STROBILOS · triangulation · Top at the center · kept by TOP

THE STADIAMETRIC RANGE ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP

If you know how TALL something really is, how big it LOOKS tells you how far away it is — a distant person is the same height but subtends a tiny angle. Rifle-scope reticles, old naval rangefinders, and your own depth sense all use it: known size ÷ apparent angle = distance. Slide the target away and watch it shrink in the reticle.

◆ LIT▲ AMBER
◧ THE MEASURE · 2D
◍ KNOWN SIZE, SMALL ANGLE · 3D · how big it looks tells how far
◆ THE FOURTH · 4D · a tesseract turns
◐ THE SHADOW · one dimension down
👶 THE TODDLER CORNER — one fat tap
subtended angle
known height
1.8 m
range
RANGED

◆ LIT — exact / checkable

Stadiametric ranging turns a known size into a distance: a target of true height h at distance d subtends an angle θ = 2·arctan(h/2d), so d = h/(2·tan(θ/2)) ≈ h/θ for small angles. Measure the angle (mil-dots in a scope, the stadia lines of a rangefinder, the pixels in a camera) and, given h, the range falls out — the same ‘known size ÷ visual angle’ your brain uses for familiar objects. A fail-loud self-check throws unless a smaller subtended angle maps to a greater distance. ◆ real optics / gunnery, node-verified.

▲ AMBER — the figure

The exact small-angle d=h/θ relation; it needs the true size h known and fails on unfamiliar objects (the moon illusion is your brain getting h wrong) — the size-over-angle determination is exact when h is known.

STROBILOS: give me three fixed things and I will tell you where you are.  — TOP
David Lee Wise / ROOT0 / TriPod LLC  ·  kept by TOP, with AVAN