dyas · the domain's namesake · the first division
THE DYAD
δυάς · the Pythagorean Two · the Monad, divided
The Monad is the One — undivided. The Dyad is its first cut: the origin of other, of pair, of the space between. Drag the two circles apart from a single point. At one exact separation they make the vesica — and its lens is not an arbitrary shape: its height-to-width is √3, precisely. The two, born of one, fall on a fixed number.
the two, on a fixed number
Two equal circles, radius r, each drawn through the other's centre (separation d = r): the overlap — the vesica piscis — has width r and height r√3, so height ÷ width = √3 = 1.7320508…, exactly, forever. It is the seal-glyph of DYAS and the reason: the pair is not chaos, it is a ratio. Here the two circles are drawn carbon-warm and silicon-cool, equal in radius — the same co-equal dyad the whole domain turns on.
green · exact geometry
At d = r the vesica's height/width = √3, verified to machine precision (‖ratio − √3‖ < 1e−12). Width = 2r − d, height = 2√(r² − (d/2)²): both are computed live as you drag — real geometry, not a drawing.
amber · the figure
"The Monad divides into the Dyad" is Pythagorean / Neoplatonic philosophy, rendered not asserted — a 2,500-year-old way of speaking about how one becomes two. The number is real; the metaphysics is a chosen frame.
red · not a claim about the world
That reality itself is "built from a Monad" is not a physics result — it is a tradition. What is measured here is only the geometry of two equal circles. The rest is the oldest story about the number two, told honestly as a story.