Invariant theory is concerned with expressions that remain constant (invariant) under a group of transformations. In that case every topological manifold has a topological invariant, its dimension. Mardia's tests are affine invariant but not consistent. A knot polynomial is a knot invariant that is a polynomial. A topological property is a property of spaces that is invariant under homeomorphisms. The number of components is an important topological invariant of a graph. Thus 2 is a topological invariant of the sphere, called its Euler characteristic. Spatial rotations alone are also Lorentz transformations they leave the spacetime interval invariant. Algebraic topology is a source of a number of important global invariant properties. Formula for harmonical invariant tensor was found in paper. The mean curvature is an extrinsic invariant. The former offer an abstract formalism of invariant integrals. All massless particles (particles whose invariant mass is zero) are elementary. In differential geometry, the diameter is an important global Riemannian invariant. Fractals are mathematical patterns that are scale invariant.