Tag Archives: number

The Natural Number Game

Posted on May 25, 2021 by Brent

Hello everyone! It has been quite a while since I have written anything here—my last post was in March 2020, and since then I have been overwhelmed dealing with online and hybrid teaching, plus a newborn (who is now almost … Continue reading →

Posted in challenges, computation, proof | Tagged computer, game, Lean, natural, number, proof | 6 Comments

Chromatic number of the plane roundup

Posted on June 28, 2018 by Brent

I’ve had fun writing about the Hadwiger-Nelson problem to determine the chromatic number of the plane, but I think this will be my last post on the topic for now! More 7-colorings Of course, the original point of the hexagonal … Continue reading →

Posted in geometry | Tagged bound, chromatic, coloring, hexagons, number, plane, seven, tiling, upper | 7 Comments

Post without words #22

Posted on June 9, 2018 by Brent

Posted in geometry, pattern | Tagged chromatic, coloring, hexagon, number, plane, tiling | 13 Comments

The chromatic number of the plane, part 4: an upper bound

Posted on June 2, 2018 by Brent

In my previous posts I explained lower bounds for the Hadwiger-Nelson problem: we know that the chromatic number of the plane is at least 5 because there exist unit distance graphs which we know need at least 5 colors. Someday, … Continue reading →

Posted in geometry, proof | Tagged bound, chromatic, graph, number, plane, proof, upper | Comments Off

The chromatic number of the plane, part 3: a new lower bound

Posted on May 15, 2018 by Brent

In my previous post I explained how we know that the chromatic number of the plane is at least 4. If we can construct a unit distance graph (a graph whose edges all have length ) which needs at least … Continue reading →

Posted in geometry, proof | Tagged bound, chromatic, graph, number, plane, proof | 1 Comment

The chromatic number of the plane, part 2: lower bounds

Posted on May 1, 2018 by Brent

In a previous post I explained the Hadwiger-Nelson problem—to determine the chromatic number of the plane—and I claimed that we now know the answer is either 5, 6, or 7. In the following few posts I want to explain how … Continue reading →

Posted in geometry, proof | Tagged bound, chromatic, graph, number, plane, proof | 3 Comments

The chromatic number of the plane, part 1

Posted on April 18, 2018 by Brent

About a week ago, Aubrey de Grey published a paper titled “The chromatic number of the plane is at least 5”, which is a really cool result. It’s been widely reported already, so I’m actually a bit late to the … Continue reading →

Posted in geometry, proof | Tagged chromatic, graph, number, plane, proof | 4 Comments

Book review: An Illustrated Theory of Numbers

Posted on March 11, 2018 by Brent

[Disclosure of Material Connection: The AMS kindly provided me with a free review copy of this book. I was not required to write a positive review. The opinions expressed are my own.] An Illustrated Theory of Numbers Martin H. Weissman … Continue reading →

Posted in books, review | Tagged book, diagrams, illustrated, number, textbook, theory | 1 Comment

Post without words #12

Posted on October 28, 2016 by Brent

Posted in fractals, geometry, pattern, posts without words | Tagged fractal, Harriss, number, plastic, spiral | 1 Comment

A Fibonacci pattern

Posted on May 13, 2011 by Brent

Recall the Fibonacci numbers, , the sequence of numbers beginning with where each subsequent number is the sum of the previous two: Try this: pick any Fibonacci number. Square it. Now, look at the two Fibonacci numbers on either side … Continue reading →

Posted in algebra, arithmetic, challenges, fibonacci, pattern, sequences | Tagged fibonacci, number, pattern | 4 Comments