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In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space.Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex.
A mathematical object is an abstract concept arising in mathematics. [1] Typically, a mathematical object can be a value that can be assigned to a symbol, and therefore can be involved in formulas.
A diagram illustrating the great-circle distance (in cyan) and the straight-line distance (in red) between two points P and Q on a sphere.. To see the utility of different notions of distance, consider the surface of the Earth as a set of points.
Euclidean space was introduced by ancient Greeks as an abstraction of our physical space. Their great innovation, appearing in Euclid's Elements was to build and prove all geometry by starting from a few very basic properties, which are abstracted from the physical world, and cannot be mathematically proved because of the lack of more basic tools.
In mathematics, a building (also Tits building, named after Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces.
Pure mathematics studies the properties and structure of abstract objects, [1] such as the E8 group, in group theory.This may be done without focusing on concrete applications of the concepts in the physical world.
In the Renaissance, an architect like Leon Battista Alberti was expected to be knowledgeable in many disciplines, including arithmetic and geometry.. The architects Michael Ostwald and Kim Williams, considering the relationships between architecture and mathematics, note that the fields as commonly understood might seem to be only weakly connected, since architecture is a profession concerned ...
Mathematics and art are related in a variety of ways.Mathematics has itself been described as an art motivated by beauty.Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles.