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It´s geometry without metric (ruler, protractor, scales etc). Just with pure geometrical contents.
Ex.: questions about planes or lines intersecting points, lines intersecting planes etc are incidence synthetic geometrical questions.
Parts of the Elements of Euclid are synthetic. Hilbert's axioms of Euclidean Geometry are synthetic because you don't need to measure segments or angles, and congruence is a primitive relation.
Birkhoff´s axioms are not synthetic because distance, scale and real numbers belongs to the axioms. You have metric Geometry.
What else can I help you with?
What did Jakob Steiner do?
was a mathematician that discovered synthetic and projective geometry
What has the author Thomas Gerald Room written?
Thomas Gerald Room has written: 'A background (natural, synthetic and algebraic) to geometry' -- subject(s): Geometry, Foundations, Congruences (Geometry)
What has the author Herbert Busemann written?
Herbert Busemann has written: 'Recent synthetic differential geometry' -- subject(s): Differential Geometry 'Geometry of Geodesics (Pure & Applied Mathematics)' 'On plane convex figures ..' -- subject(s): Plane Geometry 'The geometry of geodesics' -- subject(s): Curves on surfaces, Differential Geometry, Geodesics (Mathematics)
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
What is a point in Euclidean synthetic geometry?
An infinitesimal "object" having no volume at a single location in 3D space defined by X, Y, Z coordinates.
What are the four aspects of geometry?
* geometry in nature * for practcal use of geometry * geometry as a theory * historic practical use of geometry
Different types of geometry?
Euclidean geometry, non euclidean geometry. Plane geometry. Three dimensional geometry to name but a few
Is there more than one kind of geometry?
There are different kinds of geometry including elementary geometry, Euclidean geometry, and Elliptic Geometry.
What specific applications of geometry are used in civil engineering?
Fun geometry, specific geometry, monster geometry, egg geometry, trees, turtles.
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.
Famous geometers and their contributions in geometry?
Archimedes - Euclidean geometry Pierre Ossian Bonnet - differential geometry Brahmagupta - Euclidean geometry, cyclic quadrilaterals Raoul Bricard - descriptive geometry Henri Brocard - Brocard points.. Giovanni Ceva - Euclidean geometry Shiing-Shen Chern - differential geometry René Descartes - invented the methodology analytic geometry Joseph Diaz Gergonne - projective geometry; Gergonne point Girard Desargues - projective geometry; Desargues' theorem Eratosthenes - Euclidean geometry Euclid - Elements, Euclidean geometry Leonhard Euler - Euler's Law Katyayana - Euclidean geometry Nikolai Ivanovich Lobachevsky - non-Euclidean geometry Omar Khayyam - algebraic geometry, conic sections Blaise Pascal - projective geometry Pappus of Alexandria - Euclidean geometry, projective geometry Pythagoras - Euclidean geometry Bernhard Riemann - non-Euclidean geometry Giovanni Gerolamo Saccheri - non-Euclidean geometry Oswald Veblen - projective geometry, differential geometry
What is Non euclidean geometry?
Geometry that is not on a plane, like spherical geometry
