Information & explanations, latest texts & monographs on
Geometry (including recent related patents.)
GeometryGeometry is the branch of mathematics dealing with spatial relationships. From experience, or possibly intuitively, people characterize space by certain fundamental qualities, which are termed axioms in geometry. Such axioms are insusceptible of proof, but can be used in conjunction with mathematical definitions for points, straight lines, curves, surfaces, and solids to draw logical conclusions. Because of its immediate practical applications, geometry was one of the first branches of mathematics to be developed. Likewise, it was the first field to be put on an axiomatic basis, by Euclid. The Greeks were interested in many questions about ruler-and-compass constructions. The next most significant development had to wait until a millennium later, and that was analytic geometry, in which coordinate systems are introduced and points are represented as ordered pairs or triples of numbers. This sort of representation has since then allowed us to construct new geometries other than the standard Euclidean version. The central notion in geometry is that of congruence. In Euclidean geometry, two figures are said to be congruent if they are related by a series of reflections, rotations, and translations. Other geometries can be constructed by choosing a new underlying space to work with (Euclidean geometry uses Euclidean space, Rn) or by choosing a new group of transformations to work with (Euclidean geometry uses the inhomogeneous orthogonal transformations, E(n)). The latter point of view is called the Erlangen program. In general, the more congruences we have, the fewer invariants there are. As an example, in affine geometry any linear transformation is allowed, and so the first three figures are all congruent; distances and angles are no longer invariants, but linearity is. A discrete form of geometry is treated under Pick's theorem. See List of geometry topics. External Links
This article is adapted from from Wikipedia All Wikipedia article text is available under the terms of the GNU Free Documentation License The Golden Ratio : The Story of PHI, the World's Most Astonishing Number by Mario Livio Sir Cumference and the First Round Table: A Math Adventure by Cindy Neuschwander Sir Cumference and the Great Knight of Angleland: A Math Adventure by Cindy Neuschwander Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire Geometry and Trigonometry for Calculus by Peter H. Selby Geometry for Dummies by Wendy Arnone Sir Cumference and the Dragon of Pi: A Math Adventure by Cindy Neuschwander Sacred Geometry: Philosophy and Practice by Robert Lawlor The Divine Proportion by H. E. Huntley The Geometry of Art and Life by Matila Ghyka Geometry (Cliffs Quick Review) by Edward Kohn The Phenomenon of Life: The Nature of Order, Book 1 by Christopher Alexander Sacred Geometry by Miranda Lundy Geometry of Design: Studies in Proportion and Composition by Kimberly Elam The Joy of Pi by David Blatner Recent Geometry related patents From USPTO: 6718524: Method and apparatus for estimating state-dependent gate leakage in an integrated circuit 6718457: Multiple-thread processor for threaded software applications 6718292: Compensation of second-order non-linearity in sensors employing double-ended tuning forks 6718291: Mesh-free method and system for modeling and analysis 6718290: Systems and methods for encoding tetrahedral meshes 6718283: Method and apparatus for predicting heater failure 6718280: Measurement device for determining the three-dimensional orientation of a body relative to a reference direction 6718269: Apparatus, program product and method of estimating the stress intensity factor ratio of a material 6718268: Apparatus for measuring a contact pressure of a winding compression element in a power transformer 6718259: Adaptive Kalman filter method for accurate estimation of forward path geometry of an automobile 6718258: Method and system for obtaining user feedback regarding geographic data 6718251: System for controlling exhaust emissions produced by an internal combustion engine 6718243: System and method of controlling a vehicle steer-by-wire system applying gain scheduling control 6718236: Method for conducting a moving vehicle along a trajectory of a coordinated maneuver based on state information broadcast by other vehicles participating in the coordinated maneuver 6718233: Placement of an optical component on a substrate 6718218: CAD data model with design notes 6718211: Medical electrical lead having bending stiffnesses which increase in the distal direction 6718210: Functional neuromuscular stimulation system 6718189: Method and apparatus for non-invasive blood analyte measurement with fluid compartment equilibration 6718110: Indiffused optical waveguide structures in a substrate 6718099: Pin insertion tool and method for measuring endface surface topography of multi-fiber fiberoptic connectors 6718097: Method of incorporating optical material into an optical fiber 6718094: Large surface amplifier with multimode interferometer 6718085: Stable optical switch with reduced power consumption 6718076: Acousto-optic tunable filter with segmented acousto-optic interaction region 6718074: Method and apparatus for inspection for under-resolved features in digital images 6718068: Noise reduction method utilizing statistical weighting, apparatus, and program for digital image processing 6718062: System and method for matching curves of multiple images representing a scene 6718061: Method and system for note taking using a form with coded marks 6718054: MRA segmentation using active contour models 6718012: Electromagnetic wave energy emitter 6718009: Method of making of compound x-ray lenses and variable focus x-ray lens assembly 6718006: Fiber-optic encoding for dual transmission measurements in positron emission tomography 6717979: Method for estimating a direction of arrival 6717967: Absolutely calibrated periodic filters and sources 6717966: Calibration focus position 6717910: Method and apparatus for controlling network data congestion 6717908: Bit interleaving for orthogonal frequency division multiplexing in the transmission of digital signals 6717869: Integrated circuit having redundant, self-organized architecture for improving yield 6717846: Non-volatile semiconductor memory having split-gate memory cells mirrored in a virtual ground configuration 6717792: Emitter assembly 6717787: Current sensing IC with resistive sensing 6717785: Semiconductor switching element driving circuit 6717770: Recording head for applying a magnetic field perpendicular to the magnetizations within magnetic storage media 6717740: Scanning optical system and image recording exposure device 6717728: System and method for visualization of stereo and multi aspect images 6717722: Catadioptric optical system and exposure apparatus having the same 6717717: Dynamic wavelength shifting method 6717714: Method and system for generating enhanced gray levels in an electromechanical grating display |