Manifolding Meaning: Definition, Examples, and Translations
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manifolding
[ˈmænɪˌfoʊldɪŋ ]
Definitions
mathematics concept
Manifolding refers to the process of creating a manifold, which is a mathematical space that locally resembles Euclidean space. These structures are fundamental in various fields of mathematics and physics, allowing for the study of complex spaces and their properties.
Synonyms
complex space, geometric formation, manifold structure.
Examples of usage
- The manifolding of the surface allowed for a clearer understanding of its geometric properties.
- In algebraic topology, manifolding is crucial for analyzing the shapes of spaces.
- Researchers are exploring manifolding techniques to better model data in higher dimensions.
mathematics usage
To manifold means to form or represent as a manifold. This term is often used when discussing the process of transforming simple shapes or data sets into more complex, high-dimensional geometrical forms.
Synonyms
Examples of usage
- We can manifold this dataset to visualize higher-order relationships.
- The method allows us to manifold curves and surfaces for better analysis.
- The software can manifold geometric objects for simulation purposes.
Translations
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Interesting Facts
Art and Design
- In visual arts, manifolding can refer to creating layers of meaning in a single piece, like having multiple interpretations in a painting.
- Architectural designs often apply manifolding to explore concepts in form and function, leading to innovative structures that inspire awe.
Psychology
- Cognitive psychologists study how humans process manifold information simultaneously, like managing various tasks in everyday life.
- Manifolding in psychology can also relate to how we cope with complex emotions, often requiring us to integrate multiple feelings at once.
Mathematics
- In mathematics, manifolding is used in topology to study spaces that look flat locally but can be complex overall, such as toruses and spheres.
- Manifolds in math provide a framework for understanding complex systems, connecting different areas like geometry and physics.
Technology
- In computing, manifolding techniques assist in organizing large data sets by creating a model that highlights relationships between numerous variables.
- Machine learning uses manifolding to improve algorithms by deciphering underlying structures in vast amounts of data, enhancing efficiency.
Origin of 'manifolding'
Main points about word origin
- The word comes from 'manifold', which means 'many and various' in Old English, combining 'manig' (many) and 'feld' (field).
- Historically, 'manifold' also had meanings related to 'to make many copies' or 'to manifest', reflecting growth or expansion.
The term 'manifold' comes from the Middle English 'manifold', which means 'manyfold' or 'many times'. It is derived from the Old English 'manigfeald', where 'manig' means 'many' and 'feald' relates to 'folding' or 'layers'. In the context of mathematics, the term began to be used in the 19th century, particularly by mathematicians such as Bernhard Riemann, who formalized the concept of manifolds in differential geometry. The extension to 'manifolding' as a process emerged as the field developed, with applications expanding into various scientific disciplines, notably in physics and computer science. The broader implications of manifolding reflect the increasing complexity of representing multi-dimensional data and the need for advanced mathematical frameworks.