Leonardo Pisano (Fibonacci)

Practica Geometriae (1220), Liber Abaci (1202/1228) & Flos (1225) — Digital Scriptorium Codex & Exact Symbolic Constructions

Welcome to GEOMETOR Fibonacci (geometor-fibonacci), a synchronized four-track Digital Scriptorium Book Codex and exact symbolic SymPy / geometor.model construction suite dedicated to Leonardo Pisano (c. 1170 – c. 1245). Grounded directly in Baldassarre Boncompagni’s public-domain critical Latin editions (Scritti di Leonardo Pisano, Vol. I, 1857; Vol. II, 1862), this repository unites Fibonacci’s Latin littera, original GEOMETOR English translations, interactive .euclid-graphic geometric diagrams, and 100% exact algebraic verification.

Distinctio VI & Euclid XIII.18 — Five Regular Polyhedra in Sphere of Diameter 6 ( O A ): x**2 + y**2 - 9 = 0 [ A K ]: y = 0 / O C /: length = 3 / A C /: length = 3*sqrt(2) / K B /: length = 2*sqrt(2) / A B /: length = 2*sqrt(3) / B I /: length = 2*sqrt(6) / A N /: length = sqrt(18 - 6*sqrt(5)) / O M /: length = 3 / M I /: length = 3*sqrt(50 - 10*sqrt(5))/5 O = (0, 0) K = (-1, 0) A = (-3, 0) I = (3, 0) C = (0, 3) B = (-1, 2*sqrt(2)) M = (3*sqrt(5)/5, -6*sqrt(5)/5) N = (-3 + sqrt(12*(-2 + ((-2*sqrt(2) - 1)*(-6*sqrt(2) - 3 + (1 + 2*sqrt(2))*(2 - sqrt(2)) + (-2*sqrt(2) - 1)*(-sqrt(2) - 1)) + (2 - sqrt(2))*sqrt(-(-6*sqrt(2) - 3 + (1 + 2*sqrt(2))*(2 - sqrt(2)) + (-2*sqrt(2) - 1)*(-sqrt(2) - 1))**2 + 3*(2 - sqrt(2))**2 + 3*(-2*sqrt(2) - 1)**2))/((2 - sqrt(2))**2 + (-2*sqrt(2) - 1)**2) + sqrt(2))**2 + 12*(-2*sqrt(2) - 1 + ((2 - sqrt(2))*(-6*sqrt(2) - 3 + (1 + 2*sqrt(2))*(2 - sqrt(2)) + (-2*sqrt(2) - 1)*(-sqrt(2) - 1)) - (-2*sqrt(2) - 1)*sqrt(-(-6*sqrt(2) - 3 + (1 + 2*sqrt(2))*(2 - sqrt(2)) + (-2*sqrt(2) - 1)*(-sqrt(2) - 1))**2 + 3*(2 - sqrt(2))**2 + 3*(-2*sqrt(2) - 1)**2))/((2 - sqrt(2))**2 + (-2*sqrt(2) - 1)**2))**2)/6, sqrt(2)*sqrt(12*(-2 + ((-2*sqrt(2) - 1)*(-6*sqrt(2) - 3 + (1 + 2*sqrt(2))*(2 - sqrt(2)) + (-2*sqrt(2) - 1)*(-sqrt(2) - 1)) + (2 - sqrt(2))*sqrt(-(-6*sqrt(2) - 3 + (1 + 2*sqrt(2))*(2 - sqrt(2)) + (-2*sqrt(2) - 1)*(-sqrt(2) - 1))**2 + 3*(2 - sqrt(2))**2 + 3*(-2*sqrt(2) - 1)**2))/((2 - sqrt(2))**2 + (-2*sqrt(2) - 1)**2) + sqrt(2))**2 + 12*(-2*sqrt(2) - 1 + ((2 - sqrt(2))*(-6*sqrt(2) - 3 + (1 + 2*sqrt(2))*(2 - sqrt(2)) + (-2*sqrt(2) - 1)*(-sqrt(2) - 1)) - (-2*sqrt(2) - 1)*sqrt(-(-6*sqrt(2) - 3 + (1 + 2*sqrt(2))*(2 - sqrt(2)) + (-2*sqrt(2) - 1)*(-sqrt(2) - 1))**2 + 3*(2 - sqrt(2))**2 + 3*(-2*sqrt(2) - 1)**2))/((2 - sqrt(2))**2 + (-2*sqrt(2) - 1)**2))**2)/6) O K A I C B M N

The Four-Track Book Codex & Symbolic Engine

  • Synchronized Four-Track Book Codex (LEONARDI PISANI PRACTICA GEOMETRIAE (1220)): Read all eight Distinctiones of Practica Geometriae (1220)—together with Fibonacci’s 1225 Flos cubic and Liber Abaci Ch. 12 rabbit recurrence—across four synchronized tracks: English (GEOMETOR Translation), Latin (1220 / Boncompagni 1862), Summary, and Scholarly & Mathematical Notes.

  • Preserving Euclid’s Lost *On Divisions of Figures* (UNIT III — DISTINCTIO IV: DIVISION OF PLANAR FIGURES AMONG CONSORTS): Exact straightedge-and-compass Model reconstructions of Distinctio IV (De divisione camporum inter consortes), dividing triangles from boundary points, parallel to the base via semicircle mean proportionals, and into three equal shares at the centroid $X(2)$.

  • The Five Regular Polyhedra & Extreme and Mean Ratio (UNIT IV — DISTINCTIO V–VI: CUBE ROOTS, SOLIDS & THE FIVE REGULAR POLYHEDRA): Exact radical-tower inscriptions of the tetrahedron, cube, octahedron, dodecahedron ($e_{12} = \sqrt{15} - \sqrt{3}$), and icosahedron in a sphere of diameter $6$, forming the direct historical bridge from Euclid Books XIII–XIV to Piero della Francesca and Luca Pacioli’s De Divina Proportione (1509).

  • Exact Symbolic Python Demonstrations (Exact Symbolic Demonstrations & Python API Reference): Runnable Python 3.13 modules verifying Pisan pertica metrology, Heron’s incenter proof, Fibonacci’s 96-gon circle bounds ($\pi \approx \frac{864}{275}$), Ptolemy’s census census pentagon quartic ($x^4 + 3125 = 125x^2$), the Flos sexagesimal cubic ($1;22,7,42,33,4,40$), and Cassini’s alternating convergence $F_{n+1}/F_n \to \phi$.

Demonstrations, API & Log