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# Category Archives: geometry

## SMT solutions

In my last post I described the general approach I used to draw orthogons using an SMT solver, but left some of the details as exercises. In this post I’ll explain the solutions I came up with. Forbidding touching edges … Continue reading

Posted in computation, geometry
Tagged constraint, crossing, orthogonal, orthogons, perimeter, polygon, segments, SMT, solver
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## Drawing orthogons with an SMT solver

I’m long overdue to finish up my post series on orthogons as promised. First, a quick recap: An orthogon is a polygon with only right angles. Two orthogons are considered the same if you can turn one into the other … Continue reading

Posted in computation, geometry
Tagged constraint, drawing, global, local, orthobraces, orthogonal, orthogons, polygon, SMT, solver
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## 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

## Some words on PWW #22

There are lots of patterns to be found in the picture from my previous post! This is a really remarkable tiling. Here are a few special properties I know of: First of all, I hope you realized that the pattern … 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