Abstract
Symmetry is the study of mapping of a state space into itself that leaves a geometric object, generally a set of subspaces defined by an equivalence relation, invariant. Thus, in economics, we can examine whether there exists a transformation to which the indifference curves, subspaces defined by a preference relation, are invariant. However to appreciate the relevance of such a question, it is necessary to have an understanding of the basic principles of geometric spaces. The idea that the quantitative variables of a science are describable by geometric objects and that the laws governing these variables are expressible as geometric relation between the objects, can be traced back to Felix Klein’s inaugural address at the Erlanger University in 1872.1
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Sato, R., Ramachandran, R. (1990). Symmetry: An Overview of Geometric Methods in Economics. In: Sato, R., Ramachandran, R.V. (eds) Conservation Laws and Symmetry: Applications to Economics and Finance. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1145-6_1
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