Halloween – The Mathematics of Pumpkins and Spirals

Pumpkins are ellipsoids: x²/a² + y²/b² + z²/c² = 1. Their spiral ridges approximate logarithmic spirals (r = aeᵇθ). The seeds are packed in Fibonacci spirals (phyllotaxis). Carving a pumpkin involves geometry (stencils) and topology (the jack‑o’‑lantern’s face – three holes on a sphere). And the number of calories in pumpkin pie is a finite sum. Halloween also marks the day before All Saints’ Day – the mathematics of calendars (Samhain). So carve a pumpkin, enjoy the symmetry, and remember: even scary things have equations.