[x^2 + y^2 + (z - 1)^2] - [(x - 1)^2 + y^2 + z^2] = 0

Sun, 03 May 2026 03:32:58 +0000

Title: Solving the 3D Geometric Equation: Understanding the Surface Defined by [x² + y² + (z − 1)²] − [(x − 1)² + y² + z²] = 0 --- Introduction
The equation [x² + y² + (z − 1)²] − [(x − 1)² + y² + z²] = 0 presents a compelling geometric object within three-dimensional space. Whether you're studying surfaces in computational geometry, analytical mechanics, or algebraic modeling, this equation reveals a meaningful shape defined by balancing two quadratic expressions. This article explores how to interpret and visualize this surface, derive its geometric properties, and understand its applications in mathematics and engineering. ---