Sentences with invariants
- For example, in Euclidean geometry, the relevant invariants are embodied in quantities that are not altered by geometric transformations such as rotations, dilations, and reflections.
- Under their direction he laid the basis for the important work he was later to achieve in the fields of foundations of geometry, projective geometry, topology, differential invariants and spinors.
- At Freiburg, he took a course with Oskar Bolza on the theory of invariants, and a course on differential geometry and a history seminar with Alfred Loewy, one of the two professors at Freiburg.
- Todd generalised the arithmetic genus and the invariants of the canonical system on an algebraic variety to a system of invariants of every codimension.
- Explicitly stated program invariants can help programmers by identifying program properties that must be preserved when modifying code.