Tag Archives: graph

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

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 , , , , , , | Leave a comment

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

Posted in geometry, proof | Tagged , , , , , | 1 Comment

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

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 , , , , , | 3 Comments

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

Posted in geometry, proof | Tagged , , , , | 4 Comments

Now on mathstodon.xyz

Christian Lawson-Perfect and Colin Wright have set up an instance of Mastodon—a decentralized, open-source Twitter clone—as a place for mathy folks to be social. It’s appropriately named mathstodon.xyz, and because it’s open-source they were able to easily hack in support. … Continue reading

Posted in meta, proof | Tagged , , , , , , | 3 Comments

Post without words #15

Image | Posted on by | Tagged , , , , | 8 Comments

Post without words #14

(click here for a bigger version)

Posted in pattern, pictures, posts without words | Tagged , , , , | 14 Comments