Comparative Table of All 45 Constructions

Side-by-side comparison of algebraic number fields, Euclidean locus counts, Lemoine Géométrographie simplicity (\(S\)), and exact collinear golden sections and chains discovered automatically by geometor.divine.golden.

Code	Construction	Discoverer(s)	Year	Field	Loci	\(S\)	Sec / Chn
GC-01.01	Euclid II.11 & VI.30	Alexandria	300 BCE	\(\mathbb{Q}(\phi)\)	3	9	2 / 0
GC-01.02	Hypotenuse Transfer	Alexandria	Classical	\(\mathbb{Q}(\phi)\)	4	12	2 / 0
GC-01.03	Lemoine–Hofstetter 5-Step	Lemoine, Hofstetter	1902 / 2003	\(\mathbb{Q}(\sqrt{3}, \phi)\)	6	18	2 / 0
GC-01.04	Hofstetter 5-Step (2004)	Hofstetter	2004	\(\mathbb{Q}(\sqrt{3}, \phi)\)	5	15	2 / 1
GC-01.05	Compass-Only (5 Circles)	Hofstetter	2002	\(\mathbb{Q}(\sqrt{3}, \phi)\)	5	15	2 / 1
GC-01.06	Rusty Compass (2005)	Hofstetter	2005	\(\mathbb{Q}(\sqrt{3}, \phi)\)	6	18	1 / 0
GC-01.07	Bùi 5-Step Secant	Tuân	2014	\(\mathbb{Q}(\sqrt{5}, \sqrt{7})\)	5	15	1 / 0
GC-02.01	Odom’s Equilateral Midline	Odom, Coxeter	1983	\(\mathbb{Q}(\sqrt{3}, \phi)\)	2	6	2 / 1
GC-02.02	Bataille Triangle & Square	Bataille	2011	\(\mathbb{Q}(\sqrt{3}, \phi)\)	2	6	1 / 0
GC-02.03	Coupled Equilateral Triangles	Tuân	2011	\(\mathbb{Q}(\sqrt{3}, \phi)\)	2	6	1 / 0
GC-02.04	Reflected Equilaterals	Hung	2014	\(\mathbb{Q}(\sqrt{3}, \phi)\)	4	12	2 / 0
GC-02.05	Incircle Nested Equilaterals	Hung	2014	\(\mathbb{Q}(\sqrt{3}, \phi)\)	4	12	3 / 0
GC-02.06	Hexagon & Square Sweep	Hung	2014	\(\mathbb{Q}(\sqrt{3}, \phi)\)	3	9	2 / 0
GC-02.07	Butterfly Equilateral	Dung	2016	\(\mathbb{Q}(\sqrt{3}, \phi)\)	6	18	2 / 1
GC-03.01	Square in Semicircle	Hung	2014	\(\mathbb{Q}(\phi)\)	3	9	2 / 1
GC-03.02	Square Midpoint Circle	Hung	2015	\(\mathbb{Q}(\phi)\)	4	12	4 / 1
GC-03.03	2×2 Grid Compass Arc	Dung	2016	\(\mathbb{Q}(\phi)\)	2	6	1 / 0
GC-03.04	3×3 Grid Diagonal Circle	Hung, McGucken	2016	\(\mathbb{Q}(\sqrt{2}, \phi)\)	2	6	3 / 1
GC-03.05	3×3 Grid Incenter	Hung	2016	\(\mathbb{Q}(\sqrt{2}, \phi)\)	2	6	2 / 1
GC-03.06	Suppa’s Square Inradii	Suppa	2015	\(\mathbb{Q}(\phi)\)	4	12	2 / 0
GC-03.07	Greek Cross & Square	Tuân, Borovik	2015	\(\mathbb{Q}(\phi)\)	4	12	10 / 3
GC-03.08	Arioni’s Rotated Square	Arioni	2016	\(\mathbb{Q}(\sqrt{3}, \phi)\)	2	6	2 / 1
GC-04.01	Egyptian 3-4-5 Triangle	Huntley, Hung	1970	\(\mathbb{Q}(\phi)\)	2	6	1 / 0
GC-04.02	Kepler’s Right Triangle	Kepler	1597	\(\mathbb{Q}(\sqrt{\phi})\)	2	6	1 / 0
GC-04.03	Niemeyer’s Three Segments	Niemeyer	2011	\(\mathbb{Q}(\sqrt{3}, \phi)\)	3	9	1 / 0
GC-04.04	Van Obel Right Isosceles	Tuân	2014	\(\mathbb{Q}(\phi)\)	6	18	2 / 1
GC-05.01	Ptolemy’s Pentagon & Pentagram	Ptolemy, Alexandria	150 CE	\(\mathbb{Q}(\phi, \sqrt{10 - 2\sqrt{5}})\)	6	18	8 / 2
GC-05.02	Pentagon Edge Perpendicular	Oai, Hung	2015	\(\mathbb{Q}(\phi, \sqrt{10 - 2\sqrt{5}})\)	3	9	1 / 0
GC-05.03	Equi-Area Irregular Pentagon	Prasolov, Tuân	2006	\(\mathbb{Q}(\phi)\)	3	9	6 / 1
GC-05.04	Pentagon Inside Hexagon	Hung	2015	\(\mathbb{Q}(\sqrt{3}, \phi, \sqrt{10 - 2\sqrt{5}})\)	4	12	2 / 0
GC-05.05	Six-Pentagon Reflection Star	Hung	2016	\(\mathbb{Q}(\phi, \sqrt{10 - 2\sqrt{5}})\)	3	9	13 / 5
GC-05.06	Wu Xing Equilateral Star	Hung	2015	\(\mathbb{Q}(\sqrt{3}, \phi, \sqrt{10 - 2\sqrt{5}})\)	2	6	1 / 0
GC-06.01	Golden Circle Secants in Droves	Tuân	2014	\(\mathbb{Q}(\sqrt{3}, \phi)\)	4	12	1 / 0
GC-06.02	Two Equal Tangent Circles	McGucken, Kalogerakis	2016	\(\mathbb{Q}(\phi)\)	4	12	1 / 0
GC-06.03	Four Congruent Circles	Tuân	2015	\(\mathbb{Q}(\sqrt{3}, \phi)\)	5	15	2 / 1
GC-06.04	Three Tangent Circles	Hung, McGucken	2016	\(\mathbb{Q}(\sqrt{3}, \phi)\)	5	15	2 / 1
GC-06.05	Kocik’s Golden Window	Kocik	2010	\(\mathbb{Q}(\phi)\)	8	24	10 / 3
GC-06.06	Yin-Yang Twin Circles	Arioni	2016	\(\mathbb{Q}(\phi)\)	4	12	1 / 0
GC-06.07	Three Circles in a Semicircle	Bogomolny	2010	\(\mathbb{Q}(\phi)\)	6	18	4 / 2
GC-07.01	2:1 Rhombus Incircle	Hung	2015	\(\mathbb{Q}(\phi)\)	2	6	2 / 1
GC-07.02	Molokach’s Golden Rhombus	Molokach	2014	\(\mathbb{Q}(\phi)\)	2	6	6 / 2
GC-07.03	1:3 Trapezoid Area Bisector	Tong	2005	\(\mathbb{Q}(\phi)\)	3	9	2 / 0
GC-07.04	60° Isosceles Trapezoid	Hung	2015	\(\mathbb{Q}(\sqrt{3}, \phi)\)	3	9	1 / 0
GC-07.05	Equilateral Mixtilinear Circle	Hung, Bogomolny, Giugiuc	2016	\(\mathbb{Q}(\sqrt{3}, \phi)\)	3	9	2 / 1
GC-07.06	Hooper–Curry φ-Dissection	Hooper, Curry, Bogomolny	1794	\(\mathbb{Q}(\phi)\)	1	3	8 / 1