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Answer :
The type of geometry required for understanding the geometry of space is 1) Non-Euclidean geometry.
Euclidean geometry is based on a flat, two-dimensional plane where the well-known rules, such as the sum of the angles in a triangle being 180 degrees, apply. However, the geometry of space, especially when considering the universe on a large scale or dealing with gravity as described by Einstein's General Relativity, requires a different approach.
Non-Euclidean geometry encompasses geometries where the usual Euclidean postulates do not hold. There are two main types of non-Euclidean geometry: hyperbolic and spherical. Spherical geometry, for instance, deals with curved surfaces like those of a sphere. In this type of geometry, the sum of the angles of a triangle exceeds 180 degrees.
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Final answer:
Non-Euclidean geometry is required for the geometry of space, as it explores the properties and relationships among angles and lines on curved surfaces.
Explanation:
The type of geometry required for the geometry of space is Non-Euclidean geometry. Euclidean geometry assumes a "flat" space where straight lines are the shortest distance between two points, the sum of angles in a triangle is 180 degrees, and parallel lines never intersect. However, in the geometry of space, such assumptions do not hold true.
Non-Euclidean geometry describes the relationships among angles and lines on curved surfaces like a sphere or a hyperboloid. It explores the properties and measurements of space that deviate from Euclidean geometry. For example, on a curved surface, the sum of angles in a triangle may not equal 180 degrees.
