# Hyperfigures and Their Interpretations

• Kokichi Sugihara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2616)

## Abstract

This paper proposes a new formulation of the Minkowski algebra for figures. In the conventional Minkowski algebra, the sum operation was always defined, but its inverse was not necessarily defined. On the other hand, the proposed algebra forms a group, and hence every element has its inverse, and the sum and the inverse operation can be taken freely. In this new algebraic system, some of the elements does not correspond to the figures in an ordinary sense; we call these new elements “hyperfigures”. Physical interpretations and practical usage of the hyperfigures are also discussed.

## Keywords

Minkowski sum inverse slope-monotone curve hyperfigures algebraic extension

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