Affine Geometry
Affine geometry is a branch of geometry that focuses on the properties of shapes that remain unchanged under transformations like translation, scaling, and rotation, but not necessarily stretching or distortion. It examines concepts like points, lines, and planes without considering notions of distance or angles. This means that while it can tell us how points are aligned or how parallel lines relate, it does not provide information about length or measurement. Affine geometry is vital in fields like computer graphics and design, where understanding shapes and their relationships is crucial, but exact measurements are often secondary.
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Affine geometry is a branch of mathematics that studies the properties of shapes and spaces that remain unchanged when transformed by linear transformations, such as stretching, rotating, or translating. It focuses on concepts like points, lines, and planes, without considering measurements like lengths or angles. This means that while the shapes can change position or size, their relative arrangements and parallelism stay constant. Affine geometry is useful in various fields, including computer graphics, engineering, and robotics, as it helps describe and manipulate the spatial arrangement of objects in a consistent manner.