Polyconic Projection Class¶

Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis.

Version: v1 · 2026-09-28 · History
Domain-specific #: 11392
Domain group: Natural Sciences
Origin domain: Geology & Earth Sciences
Subdomains: Cartography, Map Projections → Geology & Earth Sciences

Core Idea¶

Polyconic Projection Class is treated here as the recurring mathematics, logic, and statistics identity summarized by this source-grounded definition: Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis.

Polyconic can refer either to a class of map projections or to a specific projection known less ambiguously as the American polyconic projection. Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. This description applies to projections in equatorial aspect.

Van der Grinten projection—projects entire earth into one circle; all meridians and parallels are arcs of circles. Nicolosi globular projection—typically used to project a hemisphere into a circle; all meridians and parallels are arcs of circles. There are many "apple-shaped" projections, almost all of them obscure.

For Polyconic Projection Class, the abstraction is narrower than the article's general subject matter: a positive case must preserve Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. Retaining only the name, a familiar example, or a downstream effect is insufficient. The specialist roles and tests remain anchored in mathematics, logic, and statistics, which is why this identity is domain-specific rather than prime.

Structural Signature¶

Sig role-phrases:

Defining carrier — A series of polyconic projections, each in a circle, was also presented by Hans Mauer in 1922, who also presented an equal-area polyconic in 1935.
Constitutive relation — Another series by Georgiy Aleksandrovich Ginzburg appeared starting in 1949.
Operating condition — American polyconic projection—each parallel becomes a circular arc having true scale, the same scale as the central meridian.
Recognition evidence — Van der Grinten projection—projects entire earth into one circle; all meridians and parallels are arcs of circles.
Admissible variation — Nicolosi globular projection—typically used to project a hemisphere into a circle; all meridians and parallels are arcs of circles.
Characteristic consequence — Most polyconic projections, when used to map the entire sphere, produce an "apple-shaped" map of the world.
Failure boundary — Some of the projections that fall into the polyconic class are.

What It Is Not¶

Not the whole field of mathematics, logic, and statistics. The node requires the specific identity stated by Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis.
Not an over-broad reading. Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis.
Not an over-broad reading. American polyconic projection—each parallel becomes a circular arc having true scale, the same scale as the central meridian.
Not an over-broad reading. Van der Grinten projection—projects entire earth into one circle; all meridians and parallels are arcs of circles.
Not automatically Latitudinally equal-differential polyconic projection. Retrieval proximity does not establish equivalence; the two identities must be compared by carrier, operation, and failure boundary.

Scope of Application¶

Polyconic Projection Class applies literally inside mathematics, logic, and statistics wherever the source-defined carrier and relation can be established. Its documented habitats include:

Rectangular polyconic projection. Nicolosi globular projection—typically used to project a hemisphere into a circle; all meridians and parallels are arcs of circles.
Rectangular polyconic projection. Most polyconic projections, when used to map the entire sphere, produce an "apple-shaped" map of the world.
Polyconic projections. American polyconic projection—each parallel becomes a circular arc having true scale, the same scale as the central meridian.
Rectangular polyconic projection. Van der Grinten projection—projects entire earth into one circle; all meridians and parallels are arcs of circles.
Rectangular polyconic projection. A series of polyconic projections, each in a circle, was also presented by Hans Mauer in 1922, who also presented an equal-area polyconic in 1935.
Polyconic projections. Some of the projections that fall into the polyconic class are.

Outside mathematics, logic, and statistics, the name should be retained only when these same operational conditions survive; otherwise the comparison belongs to the broader parent Classification or should be marked as analogy.

Clarity¶

A clear use of Polyconic Projection Class names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. The strongest recognition evidence in the frozen account is: Van der Grinten projection—projects entire earth into one circle; all meridians and parallels are arcs of circles. A report should distinguish that evidence from a proxy, consequence, or common implementation. It should also state the qualification Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. so that a reader can reproduce the classification rather than infer it from topical resemblance.

Manages Complexity¶

Polyconic Projection Class compresses multiple mathematics, logic, and statistics details into a stable diagnostic relation. The source shows both the central mechanism—another series by Georgiy Aleksandrovich Ginzburg appeared starting in 1949.—and the practical consequence—most polyconic projections, when used to map the entire sphere, produce an "apple-shaped" map of the world. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit. It is lossy by design: local history and implementation details may be omitted only when they do not alter the defining relation.

Abstract Reasoning¶

Type the carrier. Identify the mathematics, logic, and statistics entities to which the claim applies.
State the relation. Use the source-grounded identity: Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis.
Check operation and conditions. American polyconic projection—each parallel becomes a circular arc having true scale, the same scale as the central meridian.
Demand recognition evidence. Van der Grinten projection—projects entire earth into one circle; all meridians and parallels are arcs of circles.
Test variation. Change an implementation or setting while preserving nicolosi globular projection—typically used to project a hemisphere into a circle; all meridians and parallels are arcs of circles.
Run the collapse test. Remove the defining operation; if the label still seems equally apt, only a topic or correlate was retained.
Reduce cautiously. When the specialist conditions cannot be carried, route the residual comparison to Classification.

Knowledge Transfer¶

Within the home domain. Knowledge about Polyconic Projection Class transfers literally when a new case preserves the same carrier type, relation, and recognition test. Nicolosi globular projection—typically used to project a hemisphere into a circle; all meridians and parallels are arcs of circles. Most polyconic projections, when used to map the entire sphere, produce an "apple-shaped" map of the world.

Beyond the home domain. No canonical parent is asserted for Polyconic Projection Class. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.

Examples¶

Canonical¶

American polyconic projection—each parallel becomes a circular arc having true scale, the same scale as the central meridian. This case is canonical because it supplies a concrete carrier and lets the defining relation be checked rather than merely named.

Mapped back: carrier → the entities in the documented case; operation → Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis; recognition evidence → Van der Grinten projection—projects entire earth into one circle; all meridians and parallels are arcs of circles

Applied / In Practice¶

Van der Grinten projection—projects entire earth into one circle; all meridians and parallels are arcs of circles. The applied case shows how the identity is used under a second setting or qualification while keeping the same operative relation.

Mapped back: changed setting → Rectangular polyconic projection; invariant → Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis; boundary → the case exits the class when polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis

Structural Tensions¶

T1 — Stable identity versus admissible variation. Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Which changes preserve the defining relation, and which replace it?

T2 — Recognition versus proxy. American polyconic projection—each parallel becomes a circular arc having true scale, the same scale as the central meridian. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the cited evidence establish the identity or only a correlated sign?

T3 — Definition versus implementation. Van der Grinten projection—projects entire earth into one circle; all meridians and parallels are arcs of circles. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Is the observed implementation constitutive, optional, or merely common?

T4 — Scope versus overextension. Nicolosi globular projection—typically used to project a hemisphere into a circle; all meridians and parallels are arcs of circles. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Can every claimed application fill the same typed roles without metaphor?

T5 — Transfer versus domain accent. A series of polyconic projections, each in a circle, was also presented by Hans Mauer in 1922, who also presented an equal-area polyconic in 1935. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the receiving case instantiate Polyconic Projection Class literally, co-instantiate Classification, or only resemble it?

T6 — Autonomy versus reduction. Another series by Georgiy Aleksandrovich Ginzburg appeared starting in 1949. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: What does Polyconic Projection Class distinguish that the broader parent Classification leaves together?

Structural–Framed Character¶

Polyconic Projection Class is structural-leaning. Its structural side is the repeatable organization summarized by Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. Its framed side is the mathematics, logic, and statistics vocabulary that fixes the carrier, evidence, exceptions, and admissible transformations.

Evaluative weight: the identity can be stated descriptively even when applications carry practical stakes. Human-practice dependence: the source-grounded carrier determines whether the relation exists independently or is constituted by a practice. Institutional origin: disciplinary conventions stabilize the name and test. Vocabulary portability: American polyconic projection—each parallel becomes a circular arc having true scale, the same scale as the central meridian. Import versus recognition: literal transfer requires the same mechanism; shape alone is analogy.

Its portable skeleton is Classification. Its character: a recurring specialist identity whose thin organization can be abstracted, while its operational meaning remains domain-bound.

Structural Core vs. Domain Accent¶

What is skeletal. Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. The stable skeleton is the typed relation expressed in that definition and the entry's recognition and collapse tests. The source identifies these operative conditions: A series of polyconic projections, each in a circle, was also presented by Hans Mauer in 1922, who also presented an equal-area polyconic in 1935. Another series by Georgiy Aleksandrovich Ginzburg appeared starting in 1949. It further constrains recognition and variation through: American polyconic projection—each parallel becomes a circular arc having true scale, the same scale as the central meridian. Van der Grinten projection—projects entire earth into one circle; all meridians and parallels are arcs of circles.

What is domain-bound. mathematics, logic, and statistics supplies the operative entities, technical vocabulary, warrants, and exceptions that make Polyconic Projection Class literal. Its documented scope includes the condition that Nicolosi globular projection—typically used to project a hemisphere into a circle; all meridians and parallels are arcs of circles. Another bounded application condition is that Most polyconic projections, when used to map the entire sphere, produce an "apple-shaped" map of the world. These are not decorative examples; they determine which carrier and evidence can fill the abstraction's roles.

Why no parent is asserted. Removing those specialist details does not currently yield one live catalog node that is a necessary genus for every instance. The entry is therefore approved as unparented rather than attached by topical resemblance. Its collapse evidence remains specific—Nicolosi globular projection—typically used to project a hemisphere into a circle; all meridians and parallels are arcs of circles.—and future graph densification may discover a defensible relation only if it preserves that boundary.

This entry is a kind of Projection.

Approved unparented node. No current live node supplies a defensible necessary genus or structural prerequisite for Polyconic Projection Class. The reviewed identity is: Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. The accelerated suggestion was declined because topical or lexical similarity does not establish hierarchy; the node is admitted without a parent pending later graph densification.
Related reasoning operations. Evidence, representation, comparison, classification, transformation, or evaluation may participate in particular cases, but participation does not make any one of them a necessary parent of every instance.

Relationships to Other Abstractions¶

Current abstraction Polyconic Projection Class Domain-specific

Parents (1) — more general patterns this builds on

Polyconic Projection Class is a kind of Projection Prime

The polyconic class consists of map projections with circular-arc parallels and a straight equator.

Hierarchy path (1) — routes to 1 parentless root

Polyconic Projection Class → Projection → Abstraction

Neighborhood in Abstraction Space¶

Polyconic Projection Class sits in a sparse region of the domain-specific corpus (69^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Geometric Figures & Constructions (32 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With¶

Classification. The parent omits the specialist differentia. Tell: Can the case establish Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis?
Latitudinally equal-differential polyconic projection. Latitudinally equal-differential polyconic projection denotes pseudoconical compromise map projection in cartography. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Dymaxion map. Dymaxion map denotes map projection in cartography. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Wiechel Projection. A polar pseudoazimuthal equal-area map projection that retains Lambert radial spacing while twisting azimuth by half the spherical colatitude, turning meridians into a pinwheel of semicircles. Tell: Which entry's carrier, operation, and failure condition are satisfied?
A measurement, proxy, or consequence. Those may provide evidence without being the identity. Tell: Would Polyconic Projection Class remain present if the detector or downstream effect changed?
A metaphorical analogue. A similar shape outside mathematics, logic, and statistics lacks the specialist mechanism. Tell: Do the native roles transfer literally, or only the parent Classification?

References¶

Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Polyconic_projection_class (revision 1283625469).
Preserved source candidate: https://pubs.usgs.gov/pp/1453/report.pdf
Preserved source candidate: https://web.archive.org/web/20121019082015/http://pubs.usgs.gov/pp/1453/report.pdf
Preserved source candidate: http://www.quadibloc.com/maps/meq0802.htm
Preserved source candidate: http://www.radicalcartography.net/?projectionref

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.