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Tag Archives: number
The Natural Number Game
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
I’ve had fun writing about the HadwigerNelson problem to determine the chromatic number of the plane, but I think this will be my last post on the topic for now! More 7colorings Of course, the original point of the hexagonal … Continue reading
The chromatic number of the plane, part 4: an upper bound
In my previous posts I explained lower bounds for the HadwigerNelson 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
The chromatic number of the plane, part 3: a new lower bound
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
The chromatic number of the plane, part 2: lower bounds
In a previous post I explained the HadwigerNelson 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
The chromatic number of the plane, part 1
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
Book review: An Illustrated Theory of Numbers
[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
A Fibonacci pattern
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