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Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.
To a system of points, straight lines, and planes, it is impossible to add other elements in such a manner that the system thus generalized shall form a new geometry obeying all of the five groups of axioms. In other words, the elements of geometry form a system which is not susceptible of extension, if we regard the five groups of axioms as valid.
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.
Interactive geometry software (IGS) or dynamic geometry environments (DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. In most IGS, one starts construction by putting a few points and using them to define new objects such as lines , circles or other points.
In geometry, a corner-point grid is a tessellation of a Euclidean 3D volume, where the base cell has 6 faces . A set of straight lines defined by their end points define the pillars of the corner-point grid. The pillars have a lexicographical ordering that determines neighbouring pillars. On each pillar, a constant number of nodes (corner ...
Honeycomb structures are natural or man-made structures that have the geometry of a honeycomb to allow the minimization of the amount of used material to reach minimal weight and minimal material cost. The geometry of honeycomb structures can vary widely but the common feature of all such structures is an array of hollow cells formed between ...
A load-bearing wall or bearing wall is a wall that is an active structural element of a building — that is, it bears the weight of the elements above said wall, resting upon it by conducting its weight to a foundation structure. [1] The materials most often used to construct load-bearing walls in large buildings are concrete, block, or brick.
Every engineering drawing must have a title block. [13] [14] [15] The title block (T/B, TB) is an area of the drawing that conveys header-type information about the drawing, such as: Drawing title (hence the name "title block") Drawing number; Part number(s) Name of the design activity (corporation, government agency, etc.)
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