Bragg peaks. Neither kind of symmetry is possible for a traditional periodic tiling or periodic crystal structure, and the interplay between these topics led from the 1960s into the 1990s to new developments and new fundamental definitions in both mathematics and crystallography. (Wikipedia).
Using a set of points determine if the figure is a parallelogram using the midpoint formula
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determining if a set of points makes a parallelogram or not
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determining if a set of points is a rhombus, square or rectangle
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Cut-And-Project Quasicrystals: Patch Frequency and Moduli Spaces by Rene Rรผhr
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
Determine if a set of points makes up a rectangle using the distance formula
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Intrinsic Diophantine approximation (Lecture 1) by Amos Nevo
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
Numerical mathematics of quasicrystals โ Pingwen Zhang โ ICM2018
Numerical Analysis and Scientific Computing Invited Lecture 15.8 Numerical mathematics of quasicrystals Pingwen Zhang Abstract: Quasicrystals are one kind of fascinating aperiodic structures, and give a strong impact on material science, solid state chemistry, condensed matter physics an
From playlist Numerical Analysis and Scientific Computing
Determine if a set of points is a parallelogram using the distance formula
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Ancient Aliens: Mysterious Metals from Outer Space (Season 12) | History
Stay up to date on all of HISTORY's latest premieres at http://history.com/schedule Researching ancient cultures, archaeologists have found mysterious metals with no clear origin. Ancient astronaut theorists believe these mysterious alloys could be evidence of alien communication with man
From playlist Ancient Aliens: Official Series Playlist | New Episodes Fridays at 9/8c | History
The Search for Natural Quasicrystals - Paul Steinhardt
Paul Steinhardt Center for Theoretical Science, Princeton University March 7, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Yves Meyer - The Abel Prize interview 2017
0:27 Personal Journey and choosing Mathematics 6:04 Thesis on harmonic analysis in Strasbourg 9:00 Number Theory and Quasicrystals 12:24 Meyer set 14:22 Connection with Quasicrystals more specifically 16:49 Calderรณnโs Conjecture w/ Coifman and McIntosh 23:44 Wavelets 28:09 Strรถmberg and th
From playlist The Abel Prize Interviews
How to determine if a set of points makes up a rectangle using the distance formula
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determine if a set of points is a trapezoid or not
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
What are Hyperbolas? | Ch 1, Hyperbolic Trigonometry
This is the first chapter in a series about hyperbolas from first principles, reimagining trigonometry using hyperbolas instead of circles. This first chapter defines hyperbolas and hyperbolic relationships and sets some foreshadowings for later chapters This is my completed submission t
From playlist Summer of Math Exposition 2 videos
How to determine if points are a rhombus, square or rectangle
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Rhombofoam in Zome โ Scott Vorthmann
Rhombofoam is a pattern that fills 3D space in all the ways that a golden rhombohedron does, while forming dodecahedral and 16-sided cells that have the topology of foam: three cells around each edge, and four around each vertex. The result is a foam model that has the symmetries of a quas
From playlist G4G12 Videos
Material Marvels with Ainissa Ramirez - Quasicrystals
The Nobel Prize in Chemistry went to quasicrystals. But what are they? Dr. Ainissa Ramirez guides us into the strange world where atoms arrange themselves in forbidden ways and create materials with weird properties.
From playlist Material Marvels
An attempt at growing a quasicrystal
Like the simulation https://youtu.be/YjerTwsRUp0 this one shows the motion of particles coupled to a thermostat, and interacting with an anisotropic Lennard-Jones type potential. Only this time, the potential has a pentagonal symmetry instead of a square symmetry. Two isolated particles ha
From playlist Molecular dynamics
Determine if a set of points is a parallelogram by using the slope formula
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Not quite a quasicrystal (yet): Particles interacting with a potential based on the golden ratio
This new attempt at growing a quasicrystal uses a potential with rotation symmetry, which is similar to the Lennard-Jones potential, but has two stable equilibrium positions at distances whose ratio ls the golden mean Phi = 1.618.... This was suggested to me by Florian Theil. The result is
From playlist Molecular dynamics