Monthly Archives: May 2018

Iterating squared digit sums in other bases

Posted on May 25, 2018 by Brent

In a previous post I wrote about iterating the squared digit sum function, which adds up the sum of the squares of the digits of a number; for example, . Denis left a comment asking about other bases—what happens if … Continue reading →

Posted in arithmetic, computation, proof | Tagged , , , , | 7 Comments

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 , , , , , | 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 , , , , , | 3 Comments