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# Tag Archives: number

## Chromatic number of the plane roundup

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

## 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

## 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 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

## 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

## Triangular number equations via pictures: solutions

Here are some solutions to my previous post. However, they are almost certainly not the only solutions! If you have other cool ways to visualize any of these (or any other triangular number equations) feel free to post in the … Continue reading

Posted in arithmetic, pattern, pictures, proof, solutions
Tagged number, pictures, proof without words, triangular
10 Comments