Fingerprint in Germany and implemented in both Germany and Japan, the Vucetich system (developed by a Croatian-born Buenos Aires Police Officer) was developed in Argentina and implemented throughout South America, and the Henry system was developed in India and implemented in most English-speaking countries. In the Henry system of classification, there are three basic fingerprint patterns: loop, whorl, and arch, which constitute 60–65%, 30–35%, and 5% of all fingerprints respectively. There are also more complex classification systems that break down patterns even further, into plain arches or tented arches, and into loops that may be radial or ulnar, depending on the
Isotopy of loops they are equivalent from "geometric point of view". The dictionary between algebraic and geometric concepts is as follows Isotopy of loops In the mathematical field of abstract algebra, isotopy is an equivalence relation used to classify the algebraic notion of loop. Isotopy for loops and quasigroups was introduced by , based on his slightly earlier definition of isotopy for algebras, which was in turn inspired by work of Steenrod. Each quasigroup is isotopic to a loop. Let formula_1 and formula_2 be quasigroups. A quasigroup homotopy from "Q" to "P" is a triple of maps from "Q" to "P" such that