From Old English manigfeald ('many-fold'), from manig ('many') and feald ('fold, times'), related to German mannigfaltig. The engineering sense developed from the idea of a single pipe branching into many. The mathematical sense was introduced in the 19th century as a translation of German Mannigfaltigkeit, used by Bernhard Riemann in his 1854 lecture on the foundations of geometry.
What does manifold mean?
Manifold has three main senses. As an adjective (formal/literary), it means many and varied: 'manifold challenges'. As a mathematics noun, it is a topological space that locally resembles Euclidean space. As an engineering noun, it is a chamber or pipe with multiple openings for distributing fluid or gas.
What is a manifold in maths?
In mathematics, a manifold is a topological space that, near each point, looks like ordinary Euclidean space. A sphere is a 2-dimensional manifold. Manifolds are fundamental in differential geometry, topology, and physics, where spacetime is modelled as a 4-dimensional manifold.
What is an exhaust manifold?
An exhaust manifold is a cast-iron or steel component in a car engine that collects exhaust gases from the cylinders and channels them into a single outlet pipe leading to the catalytic converter and muffler. A cracked manifold can cause exhaust leaks.
What is the origin of the word manifold?
Manifold comes from Old English manigfeald, meaning 'many-fold' or 'multiplied many times'. The mathematical sense was coined in the 19th century as a translation of the German Mannigfaltigkeit, introduced by the mathematician Bernhard Riemann.
Can manifold be used as a noun?
Yes, but only in technical senses. In mathematics, a manifold is a specific type of topological space. In engineering, a manifold is a pipe fitting with multiple ports. Using manifold as a general abstract noun (e.g., 'a manifold of ideas') is non-standard — use 'multitude' or 'variety' instead.