In geometry, the Heesch number of a shape is the maximum number of layers of copies of the same shape that can surround it. Heesch's problem is the problem of determining the set of numbers that can be Heesch numbers. Both are named for geometer Heinrich Heesch, who found a tile with Heesch number 1 (the union of a square, equilateral triangle, and 30-60-90 right triangle) and proposed the more general problem. For example, a square may be surrounded by infinitely many layers of congruent squares in the square tiling, while a circle cannot be surrounded by even a single layer of congruent circles without leaving some gaps. The Heesch number of the square is infinite and the Heesch number of the circle is zero. In more complicated examples, such as the one shown in the illustration, a polygonal tile can be surrounded by several layers, but not by infinitely many; the maximum number of layers is the tile's Heesch number. (Wikipedia).
Heesch Numbers and Tiling - Numberphile
Get your first audiobook free with an Audible 30-day trial. Go to http://www.audible.com/numberphile or text numberphile to 500 500. More links & stuff in full description below ↓↓↓ This video features Edmund Harriss from University of Arkansas. Extra footage from this interview: https:/
From playlist Edmund Harriss on Numberphile
On Surrounding a Polygon & JMA Outstanding Paper Award – Craig Kaplan
I introduce the problem of computing the Heesch number of a polygon, give some new results of non-trivial Heesch numbers of simple shapes like polyominoes, and demonstrate Good Fences, a mobile game I developed based on surrounding polygons. I reveal the short list of nominees for the 201
From playlist G4G12 Videos
The Plastic Ratio - Numberphile
Ed Harriss discusses the plastic ratio - more amazing than the golden ratio? You decide! More links & stuff in full description below ↓↓↓ See our golden ratio videos: http://bit.ly/Golden_Ratio Previous video with Ed (Heesch Numbers): https://youtu.be/6aFcgATW9Mw Ed Harriss is online at
From playlist Edmund Harriss on Numberphile
How to solve a de broglie wavelength problem
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From playlist Modern Physics
This is one of my all-time favorite differential equation videos!!! :D Here I'm actually using the Wronskian to actually find a nontrivial solution to a second-order differential equation. This is amazing because it brings the concept of the Wronskian back to life! And as they say, you won
From playlist Differential equations
Physicist Explains Wikipedia Page: The Schrodinger Equation
Why are Wikipedia Physics pages so difficult to understand? Hey guys, I'm back with a new video! This time, I'm looking at how certain Wikipedia pages can be so complicated to understand, and so here's a Wikipedia page made easy! Now I can totally understand that a wiki page is meant to p
From playlist Quantum Physics by Parth G
10% Students Solve This Trig Equation Wrong (Including me!)
Once you have a solid idea for how to solve trigonometric equations it is time for a challenge. A problem that will test you knowledge and ability to apply algebraic concepts to trigonometric equations. This problem does exactly that. ✅ Know when to use identities https://youtu.be/UArTc
From playlist Challenged and Confused Videos
Practice Problem: Henderson-Hasselbalch Equation Calculations
David Hasslehoff did chemistry?! No wait, Hasselbalch. And Henderson. Anyway there's this equation, and it relates the pH of a buffer solution to the pKa of the acid and the ratio of the concentrations of the acid and conjugate base. It's easy to use, give it a try! Try all of the general
From playlist General Chemistry Practice Problems
Practice Problem: Launching Things With Springs
You're a mischievous little physicist, aren't you? Well I guess there's no harm in projecting a toy into the air, especially if it's part of your scientific research. Given a spring constant and some other information, how high will this little army guy go? Let's find out! Try all of the
From playlist Classical Physics Practice Problems
Separation of variables and the Schrodinger equation
A brief explanation of separation of variables, application to the time-dependent Schrodinger equation, and the solution to the time part. (This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at http://www.youtube.com/
From playlist Mathematical Physics II - Youtube
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Now that we understand the Schrödinger equation, it's time to put it to good use, and solve a quantum problem. Let's find the eigenfunctions and eigenenergies associated with a quantum particle restricted to an infinite square well. This is also known as the famous "Particle in a Box" prob
From playlist Modern Physics
The Complexity of Gradient Descent: CLS = PPAD ∩ PLS - Alexandros Hollender
Computer Science/Discrete Mathematics Seminar I Topic: The Complexity of Gradient Descent: CLS = PPAD ∩ PLS Speaker: Alexandros Hollender Affiliation: University of Oxford Date: October 11, 2021 We consider the problem of computing a Gradient Descent solution of a continuously different
From playlist Mathematics
Lecture 20 - Introduction to NP-completeness
This is Lecture 20 of the CSE373 (Analysis of Algorithms) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1997. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/1997/lecture22.pdf
From playlist CSE373 - Analysis of Algorithms - 1997 SBU
MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Erik Demaine View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This lecture discusses computational complexity and introduces termi
From playlist MIT 6.006 Introduction to Algorithms, Spring 2020
Problem Solving Skills | How to Improve Your Problem Solving Skills? | Softskills | Simplilearn
This video on how to improve your problem-solving skills is focused on excellent tips that will enhance your Problem-Solving skill like Decision making, Critical Thinking, Active listening, Creativity, and many more, both in your personal and professional life. In this tutorial, we will se
From playlist Interview Tips | Interview Tips in English | Simplilearn 🔥[2022 Updated]
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From playlist Leadership & Management
The Schrodinger equation made simple | Linearity
We've talked about the quantum state plenty- but what happens to it over time? That's exactly the question the Schrodinger equation solves. This video we talk about 'Linearity'. In the next video we discuss the equation itself and its derivation. Click here fore that: https://youtu.be/DEgW
From playlist Quantum Mechanics (all the videos)
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From playlist Problem Solving