Schema for horizontal dials¶
A compass-and-straightedge geometric construction that projects an equatorial sundial’s hour divisions onto a horizontal dial for a specified latitude.
Core Idea¶
Historical schemas differ in layout, geographic latitude and true-north orientation are constitutive and graphical construction approximates trigonometric hour-angle formulas. A polar-pointing gnomon and equatorial hour circle are represented in projection, and rays or auxiliary semicircles transfer equal hour angles into unequal horizontal hour-line angles. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
The load-bearing residual is not the broad topic of gnomonics. It is the domain-specific identity fixed by the site latitude and hemisphere, horizontal dial plane, north-south meridian and dial center, polar-style direction and height, equatorial reference circle, hour angles and labels, projection construction and resulting hour lines, civil-time corrections excluded and graphical accuracy and historical variant are explicit.
Scope of Application¶
Schema for horizontal dials belongs to gnomonics and is useful where the analyst can specify the typed gnomonics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the site latitude and hemisphere, horizontal dial plane, north-south meridian and dial center, polar-style direction and height, equatorial reference circle, hour angles and labels, projection construction and resulting hour lines, civil-time corrections excluded and graphical accuracy and historical variant are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the site latitude and hemisphere, horizontal dial plane, north-south meridian and dial center, polar-style direction and height, equatorial reference circle, hour angles and labels, projection construction and resulting hour lines, civil-time corrections excluded and graphical accuracy and historical variant are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Schema for horizontal dials. Schema for horizontal dials compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed gnomonics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the site latitude and hemisphere, horizontal dial plane, north-south meridian and dial center, polar-style direction and height, equatorial reference circle, hour angles and labels, projection construction and resulting hour lines, civil-time corrections excluded and graphical accuracy and historical variant are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of gnomonics because they reuse the typed gnomonics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, A polar-pointing gnomon and equatorial hour circle are represented in projection, and rays or auxiliary semicircles transfer equal hour angles into unequal horizontal hour-line angles., and type the carrier, state every parameter and convention in the definition, test that the site latitude and hemisphere, horizontal dial plane, north-south meridian and dial center, polar-style direction and height, equatorial reference circle, hour angles and labels, projection construction and resulting hour lines, civil-time corrections excluded and graphical accuracy and historical variant are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Schema for horizontal dials Domain-specific
Parents (1) — more general patterns this builds on
-
Schema for horizontal dials is a kind of Representation Prime
The proposed strict upward parent is
prime:representation.
Hierarchy path (1) — routes to 1 parentless root
- Schema for horizontal dials → Representation → Abstraction
Neighborhood in Abstraction Space¶
Schema for horizontal dials sits in a sparse region of the domain-specific corpus (60th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Geodesy, Orbits & Coordinate Frames (25 abstractions)
Nearest neighbors
- Northern celestial hemisphere — 0.89
- Equator — 0.88
- Earth-centered, Earth-fixed coordinate system — 0.87
- Cissoid — 0.86
- Log-polar coordinates — 0.86
Computed from structural-signature embeddings · 2026-09-08