In the mathematical theory of tessellations, the Conway criterion, named for the English mathematician John Horton Conway, is a sufficient rule for when a prototile will tile the plane. It consists of the following requirements: The tile must be a closed topological disk with six consecutive points A, B, C, D, E, and F on the boundary such that: * the boundary part from A to B is congruent to the boundary part from E to D by a translation T where T(A) = E and T(B) = D. * each of the boundary parts BC, CD, EF, and FA is centrosymmetric—that is, each one is congruent to itself when rotated by 180-degrees around its midpoint. * some of the six points may coincide but at least three of them must be distinct. Any prototile satisfying Conway's criterion admits a periodic tiling of the plane—and does so using only 180-degree rotations. The Conway criterion is a sufficient condition to prove that a prototile tiles the plane but not a necessary one. There are tiles that fail the criterion and still tile the plane. Every Conway tile is foldable into either an isotetrahedron or a rectangle dihedron and conversely, every net of an isotetrahedron or rectangle dihedron is a Conway tile. (Wikipedia).
Doris Schattschneider - Two Conway Geometric Gems - CoM Oct 2021
John Conway enjoyed discovering unusual properties of triangles and also enjoyed discovering properties of tilings. Two of his discoveries bear his name: The Conway Circle, and The Conway Criterion. I’ll talk about these two gems; one led to a new tiling app. Doris Schattschneider, profes
From playlist Celebration of Mind 2021
How to determine if a piecewise function is continuous or not with limits
👉 Learn how to evaluate the limit of a piecewice function. A piecewise function is a function that has different rules for a different range of values. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at
From playlist Evaluate the Limit (PC)
A Tribute to Berlekamp, Conway, Guy, Graham, and Randi - G4G14 Apr 2022
In the long four years between G4G13 and G4G14, we lost some towering figures from the G4G community. It is hard for many of us to see how we can go on without them, but their legacy will live on. In this tribute session, we honor Elwyn Berlekamp, John Conway, Richard Guy, Ron Graham, and
From playlist G4G14 Videos
Evalauate the limit of a piecewise function with a hole
👉 Learn how to evaluate the limit of a piecewice function. A piecewise function is a function that has different rules for a different range of values. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at
From playlist Evaluate the Limit (PC)
This is an experimental video where I give answers to the (mostly) mathematical questions asked by viewers.
From playlist Math talks
Learn how to evaluate the limit of a piecewise function with a hole
👉 Learn how to evaluate the limit of a piecewice function. A piecewise function is a function that has different rules for a different range of values. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at
From playlist Evaluate the Limit (PC)
James Propp - Conjectural Enumerations of Trimer Covers of Finite Subgraphs of the Triangular (...)
The work of Conway and Lagarias applying combinatorial group theory to packing problems suggests what we might mean by “domain-wall boundary conditions” for the trimer model on the infinite triangular lattice in which the permitted trimers are triangle trimers and three-in-a-line trimers.
From playlist Combinatorics and Arithmetic for Physics: special days
How to evaluate the limit of a function by observing its graph
👉 Learn how to evaluate the limit of an absolute value function. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time. The absolute value function is a function which only takes the positive val
From playlist Evaluate Limits of Absolute Value
Evaluate the limit of a piecewise function with a hole
👉 Learn how to evaluate the limit of a piecewice function. A piecewise function is a function that has different rules for a different range of values. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at
From playlist Evaluate the Limit (PC)
Evaluate the limit of a piecewise function with jump discontinuity
👉 Learn how to evaluate the limit of a piecewice function. A piecewise function is a function that has different rules for a different range of values. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at
From playlist Evaluate the Limit..........Help!
Evaluate the limit for a value of a function
👉 Learn how to evaluate the limit of an absolute value function. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time. The absolute value function is a function which only takes the positive val
From playlist Evaluate Limits of Absolute Value
Epsilon delta limit (Example 3): Infinite limit at a point
This is the continuation of the epsilon-delta series! You can find Examples 1 and 2 on blackpenredpen's channel. Here I use an epsilon-delta argument to calculate an infinite limit, and at the same time I'm showing you how to calculate a right-hand-side limit. Enjoy!
From playlist Calculus
Is the Conway knot slice? (After Lisa Piccirillo)
This is a talk on the recent work by Lisa Piccirillo showing that the Conway know is not a slice knot. We first review the definitions of the Conway know and slice knots, and then give an overview of her proof. The paper on this by Lisa Piccirillo can be found at https://arxiv.org/pdf/1
From playlist Math talks
SDS 501: Statistical Programming with Friends — with Jared Lander
Jared Lander joins us to discuss his work as an R meetup organizer, the upcoming virtual R Conference, and his work as a consultant for a variety of companies from metal workers to professional football teams. In this episode you will learn: • Jared’s R meetups and our professional histor
From playlist Super Data Science Podcast
Remembering John Conway - Part 8
Bay Area Artists and Mathematicians - BAAM! with Gathering 4 Gardner - G4G present Remembering John Conway Mathematician John Horton Conway died of COVID-19 on April 11, 2020. On April 25th, the Bay Area Artists and Mathematicians (BAAM!) hosted an informal Zoom session to share memories
From playlist Tributes & Commemorations
Remembering John Conway - Part 7
Bay Area Artists and Mathematicians - BAAM! with Gathering 4 Gardner - G4G present Remembering John Conway Mathematician John Horton Conway died of COVID-19 on April 11, 2020. On April 25th, the Bay Area Artists and Mathematicians (BAAM!) hosted an informal Zoom session to share memories
From playlist Tributes & Commemorations
Remembering John Conway - Part 4
Bay Area Artists and Mathematicians - BAAM! with Gathering 4 Gardner - G4G present Remembering John Conway Mathematician John Horton Conway died of COVID-19 on April 11, 2020. On April 25th, the Bay Area Artists and Mathematicians (BAAM!) hosted an informal Zoom session to share memories
From playlist Tributes & Commemorations
Remembering John Conway - Full Video
Bay Area Artists and Mathematicians - BAAM! with Gathering 4 Gardner - G4G present Remembering John Conway Mathematician John Horton Conway died of COVID-19 on April 11, 2020. On April 25th, the Bay Area Artists and Mathematicians (BAAM!) hosted an informal Zoom session to share memories
From playlist Tributes & Commemorations
Evaluate the limit of a piecewise function by graphing
👉 Learn how to evaluate the limit of a piecewice function. A piecewise function is a function that has different rules for a different range of values. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at
From playlist Evaluate the Limit (PC)