betti number
Word Rarity
Very rare
Frequency: Zipf frequency 1.80 in modern English
17
Scrabble Score
11
Letters
3
Syllables
8
Unique Chars
Meaning
Example Sentences
- "Poincaré proved that Betti numbers are invariants and used them to extend Euler's polyhedral formula to higher dimensional spaces."
- "1979 [W. H. Freeman & Company], Michael Henle, A Combinatorial Introduction to Topology, 1994, Dover, page 163, Prove that, for compact surfaces, the zeroth Betti number is the number of components of the surface, where a component is a connected subset of the surface, such that any larger containing subset is not connected."
- "2007, Oscar García-Prada, Peter Beier Gothen, Vicente Muñoz, Betti Numbers of the Moduli Space of Rank 3 Parabolic Higgs Bundles, American Mathematical Society, page 7, PROPOSITION 2.1. Fix the rank r. For different choices of degrees and generic weights, the moduli spaces of parabolic Higgs bundles have the same Betti numbers."
- "The goal is to compute Betti numbers in 2D and 3D image partitions using the practical definition of Betti numbers. Thus, depending on the dimension of the topological map, we count the number of connected components, the number of tunnels, and the number of cavities to obtain the Betti numbers.[…]The number of connected components of region r in a 2D image partition is equal to the first Betti number b#95;0(r)."
Etymology
A calque of French nombre de Betti, coined in 1892 by Henri Poincaré; named after Italian mathematician Enrico Betti in recognition of an 1871 paper.
Origin
- Source language: French
Word Breakdown
Inflected Forms
Phrases
Poincaré polynomial
Frequently Paired Words
Poincaré polynomial