The equation x² + y² + z² = 1 represents the equation of a sphere in three-dimensional space. In this equation, x, y, and z are the coordinates of any point on the surface of the sphere, while the number 1 indicates that the radius of the sphere is 1 unit. This means that all points satisfying this equation are exactly 1 unit away from the center of the sphere, which is located at the origin (0, 0, 0). This mathematical representation is fundamental in various fields, including geometry, physics, and computer graphics. It helps in visualizing and understanding three-dimensional shapes and their properties. The sphere is a perfect example of symmetry and uniformity, making it a common subject of study in both theoretical and applied mathematics.