Geometry

The Desmos geometry calculator draws constructions: a segment between two points, the circle through a point, where two lines cross, a triangle turned about a point. Axis writes them as functions, and a file asks for that calculator in its config:

config { calculator: GEOMETRY }
A = (0, 0)
B = (4, 1)
C = (1, 3)
s = segment(A, B)
c = circle(A, B)
P = intersection(c, line(B, C))

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A construction is a value like any other. It can be named, passed to another construction, and measured - as a call, or as a member:

config { calculator: GEOMETRY }
A = (0, 0)
B = (4, 1)
C = (1, 3)
T = polygon(A, B, C)
a = area(T)
side = segment(A, B).length
rotate(T, A, pi / 2)

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The function reference lists every one. They exist on the geometry calculator and nowhere else - triangle and sphere only on the 3D one - so anywhere else the compiler says so before Desmos does:

s = segment((0, 0), (4, 1))

Their names are built in all the same, whichever calculator the file is for, so area, center or line cannot be defined as names of your own.

Tokens

A construction made by pointing and clicking on the geometry calculator has no name the person gave it. Desmos names it itself, with a token, and Axis writes a token as $ and its number:

config { calculator: GEOMETRY }
$1 = (0, 0)
$2 = segment($1, (4, 1))
m = $2.length

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A token is a name like any other, but Desmos keeps the definitions of tokens in a hidden folder of the geometry calculator’s own and accepts them nowhere else. The compiler puts them there, wherever the file wrote them, so a graph made on the calculator decompiles to a file that builds it again exactly. Written in a file for any other calculator, a token is requires-calculator.