Meaning
A triangular number counts the dots in a triangle: one dot, then a row of two below it, then three, and so on. The nth triangular number is 1 + 2 + … + n. The Trigonal cipher gives each letter the triangular number of its place: A is 1, B 3, C 6, D 10, and Z, the 26th letter, 351. Values grow fast, so the later letters dominate a total much as they do in Agrippa's table, but smoothly rather than in jumps.
Figurate numbers of this kind were studied in Greek arithmetic, and the Pythagoreans are credited with them in later tradition. The cipher is something else: a way of valuing the English alphabet listed on Gematrinator in the 2010s, with no older source. One triangular number explains another of the community's ciphers: 1 + 2 + … + 36 is 666, which is why the cipher we call Offset 36 begins at 36.
How it is counted
GEMATRIA: G 28 + E 15 + M 91 + A 1 + T 210 + R 171 + I 45 + A 1 = 562; reduced to 13, then to 4. ALPHABET: A 1 + L 78 + P 136 + H 36 + A 1 + B 3 + E 15 + T 210 = 480; reduced to 12, then to 3.
Each value can be checked by the formula n(n + 1) ÷ 2: R, the 18th letter, is 18 × 19 ÷ 2 = 171.
What this page leaves out
The reverse form of this cipher, which our old chart showed, was dropped in October 2026 with the other mirrors. We give no reading of a Trigonal total.
How it relates to the other ciphers
Since the nth triangular number is half of n squared plus n, a word's Trigonal total is half the sum of its Squares and English Ordinal totals. GEMATRIA gives 1,050 and 74, whose sum halved is 562; ALPHABET gives 895 and 65, halved 480. The three ciphers are one piece of arithmetic seen three ways, and a match under one of them is often a match under the others for the same reason.
Correspondences
Each item with how it stands: “sourced” is in the work cited, “our construction” is EsoTerrier’s own, and “disputed” means the sources disagree.
- Name on the popular sites
- "Trigonal" (Gematrinator) sourced
- Triangular numbers
- The figurate numbers of Greek arithmetic, dots set out in triangles sourced
- Tradition
- None for the cipher; triangular numbers are old, applying them to English letters is not sourced
How the schools read it
- Gematrinator
- Lists it, with a reverse form we do not compute.
- EsoTerrier
- Behind "more ciphers", labelled as a modern cipher.
Claims about it
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The Trigonal cipher is Pythagorean, because triangular numbers are.
falseWhat the record shows: Triangular numbers belong to Greek arithmetic; this cipher, which applies them to the English alphabet, appears on the gematria sites of the 2010s.
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Two words or names with the same value under this cipher are connected.
falseWhat the record shows: Equal values are what any table of this kind produces in quantity; the tradition reads them together as a way of interpreting a text.
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Totals under this cipher show that news events are planned by their numbers.
falseWhat the record shows: A search with dozens of ciphers and millions of phrases always finds a match; fact-checkers have shown it. Nothing on this site reads events, dates or news by number.
