Content of type 'notes'
Unit I — Meno: Definition of Figure, Doubling the Square & Geometric Hypothesis — Notes
In geometor.plato.constructions.construct_meno_diagonal_doubling (see /demos/index), Socrates’ sand diagram (82b–85b) is modeled with 100% exact rational coordinates over \(\mathbb{Q}\) without introducing irrational square roots until linear magnitude is requested—directly vindicating Rational Trigonometry’s primacy of quadrance:
Unit II — Theaetetus: Theodorus’s Radical Constructions & Classification of Powers — Notes
In geometor.plato.constructions.construct_theodorus_spiral and classify_theaetetus_powers (see /demos/index), Theodorus's lesson (147d) is modeled by iterating pure Euclidean perpendicular erection (I.11) and unit compass transfer (Post. 3):
Unit III — Republic VI–VII: The Divided Line, Dianoia & the Quadrivium — Notes
In geometor.plato.constructions.construct_divided_line and verify_divided_line_identity (see /demos/index), Socrates’ double proportional section (509d6–8) is proved symbolically over an arbitrary ratio \(r > 0\) and constructed by compass and straightedge under the canonical Academic Golden Section (\(r = \phi = \frac{1+\sqrt{5}}{2}\), Elements II.11 & VI.30):
Unit IV — Timaeus: Geometric Proportion & Harmonic Division of the World-Soul — Notes
In geometor.plato.harmonics and construct_timaeus_proportion_circles (see /demos/index), both proportions of Timaeus 31b–36d are verified in 100% exact rational and quadratic arithmetic:
Unit V — Timaeus: Elementary Right Triangles & Construction of the Cosmic Polyhedra — Notes
In geometor.plato.constructions.construct_timaeus_triangles and construct_timaeus_cube_face (see /demos/index), Plato’s two elementary right triangles (53c–55c) are constructed purely by compass and straightedge and audited via Rational Trigonometry invariants:
Unit VI — Parmenides, Philebus & Laws VII: Straightness, Limit & Incommensurability — Notes
In geometor.plato.constructions.construct_compass_and_peras (see /demos/index), the three foundational motifs of Parmenides, Philebus, and Laws VII are unified in a single compass-and-straightedge plate (foundations_peras_compass.svg):