equation-authoring

Equation Authoring

Overview

An equation is a claim about how observables relate, not a result to plug into. Present it so the student can read it. The most common unaided failure: unpacking each symbol's meaning but skipping its units and the dimensional check — which leaves the equation abstract and unverifiable.

The discipline — every key equation

• Unpack every symbol — meaning AND units. Not "$m$ is mass" but "$m$ is mass (g)". A unit-less term list is half a definition.
• Show the dimensional check. Demonstrate the units cancel to the result's units. Non-optional — it's how students (and you) catch errors, and it makes the equation do work instead of sitting decorative.
• Connect to an observable. State what you measure and what you infer; the equation is the bridge ("measure the color → infer the temperature").
• Read the structure. What's on top vs bottom; the exponents. A scaling answer is judged by its exponents, not a coefficient ("$\propto r^{-1/2}$: quadruple $r$ to halve $v$"). Use the solve-for-the-observable form when that mirrors the inferential move.

Registry vs inline

• Load-bearing or reused equation → the <KeyEquation refId="…"> registry (one canonical statement, cross-referenceable).
• One-off inline relation → $…$.
• Mechanics (refId, registry) → docs/website/reference/chapter-components.md.

Units convention

Show units always and check dimensions always — but which system (CGS, SI, solar) is a course decision. Follow the course's voice/math-grammar; don't impose a unit system from here.

Red flags — STOP

• A symbol defined by meaning but with no units, or left undefined.
• No dimensional check.
• Plug-and-chug: a number with no structural/scaling reading.
• An equation dropped cold — no observable it connects to.
• A reused/key equation typed inline instead of registered as <KeyEquation>.

See also figure-authoring (visualizing an equation) and the course's voice/math-grammar for the unit convention.