Abstract
In his book about coincidence in the solar system John Martineau (2001) reviews various geometric patterns that have strong correlations with ratios between planetary orbits. Here, remarkably simple equations are derived from these geometric patterns. They contain only the natural numbers (1, 2, 3….etc), and their square roots (√2, √3….etc). The solutions could all be depicted by three fundamental geometrical shapes: the equilateral triangle, the square and the Golden Ratio Quadrangle, and multiples or combinations of these. At the heart of astrology is the symbolism of celestial pattern but these patterns are more usually interpreted through geometry and time. Both geometry and time rely on number, and it was found that the ratio between the orbits of pairs of neighbouring planets appeared to express a particular number. The philosophy of number in Ancient Greek cosmology is nowhere more thoroughly explained than by Thomas Taylor, ‘The English Platonist’ (Prometheus Trust, 2023). From this perspective, the cosmological meaning inferred in the relationships between planets is described. The solar system appears to symbolise a pattern which has an intriguing parallel with the writings of the great philosophers of the Platonic tradition about the nature of reality.