Flattening

Flattening is a general term used across disciplines to describe the process of making something flatter, more uniform, or more flattened along one dimension. In geometry, flattening refers to the flattening of a three-dimensional body into a two-dimensional surface. In the context of the Earth, the Earth is modeled as an oblate spheroid with a flattening parameter f = (a−b)/a, where a is the equatorial radius and b the polar radius. This parameter explains why meridians shorten with latitude and is used in map projections and geodetic calculations; the Earth's flattening is about 1/298.

In computing and data processing, flattening describes converting nested data structures into a single, flat sequence. Flattening an array of arrays, for example, produces one list containing all elements. In JSON and XML processing, flattening helps transform hierarchical data into tabular forms, enabling easier querying and storage.

In image and audio processing, histogram flattening or histogram equalization adjusts the distribution of intensity or amplitude values to be more uniform, often improving contrast or dynamic range.

In finance, yield-curve flattening occurs when the difference between short-term and long-term interest rates shrinks, signaling changing expectations about growth and inflation; it can precede an economic transition.

In statistics and machine learning, flattening can describe reducing the peakedness of distributions or smoothing loss landscapes, although terminology varies by field.

Applications and methods vary by domain, but the core idea of flattening is to reduce curvature, variation, or hierarchical complexity to achieve a simpler, more uniform form.