Mission

Gather Knowledge · Uncover Patterns · Share Wonder

GEOMETOR is dedicated to exploring the ordering principles of form, proportion, and mind—beginning with the simplest compass-and-straightedge relationships on an unmarked plane and following them wherever exact deductive necessity leads.

Circle c Circle c: Circle through B with center A Circle d Circle d: Circle through A with center B Line a Line a: Line A, B Line b Line b: Line D, C Line h Line h: Line A, C Line i Line i: Line B, C Line k Line k: Line H, I Triangle t1 Triangle t1: Polygon D, J, K Circle e Circle e: Circle through K with center L Line f Line f: Line A, D Line g Line g: Line B, D Line j Line j: Line J, K Line l Line l: Line J, B Line m Line m: Line K, A Line n Line n: Line D, O Line p Line p: Line D, M Line q Line q: Line D, R Line r Line r: Line D, P Line s Line s: Line D, N Line t Line t: Line D, Q Segment g001c_1 Segment g001c_1: sectionAB(J, T, S) Segment g001c_1 Segment g001c_1: sectionAB(J, T, S) Segment g001d_1 Segment g001d_1: sectionAB(J, T, S) Segment g001d_1 Segment g001d_1: sectionAB(J, T, S) Segment g001c_2 Segment g001c_2: sectionAB(K, Z, A_1) Segment g001c_2 Segment g001c_2: sectionAB(K, Z, A_1) Segment g001d_2 Segment g001d_2: sectionAB(K, Z, A_1) Segment g001d_2 Segment g001d_2: sectionAB(K, Z, A_1) Segment g001b_1 Segment g001b_1: sectionBAB(J, U, V, K) Segment g001b_1 Segment g001b_1: sectionBAB(J, U, V, K) Segment g001a Segment g001a: sectionBAB(J, U, V, K) Segment g001a Segment g001a: sectionBAB(J, U, V, K) Segment g001b_2 Segment g001b_2: sectionBAB(J, U, V, K) Segment g001b_2 Segment g001b_2: sectionBAB(J, U, V, K) Point A Point A: Point on xAxis Point A Point A: Point on xAxis Point B Point B: Point on xAxis Point B Point B: Point on xAxis Point D Point D: Intersection point of c, d Point D Point D: Intersection point of c, d Point C Point C: Intersection point of c, d Point C Point C: Intersection point of c, d Point E Point E: Intersection of a and b Point E Point E: Intersection of a and b Point F Point F: Intersection of c and a Point F Point F: Intersection of c and a Point G Point G: Intersection of d and a Point G Point G: Intersection of d and a Point H Point H: Intersection of c and h Point H Point H: Intersection of c and h Point I Point I: Intersection of d and i Point I Point I: Intersection of d and i Point J Point J: Intersection of c and f Point J Point J: Intersection of c and f Point K Point K: Intersection of d and g Point K Point K: Intersection of d and g Point L Point L: Intersection of l and m Point L Point L: Intersection of l and m Point M Point M: Intersection point of e, a Point M Point M: Intersection point of e, a Point N Point N: Intersection point of e, a Point N Point N: Intersection point of e, a Point O Point O: Intersection point of e, h Point O Point O: Intersection point of e, h Point P Point P: Intersection point of e, h Point P Point P: Intersection point of e, h Point Q Point Q: Intersection point of e, i Point Q Point Q: Intersection point of e, i Point R Point R: Intersection point of e, i Point R Point R: Intersection point of e, i Point S Point S: Intersection of j and n Point S Point S: Intersection of j and n Point T Point T: Intersection of j and p Point T Point T: Intersection of j and p Point U Point U: Intersection of q and j Point U Point U: Intersection of q and j Point V Point V: Intersection of r and j Point V Point V: Intersection of r and j Point Z Point Z: Intersection of s and j Point Z Point Z: Intersection of s and j Point A_1 Point A_1: Intersection of t and j Point A_1 Point A_1: Intersection of t and j

Motivation: Where Arithmetic and Geometry Meet

Since antiquity, geometers, natural philosophers, and architects have marveled at a remarkably simple relationship between two unequal magnitudes \(a\) and \(b\)—that the lesser is to the greater as the greater is to the whole:

\[\frac{a}{b} = \frac{b}{a + b}\]

Out of this single proportion—Euclid’s division in extreme and mean ratio, Luca Pacioli’s Divina Proportione, and modern mathematics’ Golden Ratio \(\phi = \frac{1 + \sqrt{5}}{2}\)—unfold principles of self-similarity, harmonic division, polyhedral symmetry, and living growth that are staggering in their coherence.

The Golden Ratio behaves as an inflection point between arithmetic and geometry. It emerges naturally at the intersection of unlike proportions—where equilateral (\(\sqrt{3}\)) and orthogonal (\(\sqrt{2}\)) symmetries meet not in discord, but in harmony.

The Threefold Motion

Every initiative within GEOMETOR participates in three complementary movements:

  1. Gather Knowledge Reconstruct the foundational canon of geometric, projective, rational, and epistemological thought—Euclid, Aristotle, Pappus, Proclus, Aquinas, Pacioli, Kepler, Hilbert, Bertrand Russell, Altshiller-Court, Hoenen, Seelig, Walter & Lao Russell, Kimberling, and Wildberger—in clean, multi-track Book Codices cross-referenced down to the individual proposition and figure.

  2. Uncover Patterns Build an exact assembly language for constructive geometry (geometor.model, geometor.divine, geometor.elements) capable of constructing thousands of symbolic loci without floating-point drift, tracking full ancestral dependency graphs, and automatically detecting emergent golden sections, harmonic ranges, and projective collineations.

  3. Share Wonder Give pure logic a visible and audible form. Every diagram, interactive WebGL meristem, print folio, and dual-format broadcast on @geometor treats rigorous proof as an object of contemplation, clarity, and beauty.

Ethos

The pursuit of unequivocal mathematical truth is a discipline of patience, precision, and humility. GEOMETOR seeks to:

  • Share knowledge openly in durable, inspectable formats;

  • Require exactness, never mistaking a decimal approximation for an algebraic proof;

  • Bridge epochs and disciplines, uniting classical synthetic prose, rational algebra, botanical morphogenesis, and machine program synthesis;

  • Remain humble before the depth of order uncovered in even the simplest geometric figure.

Architectural Essays