x²/a² - z²/c² = 1 — Hyperbola Vase

The Hyperbola Vase

A hyperboloid of one sheet — the dramatic waisted form.

Formula: x²/a² + y²/b² - z²/c² = 1

This doubly-ruled surface can be created entirely from straight lines, yet curves gracefully. Found in cooling towers, and now, your living room.

The classic silhouette for roses and peonies.