References & Sources

The books, papers, and authoritative online resources behind every formula on this site. Updated June 2026.

The formulas, derivations, and worked examples on Geometry Calculator are drawn from the following references. We list them not as a courtesy but as a practical resource: if our derivation is not detailed enough on a particular calculator page, the source below will have it.

Primary mathematical references

  • Euclid. The Thirteen Books of Euclid's Elements, translated by Sir Thomas L. Heath, 3 vols., Cambridge University Press, 1908 (Dover reprint 1956). Books I, III, and VI are our standard reference for plane geometry definitions, the SSS / SAS / ASA congruence postulates, and the basic theorems on similar triangles.
  • Coxeter, H. S. M. Introduction to Geometry, 2nd ed., John Wiley & Sons, 1969. Chapters 1, 3, and 12 supply the modern statements of the Law of Sines and Cosines we use throughout the Triangle Solver, plus the inversive and projective material behind a handful of the advanced calculators.
  • Hartshorne, Robin. Geometry: Euclid and Beyond, Springer Undergraduate Texts in Mathematics, 2000. Our reference for the modern axiomatic treatment of congruence — particularly when validating the proofs returned by the AI Solve feature on the Congruent Triangles tools.
  • Beyer, William H. (ed.). CRC Standard Mathematical Tables and Formulae, 30th ed., CRC Press, 1996. Used as a cross-check for surface-area, volume, and special-shape constants. When our derivation produces a result that disagrees with CRC, we re-derive from first principles before deploying.
  • Polya, George. How to Solve It, Princeton University Press, 1945 (1971 second edition). Not used for formulas but for the step-by-step heuristic structure that drives our AI Solve system prompts. The "Understand the problem → Devise a plan → Carry out the plan → Look back" sequence is the explicit scaffolding behind the prompt we send for proof-style problems.

Authoritative online resources

  • NIST Digital Library of Mathematical Functions — dlmf.nist.gov. The successor to Abramowitz & Stegun. Our reference for trigonometric identities, series expansions, and tolerance bounds on the inverse trigonometric functions used in the SSS, SAS, ASA, AAS, and SSA branches of the Triangle Solver.
  • Wolfram MathWorld — mathworld.wolfram.com. We use MathWorld as a tertiary cross-reference. When a textbook gives a formula in one form and MathWorld in another, we present both and note the equivalence on the calculator page.
  • OEIS — The On-Line Encyclopedia of Integer Sequences — oeis.org. Consulted for any calculator whose output is a sequence of integers (Pascal's triangle entries, regular polygon vertex counts, polyhedron face counts).
  • Khan Academy Geometry curriculum — khanacademy.org/math/geometry. For pedagogical structure — how to introduce a topic to a new learner. The "How to use this calculator" sections on our high-traffic pages mirror Khan Academy's progression where applicable.
  • Project Gutenberg — Euclid's Elements — gutenberg.org/ebooks/21076. The public-domain text of Heath's translation. Linked from individual calculator pages when we cite a specific proposition (e.g., Proposition I.47 = Pythagorean theorem).

Numerical computing references

  • Kahan, William. "Miscalculating Area and Angles of a Needle-like Triangle." Lecture notes, UC Berkeley, 2014. The source of the numerically-stable Heron's formula rearrangement we ship in gcHeron().
  • Goldberg, David. "What Every Computer Scientist Should Know About Floating-Point Arithmetic." ACM Computing Surveys, vol. 23, no. 1, 1991. Our reference for the clamping pattern in gcAcos() / gcAsin() and for our general approach to catastrophic cancellation.
  • IEEE 754-2008: IEEE Standard for Floating-Point Arithmetic. The arithmetic model we assume on every modern browser. All calculators on this site use double-precision (binary64) values.

Web standards we follow

  • Schema.org — schema.org. Our JSON-LD structured data follows the WebApplication, EducationalApplication, Course, and FAQPage vocabularies plus Person / Organization schemas for author authority.
  • W3C ARIA Authoring Practices — w3.org/WAI/ARIA/apg. Our reference for the accessible widget patterns used in the FAQ accordion, the AI Solve disclosure, and the language switcher.
  • BCP-47 language tags — IETF RFC 5646. All hreflang and inLanguage declarations on this site use BCP-47 (en, zh-CN, ja, fr, de, es, pt, ko), not the underscore form used in og:locale.

Spotted an error in a reference?

If you find a formula on this site that disagrees with one of the sources above — or with a source you trust more — please email us via the Contact page with the page slug, the disagreement, and the source you are citing. We respond to corrections within 48 hours and bump the affected page's "Last updated" date the same day. See Editorial Policy for our full corrections process.