bipolar coordinates

2-dimensional orthogonal coordinate system based on Apollonian circles
Thing general Q2383591
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bipolar coordinates

Summary

bipolar coordinates ranks in the top 2% of general entities by monthly Wikipedia readership (57 views/month).[1]

Key Facts

  • bipolar coordinates's image is recorded as Iso1.svg[2].
  • bipolar coordinates's subclass of is recorded as coordinate system[3].
  • bipolar coordinates's Commons category is recorded as Bipolar coordinates[4].
  • bipolar coordinates's Freebase ID is recorded as /m/04gjdd[5].
  • bipolar coordinates's different from is recorded as two-center bipolar coordinates[6].
  • bipolar coordinates's different from is recorded as biangular coordinates[7].
  • bipolar coordinates's defining formula is recorded as \begin{aligned}x&=a\frac{\sinh\tau}{\cosh\tau-\cos \sigma }\y&=a\frac{\sin \sigma }{\cosh \tau -\cos \sigma}\end{aligned}[8].
  • bipolar coordinates's MathWorld ID is recorded as BipolarCoordinates[9].
  • bipolar coordinates's maintained by WikiProject is recorded as WikiProject Mathematics[10].
  • bipolar coordinates's Microsoft Academic ID is recorded as 206647686[11].
  • bipolar coordinates's OpenAlex ID is recorded as C206647686[12].

Why It Matters

bipolar coordinates ranks in the top 2% of general entities by monthly Wikipedia readership (57 views/month).[1] It has Wikipedia articles in 10 language editions, a strong signal of global cultural recognition.[13] It is known by 7 alternative names across languages and contexts.[14]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [2] . wikidata.org.
  2. [3] . wikidata.org.
  3. [4] . wikidata.org.
  4. [5] . Freebase Data Dumps. wikidata.org.
  5. [6] . wikidata.org.
  6. [7] . wikidata.org.
  7. [8] . wikidata.org.
  8. [9] . wikidata.org.
  9. [10] . wikidata.org.
  10. [11] . wikidata.org.
  11. [12] . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.

Aggregate / graph-position facts

  1. [1] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [13] . Wikidata sitelinks. wikidata.org.
  3. [14] . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). bipolar coordinates. Retrieved April 10, 2026, from https://4ort.xyz/entity/bipolar-coordinates
MLA “bipolar coordinates.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/bipolar-coordinates.
BibTeX @misc{4ortxyz_bipolar-coordinates_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{bipolar coordinates}}, year = {2026}, url = {https://4ort.xyz/entity/bipolar-coordinates}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): bipolar coordinates — https://4ort.xyz/entity/bipolar-coordinates (retrieved 2026-04-10)

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