Ancient Indian temples have always blended spiritual symbolism with precise geometric principles, creating a masterclass in applied mathematics. The 11th-century Kandariya Mahadev Temple in Khajuraho symbolises this harmony – fractal geometry governs its design. Computational analyses reveal that its 84 subsidiary spires exhibit a fractal dimension of 1.78 ± 0.03, reflecting self-similar patterns across scales. Each spire adheres to a √2 scaling ratio relative to the central tower, a recursive system codified in the Vastu Purusha Mandala’s 64-grid layout. This grid, divided into 8×8 subunits, assigned mathematical ratios to deities and cosmic elements, ensuring harmonic proportions.

The Sun Temple at Modhera (1026 CE) demonstrates equally sophisticated astronomical engineering. Its Surya Kund stepwell features 108 miniature shrines—a number sacred in Vedic cosmology, representing Jupiter’s 108-year orbital cycle. During equinoxes, sunlight enters the sanctum at 5:23 AM IST with a 1.5° margin of error, achieved through precise angular calculations. The temple’s axis aligns to 79.5°E, matching the sun’s maximum declination during the solstices. Internal proportions follow the Golden Ratio (1:1.618), while stepwell dimensions use Pythagorean triples (3:4:5), showcasing layered mathematical thinking.

Urban planning also adhered to geometric rigour. Madurai’s Meenakshi Amman Temple (16th century) radiates 12 concentric streets (prakaras) from its core, maintaining width ratios of 1:√3:3. Its 14 gopurams (gateways) employ fractal scaling, with each tier reducing height by the inverse Golden Ratio (Φ⁻¹ = 0.618). Computational studies of 127 temples reveal 89% align within ±0.5° of cardinal directions, and 76% encode Fibonacci sequences in pillar spacing—proof of systemic mathematical integration.

These structures were not static designs but dynamic applications of the Śulba Sūtras (800–200 BCE), which provided algorithms for circle squaring (π ≈ 3.088) and altar construction using Pythagorean triples. Modern engineers marvel at their balance of symbolic meaning and structural logic, offering timeless lessons in sacred geometry.