Euler characteristic

[/ˈɔɪlər ˌkærəktəˈrɪstɪk/]
nounpl: Euler characteristics
característica de Euler
1. A topological invariant of a space that is a number which describes a fundamental property of a surface or polyhedron, calculated as V - E + F (vertices minus edges plus faces)
The Euler characteristic of a sphere is 2, while that of a torus is 0.
A característica de Euler de uma esfera é 2, enquanto a de um toro é 0.
2. In algebraic topology, a number assigned to a topological space that remains invariant under homeomorphism
The Euler characteristic is a fundamental tool in topological classification of surfaces.
A característica de Euler é uma ferramenta fundamental na classificação topológica de superfícies.
The Euler characteristic is named after Swiss mathematician Leonhard Euler and is a foundational concept in modern mathematics, particularly in topology and algebraic geometry. It is taught in advanced undergraduate and graduate mathematics courses in both Brazil and the USA. The term is highly specialized and used primarily within academic and mathematical professional contexts.
Synonyms / Sinônimos
Euler-Poincaré characteristictopological invariantcharacteristic number

Regional Variations

General Brazilian
característica de Euler
Standard academic usage in mathematics
Portugal
característica de Euler
Same as Brazilian Portuguese; used in academic contexts
Technical/Academic
χ (chi)
Often denoted by the Greek letter chi in mathematical notation

Related Words

topologypolyhedronsurfacehomeomorphismPoincaréverticesedgesfaces
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