Motion (geometry)

[3][4] Given a geometry, the set of motions forms a group under composition of mappings.

He was criticised by Omar Khayyam who pointed that Aristotle had condemned the use of motion in geometry.

He proposed using symmetry groups in his Erlangen program, a suggestion that was widely adopted.

The term motion, shorter than transformation, puts more emphasis on the adjectives: projective, affine, Euclidean.

The context was thus expanded, so much that "In topology, the allowed movements are continuous invertible deformations that might be called elastic motions.

"[10] The science of kinematics is dedicated to rendering physical motion into expression as mathematical transformation.

Rotation in space is achieved by use of quaternions, and Lorentz transformations of spacetime by use of biquaternions.

In the 1890s logicians were reducing the primitive notions of synthetic geometry to an absolute minimum.

Giuseppe Peano and Mario Pieri used the expression motion for the congruence of point pairs.

Alessandro Padoa celebrated the reduction of primitive notions to merely point and motion in his report to the 1900 International Congress of Philosophy.

In his book Principles of Mathematics (1903), Russell considered a motion to be a Euclidean isometry that preserves orientation.