Manifold
/ˈmænɪfəld/
Manifold refers to something with many forms or components, a mathematical space that is locally Euclidean, or an engineering device that collects or distributes fluid or gas through multiple channels.
Examples
- She faced manifold challenges during the project's development.
- Technicians replaced the faulty manifold before the race.
- The artist's work displays a manifold range of styles and influences.
- His talents are manifold, spanning music, writing, and design.
- The intake manifold delivers air to each cylinder in the engine.
Meanings
The word originates in Old English as manigfeald, combining manig (many) and -feald (fold, as in 'double' or 'triple'). It evolved into Middle English manifold, retaining the sense of multiplicity. By the 14th century, it was used to describe things with numerous elements. The modern sense expanded into mathematics and engineering.
Examples
- The artist's work displays a manifold range of styles and influences.
- She faced manifold challenges during the project's development.
- His talents are manifold, spanning music, writing, and design.
- The problem has manifold causes that must be addressed individually.
- A manifold of possibilities opened up after the discovery.
In the 1850s, German mathematician Bernhard Riemann introduced Mannigfaltigkeit (literally 'manifoldness') to describe variable quantities in multiple dimensions. The term was translated into English as 'manifold'. It shifted from a general sense of multiplicity to a precise mathematical concept describing spaces with consistent local structure.
Examples
- The surface of a sphere is a two-dimensional manifold.
- Physicists model spacetime as a four-dimensional manifold.
- Smooth manifolds allow for the application of calculus.
- The theory requires compact, orientable manifolds for proof.
- Differential geometry studies properties of curved manifolds.
The engineering sense emerged in the 1900s to describe a component with multiple connections. For example, an intake manifold distributes air to multiple engine cylinders. The name reflects its function of gathering or dispersing flow through many channels, extending the original idea of multiplicity into mechanical design.
Examples
- The intake manifold delivers air to each cylinder in the engine.
- A cracked exhaust manifold can cause dangerous gas leaks.
- Modern fuel injection systems integrate with the manifold.
- Technicians replaced the faulty manifold before the race.
- The turbocharger connects directly to the exhaust manifold.