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What is Euclidean geometry mean in math?
Euclidean geometry is the traditional geometry: it is the geometry of a plane surface, as developed by Euclid. Among other things, it is based on Euclid's parallel postulate which said (in effect) that given a line and a point outside that line there could only be one line through that point that was parallel to the given line. It has since been discovered that both alternatives to that postulate - that there are many such lines possible and that there are none - give rise to consistent geometries. These are non-Euclidean geometries.
What artists have used geometry to great advantage in their work?
One problem with geometry, is that most people learn Euclidean geometry. It is intuitive but his parallel postulate creates great problems for mathematicians. It can neither be proved or disproved. There are consistent geometries if you accept that postulate, but there are equally consistent geometries for the two possible negations (no parallel lines and many). Artists are not necessarily constrained by geometric "realities" or restrictions. And many have either used geometry or ignored it to great effect. For example, many renaissance artists used projective geometry and the idea of a vanishing point in their art. This gave their work a better 3-d perspective than earlier works which often looked flat. Images in the background used to be unrealistically large and so on. In the 20th century, artists like MC Escher played on geometry, perspective, tessellation (tiling). Finally, many cubists chose not to use "normal" geometry, but chose to simultaneously portray things from several perspectives at the same time.
What is a characteristic of Euclidean geometry?
One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.
What is the electron geometry for OF2?
molecular geometry is bent, electron geometry is tetrahedral
What is the structural geometry of NOF?
Molecular geometry will be bent, electron geometry will be trigonal planar
Why don't parallel lines exist in elliptical geometry?
Elliptical geometry is a non-Euclidean geometry. The parallel postulate of Euclidean geometry was replaced by the statement that through any point in the plane, there exist no lines parallel to a given line. A consistent geometry - of a space with positive curvature - was developed on that basis.It is, therefore, by definition that parallel lines do not exist in elliptical geometry.
Is good for your health to wake up in early morning?
If you had enough sleep then it is. Good consistent sleep is what matters.
What is a synonym for compatible?
consistent, in keeping, congruous, like-minded, harmonious, in harmony
What does in keeping with the situation mean?
"In keeping with the situation" means consistent or appropriate with the current circumstances or context. It implies that something aligns well with or is suited to the situation at hand.
What does it mean for a system to be consistent or inconsistent?
does it stay the same or not? Actually, a system is inconsistent if you can derive two (or more) statements within the system which are contradictory. Otherwise it is consistent. For example, Eucliadean geometry requires that given a line and a point not on that line, you can have one and only one line through the point which is parallel to the original line. However, you can have a consistent system of geometry if you assume that there is no such parallel line. This is known as the projective plane. You can assume that there will be an infinite number of parallel lines through a point not on the line. And again you can have a consistent system. Consistency or inconsistency has nothing whatsoever to do with time.
Can a triangle can have two parellel sides?
A Plane triangle cannot have parallel sides. A triangle on a sphere, represented in Mercator projection may do so, but that still does not make it so, for that is in spherical geometry. And there are other geometries than Euclidean (plane). Hyperbolic Geometry and Elliptic Geometry are the names of another two. These geometries are consistent within themselves, but some of the theorems in Euclidean geometry have different answers in these alternate geometries.
What are some real world applications of geometry?
Euclidean geometry has become closely connected with computational geometry, computer graphics, convex geometry, and some area of combinatorics. Topology and geometry The field of topology, which saw massive developement in the 20th century is a technical sense of transformation geometry. Geometry is used on many other fields of science, like Algebraic geometry. Types, methodologies, and terminologies of geometry: Absolute geometry Affine geometry Algebraic geometry Analytic geometry Archimedes' use of infinitesimals Birational geometry Complex geometry Combinatorial geometry Computational geometry Conformal geometry Constructive solid geometry Contact geometry Convex geometry Descriptive geometry Differential geometry Digital geometry Discrete geometry Distance geometry Elliptic geometry Enumerative geometry Epipolar geometry Euclidean geometry Finite geometry Geometry of numbers Hyperbolic geometry Information geometry Integral geometry Inversive geometry Inversive ring geometry Klein geometry Lie sphere geometry Non-Euclidean geometry Numerical geometry Ordered geometry Parabolic geometry Plane geometry Projective geometry Quantum geometry Riemannian geometry Ruppeiner geometry Spherical geometry Symplectic geometry Synthetic geometry Systolic geometry Taxicab geometry Toric geometry Transformation geometry Tropical geometry
Ways to maintain confidentilaity?
By keeping secrets. Ensuring private matters and papers are kept secure. By not divulging sensitive information.
What is Euclidean geometry mean in math?
Euclidean geometry is the traditional geometry: it is the geometry of a plane surface, as developed by Euclid. Among other things, it is based on Euclid's parallel postulate which said (in effect) that given a line and a point outside that line there could only be one line through that point that was parallel to the given line. It has since been discovered that both alternatives to that postulate - that there are many such lines possible and that there are none - give rise to consistent geometries. These are non-Euclidean geometries.
What artists have used geometry to great advantage in their work?
One problem with geometry, is that most people learn Euclidean geometry. It is intuitive but his parallel postulate creates great problems for mathematicians. It can neither be proved or disproved. There are consistent geometries if you accept that postulate, but there are equally consistent geometries for the two possible negations (no parallel lines and many). Artists are not necessarily constrained by geometric "realities" or restrictions. And many have either used geometry or ignored it to great effect. For example, many renaissance artists used projective geometry and the idea of a vanishing point in their art. This gave their work a better 3-d perspective than earlier works which often looked flat. Images in the background used to be unrealistically large and so on. In the 20th century, artists like MC Escher played on geometry, perspective, tessellation (tiling). Finally, many cubists chose not to use "normal" geometry, but chose to simultaneously portray things from several perspectives at the same time.
Why is it not a guideline for keeping verb tense consistent?
In writing, keeping verb tense consistent is important for maintaining clarity and coherence. It helps avoid confusion for the reader and ensures smooth transitions between ideas. Inconsistencies in verb tense can disrupt the flow of the narrative and make it harder for the reader to follow along.
What are the four aspects of geometry?
* geometry in nature * for practcal use of geometry * geometry as a theory * historic practical use of geometry
