Clarification on <SG2>

Also tagging @kmmohn.

That’s not what the rule says. Let’s take a look at the rule again:

Once the Match begins, Robots may expand, but no horizontal dimension can exceed 36” (914.4 mm) at any point during the Match.

There is no mention of a circle in this definition, because the expansion limit is not (necessarily) a circle. For example, let’s think of a simple shape, say a triangle with sides of length 36", that does not violate this rule but would not fit into a 36" diameter circle. Here is such a triangle superimposed onto a 36" circle:


We can also draw other shapes that abide by this rule but do not fit in a circle, such as this reuleaux triangle:

These shapes abide by the rule’s requirement that no two points on the robot my measure more than 36" apart, while not fitting within a 36" circle.

Why would the GDC do this instead of a circle/cylinder, you ask? Because a circle/cylinder would be nigh unenforceable. Take a triangular robot for instance that barely fits inside a 36" diameter circle:


As you can see, despite only barely fitting within the circle, the largest distance between any two points is several inches less than 36", 31". Say we increase the size of the robot a bit:

Now our robot is sticking out of the 36" diameter circle (illegal if that’s what the rule said), but if a ref takes their 36" sizing tool and measures the robot, it will still seem to be more than 2" under the limit. Ultimately, we see that if the limit were actually a circle, it would be impossible to use a linear form of measurement to determine legality, and instead every robot would have to be sized using a large and impractical 36" circular box. In fact, back in ITZ, the rule originally specified a 36" diameter cylinder, but was changed to the current wording for this reason. The current wording is actually enforceable with a simple stick.