Geometry.Net - the online learning center
Home  - Pure_And_Applied_Math - Manifolds
e99.com Bookstore
  
Images 
Newsgroups
Page 3     41-60 of 65    Back | 1  | 2  | 3  | 4  | Next 20

         Manifolds:     more books (100)
  1. Differential Geometry and Analysis on CR Manifolds (Progress in Mathematics) by Sorin Dragomir, Giuseppe Tomassini, 2006-03-17
  2. Time (Manifold 1) by Stephen Baxter, 2000-08-07
  3. Differential Manifolds (Dover Book on Mathematics) by Antoni A. Kosinski, 2007-10-19
  4. Foundations of Hyperbolic Manifolds (Graduate Texts in Mathematics) by John Ratcliffe, 2010-11-02
  5. 3-Manifolds (AMS Chelsea Publishing) by John Hempel, 2004-11
  6. Invariant Manifolds for Physical and Chemical Kinetics (Lecture Notes in Physics) by Alexander N. Gorban, Iliya V. Karlin, 2010-11-30
  7. Optimization Algorithms on Matrix Manifolds by P.-A. Absil, R. Mahony, et all 2007-12-03
  8. Relativity on Curved Manifolds (Cambridge Monographs on Mathematical Physics) by F. de Felice, C. J. S. Clarke, 1992-03-27
  9. Geometric Mechanics on Riemannian Manifolds: Applications to Partial Differential Equations (Applied and Numerical Harmonic Analysis) by Ovidiu Calin, Der-Chen Chang, 2004-10-25
  10. Differential and Riemannian Manifolds (Graduate Texts in Mathematics) by Serge Lang, 1995-03-09
  11. The Arithmetic of Hyperbolic 3-Manifolds (Graduate Texts in Mathematics) by Colin Maclachlan, Alan W. Reid, 2010-11-02
  12. The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44) by John W. Morgan, 1995-12-11
  13. Branched Standard Spines of 3-manifolds (Lecture Notes in Mathematics) by Riccardo Benedetti, Carlo Petronio, 1997-04-18
  14. 4-Manifolds and Kirby Calculus (Graduate Studies in Mathematics) by Andras I. Stipsicz Robert E. Gompf, 1999-08-31

41. Plumbing Fittings Manifolds
Sulfone polymers can successfully replace brass, copper and stainless steel traditionally used in fittings and manifolds for drinking water.
http://www.solvayadvancedpolymers.com/markets/marketplumbing/plumbingpipefitting
var varServerName='/static'; document.write(" Contact Us "); document.write(" Sitemap "); document.write(" Members "); document.write(" EN "); document.write (" You are here: "); Solvay Advanced Polymers Markets Plumbing Fittings and Manifolds Other Solvay Sites Solvay.com Business Portals PLASTICS PORTAL Benvic Dacarto Benvic Ixan-Diofan Padanaplast Pipelife (JV) Priex Semi Conductors Solvay Advanced Polymers Solvay Engineered Polymers Solvay Indupa Solvay Membranes Solvay Plumbing Solvay Solexis SolVin (JV) Vinyloop Vinythai PHARMACEUTICALS PORTAL CHEMICALS PORTAL > Other sites by Businesses - Country Portals - Solvay Austria Solvay China Solvay Deutschland Solvay France Solvay Iberica Solvay Italia Solvay Nordic Solvay North America Solvay Portugal Solvay Schweiz > Other sites by Regions This Site All Sites var ColorMenuBack="#FFFFFF"; var ColorMenuServices="#FFFFFF"; var ColorMenuSiteIn="#BBE3FF"; var ColorMenuSiteOut="#BBE3FF"; var ColorMenuSolvay="#FFFFFF"; var ColorMenuHome="#FFFFFF"; var ColorServicesSelect="#D0D0D0"; var ColorMenuSelect="#D0D0D0"; Markets Aircraft Aircraft Overview Aircraft Interiors ... Procurement Terms
Plumbing
Fittings and Manifolds for Drinking Water Sulfone polymers can successfully replace brass, copper and stainless steel traditionally used in fittings and manifolds for drinking water. Globally approved for drinking water, these high-performance plastics provide greater design freedom and a host of performance attributes:

42. Www.manifoldwarehouse.com - Marine Exhaust Manifolds And, Risers And Elbows, Hea
Marine exhaust manifold, Marine Heat Exchangers, Volvo Penta Diesel Engine Elbow, Detroit Diesel Engine Elbow, Chrysler marine exhaust manifolds,
http://www.manifoldwarehouse.com/
Autoredirect to Manifoldwarehouse.com Home Page

43. PEX Plumbing Part 5, MANIFOLDS - Associated Content
Check out PEX Plumbing Part 5, manifolds Submitted by blbaird725 at Associated Content.
http://www.associatedcontent.com/article/551163/pex_plumbing_part_5_manifolds.ht
Find Publish Community Join ... Home Improvement
PEX Plumbing Part 5, MANIFOLDS
I have received many questions from my guides on PEX plumbing. One of the most asked is about manifolds. This guide might get a little long but I hope to answer as many questions as possible. I have also found an E-bay seller that has the type of manifold I used in my system.
First let's start with a general definition of the word manifold, 1) Consisting of or operating several devices of one kind at the same time. 2) A pipe or chamber having multiple apertures for making connections. More simply put, for plumbing, it is a control center for hot and/or cold water that feeds "flexible plastic supply lines" (PEX) to individual fixtures. Please note that in my guides I am addressing potable (drinking) water PEX systems. A lot of the same information applies to radiant heating systems but these are usually found under floors and have differences in installation.
There are many benefits to the PEX manifold system. 1) Because most of the connections are made at one central point, any leakage is visible and easier to correct. 2) Individual branches of the system can be shut off for service without shutting down all of the water to the system/residence. 3) This system provides a much more regulated water pressure supply!
To understand the improvement in water pressure picture yourself with a 50' or longer garden hose. This hose has holes, of equal size, every five feet or so from the faucet handle to the end of the hose. The first hole in this series will have the largest, strongest, spray of water. As it continues down the hose each subsequent hole has slightly less pressure spray until it gets to the end where you are trying to water your

44. G-equivariant Embeddings Of Manifolds « The Everything Seminar
I guess the moral of the story is that compact manifolds are really just “nice” subsets of Euclidean space, and a compact manifold with a finite group
http://cornellmath.wordpress.com/2007/10/24/g-equivariant-embeddings-of-manifold
var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E"));
The Everything Seminar
Geometry, Topology, Categories, Groups, Physics, . . . Everything Symplectic Mechanics and Symmetry Chord Diagrams
G-equivariant embeddings of manifolds
acting on a compact manifold . The Whitney embedding theorem says that we can embed into for sufficiently large , and what I want to show in this post is that you can do this in a -equivariant way, i.e. there is an embedding and an injective homomorphism such that and then we show that this embedding is -equivariant. Pick a finite covering of by coordinate charts and a partition of unity which is subordinate to the cover of . To make the notation a little more clear later, we can break up the into their components . Now we let be the standard basis for with , and be the standard basis for . Now let be the vector space spanned by and . Then we can define our embedding with the following formula: (In this formula we are defining if even if is undefined.) Since all the functions involved are smooth, this is obviously a smooth map, so to show it is an embedding it is sufficient to show it is a homeomorphism. Since

45. For Sale: Engine Parts :: Intake Manifolds And Carbs
Edelbrock Torker II Manifold SBC $92.99 Edelbrock Torker II Manifold SBC 930 AED CARB AND HOLLY RACE INTAKE $700.00 930 AED CARB AND HOLLY RACE INTAKE
http://www.racingjunk.com/category/98/Intake_manifolds_and_carbs.html
You are not logged in. Login Sign up Find Ads Search by Ad Number or Key Word Advanced Search Engine Parts Intake manifolds and carbs Search For: In Engine Parts Engine Parts :: Intake manifolds and carbs
PROFORM Race Series Carburetors 850 CFM
PROFORM Race Series Carburetors 750 CFM
Show four more
Intake manifolds and carbs Categories: Go back to category Engine Parts. Last Post: Today
Premiere Ads
Barry Grant BG400,BG280,BG 220 fuel pump seal
PROFORM Race Series Carburetors 950 CFM
MagnaFlow Pro Star 500 16V w/filter $350
New Rons Fuel Injection System- save $1100.00
SBF parts intake, heads, rockers, cam, crank,
QUICK FUEL TECHNOLOGY CARBS!!
Chevrolet, Big Block, DART Intake Manifold
holley carb
BRAND NEW DART BBC MANIFOLD ABS PLASTIC SCOOP TRAY INSERT View All 493 Classified Ads Classified Categories Post A Classified Antique/Classic Asphalt Oval Racing Cars Boats ... Vipers Racing Junk Legend Club Racing Junk Member - Displayed on all classifieds posted by an official Club Racing Junk Member or Dealer. Honor Member - Displayed on all classified ads that are posted by Racing Junk members who have made and Honor Payment to us.

46. Wiley::Multivariable Mathematics: Linear Algebra, Multivariable Calculus, And Ma
Multivariable Mathematics Linear Algebra, Multivariable Calculus, and manifolds. Theodore Shifrin. ISBN 9780-471-52638-4. Hardcover. 504 pages
http://www.wiley.com/WileyCDA/WileyTitle/productCd-047152638X.html
United States Change Location

47. A Self-organizing Principle For Learning Nonlinear Manifolds -- Agrafiotis And X
Unlike previous approaches, our method can reveal the underlying geometry of the manifold without intensive nearestneighbor or shortest-path computations
http://www.pnas.org/cgi/content/full/99/25/15869
Published online on November 20, 2002, 10.1073/pnas.242424399
December 10, 2002
This Article Abstract Full Text (PDF) Supporting Text ... Citation Map Services Email this article to a colleague Similar articles in this journal Similar articles in ISI Web of Science Similar articles in PubMed ... Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via CrossRef Citing Articles via ISI Web of Science (24) Citing Articles via Google Scholar Google Scholar Articles by Agrafiotis, D. K. Articles by Xu, H. Search for Related Content PubMed PubMed Citation Articles by Agrafiotis, D. K. Articles by Xu, H. Social Bookmarking
What's this?
Previous Article Table of Contents Next Article Computer Sciences
A self-organizing principle for learning nonlinear manifolds Dimitris K. Agrafiotis , and Huafeng Xu 3-Dimensional Pharmaceuticals, Inc., 665 Stockton Drive, Exton, PA 19341 Edited by Michael Levitt, Stanford University School of Medicine, Stanford, CA, and approved October 9, 2002 (received for review July 17, 2002)
Abstract Top
Abstract
Methods
Results and Discussion
References
Modern science confronts us with massive amounts of data: expression profiles of thousands of human genes, multimedia documents, subjective

48. Marine Exhaust Manifolds
Marine Exhaust manifolds Featured Listings for Marine Exhausts manifolds Marine Exhaust manifolds Premier Listings
http://www.charternet.com/greatgear/marine-exhaust-manifolds.html
Marine Exhaust Manifolds Home Featured Listings for Marine Exhausts Manifolds
Put Your Company Link Here

Advertise your company here to get qualified traffic to your site. Marine Exhaust Manifolds- Premier Listings
AAA Marine Parts Wholesale

Go 2 Marine

Marine Warehouse

Additional Listings 3M Marine Trades Palm City FL Above Board Controls, Inc. Plantation FL Advanced Resources Inc Atlanta GA Alfa Laval Separation, Inc. Marine Warminster PA Alxzka Fuel Purifiers Southbury CT American Vulkan Corp. Winter Haven FL Armstrong Nautical Products Stuart FL B Bracket Dania FL Pompano Beach FL Bob's Machine Shop, Inc. Ruskin FL C.J. Worldwide Export, Inc. Ft Lauderdale FL CK Power Products Corp. Ocala FL C-Level Inc. Noank CT Carey's Diesel, Inc. Dover DE Central Marine Service St. Petersburg FL

49. BoatUS BoatTECH Guides: Exhaust Manifolds
Exhaust manifolds last forever, don t they? Even if they do fail, it isn t a major problem, right? These are common reactions when people are asked about
http://www.boatus.com/boattech/exh.htm

Exhaust Manifolds
Exhaust manifolds last forever, don't they? Even if they do fail, it isn't a major problem, right? These are common reactions when people are asked about their boat's manifold. Unfortunately, exhaust manifolds are important, and ignoring them can potentially lead to expensive problems, perhaps an engine rebuild. There is an additional hassle-manifolds are normally damaged by corrosion, so they're not covered by your insurance policy. All of this makes the outlook seem rather bleak. It's not as bad as it seems, though. All that's needed is a change in attitude. Rather than seeing it as a "sealed for life" component, view a manifold as a service item to be replaced at regular intervals. If you do this, major problems can be avoided. Life Expectancy How long will a manifold last? Obviously the way you use your boat will be a factor, as will the type of water it's on. Saltwater boats are going to see a shorter manifold life when compared to their freshwater counterparts. Most experts suggest that a manifold will have a life expectancy of six to eight years. However, heavy use in saltwater can see this drop to as low as three years, while lightly used freshwater boats can get up to 20 years out of a manifold. One thing is for certain, the older your manifold gets, the more likely it is to fail. This is clearly shown in the chart below.

50. MicroAdvances: Plastic Manifolds, Fluid Circuits, Pneumatic Components
MicroAdvances designs fluid circuits in bonded plastic plates. We also carry many standard manifolds for miniature valves.
http://microadvances.com/
State-of-the-art fluid circuits in bonded plastic plates Similar to the conceptual jump in the electrical industry from discrete components to integrated circuits, MicroAdvances manufactures fluid circuits and manifolds in plastic plates. Circuits in plastic offer many advantages over traditional methods.

Manifold of the month click for larger image)
Six layer acrylic manifold
acrylic manifold, PMMA manifold, PVC manifold

51. Analysis, Manifolds And Physics - Elsevier
Differential manifolds, finite dimensional case IV. Integration on manifolds V. Riemannian manifolds, kahlerian manifolds Vbis. Connections on a principal
http://www.elsevier.com/wps/product/cws_home/600404
Home Site map Elsevier websites Alerts ... Analysis, Manifolds and Physics Book information Product description Author information and services Ordering information Bibliographic information Conditions of sale Volume information Part I Part II Set Book-related information Submit your book proposal Other books in same subject area About Elsevier Select your view ANALYSIS, MANIFOLDS AND PHYSICS
http://books.elsevier.com/elsevier/?isbn=0444860177

By
Y. Choquet-Bruhat
C. DeWitt-Morette
Contents

Contents. I. Review of fundamental notions of analysis II. Differential calculus on banach spaces III. Differential manifolds, finite dimensional case IV. Integration on manifolds V. Riemannian manifolds, kahlerian manifolds Vbis. Connections on a principal fibre bundle VI. Distributions VII. Differentiable manifolds, infinite dimensional case Problems and exercises References Symbols Index
Volumes
Part I

Part II

Set
Part I Hardbound, ISBN: 0-444-86017-7, 650 pages, publication date: JAN-1982 Imprint: NORTH-HOLLAND Price: Order form USD 71.95 GBP 41 EUR 62 Part II Hardbound, ISBN: 0-444-87071-7, 462 pages, publication date: NOV-1996

52. Turbo Kits, Turbo Manifolds, Import Performance Products, SSAutochrome Inc.
Turbos, turbo kits, manifolds, turbo manifolds, internal wastegates, external wastegates, Nissan turbos, Civic turbos, Integra turbos, B16 turbos,
http://www.ssautochrome.com/
SSAutochrome is the premier source for all your Import Performance Products. We carry a vast inventory of Turbos, turbo kits, manifolds, turbo manifolds, wastegates, internal wastegates, external wastegates, Nissan turbos, Civic turbos, Integra turbos, B16 turbos, B18 turbos, D16 turbos, fuel rails, intake manifolds, headers, catbacks, exhausts and more! On our website and available for online purchase you will find Turbo Downpipes, Dump Pipes for Honda, Acura, Hyundai, Mazda, Mitsubishi, Nissan, Toyota, WRX, Subaru, 3000gt Stealth Downpipe 3000GT or Stealth, 100% T-304 stainless, Toyota Celica GT4 / MR2 3S-GTE Turbo Downpipe v-band stainless steel. We stock Turbo Kits for Honda, Integra, Mitsubishi, DSM, Nissan, Toyota including B series turbo manifold and stainless steel downpipe, DSM 1g, 2g evo 4g63 super big 16g EVO III turbo kit, Integra B series turbo combo kit, Civic D series, 2jzgte super t4 turbo setup. We have Nissan Turbos and Turbo Chargers, T3 Turbo 4 Bolt Exhaust Flange, EVO 3 16G Ported Turbo/DSM 1G 2g, NISSAN T25 / T28 GTRS Disco French-Fry, Super T70 Turbo T70 / .84 P Trim, T3/T4 Turbo Charger, T4 Turbo Stage 5.

53. International Conference On Geometry And Analysis On Manifolds
International Conference on Geometry and Analysis on manifolds. Santa Barbara March 1420, 2008. The conference theme is the Atiyah-Singer index theory and
http://www.math.ucsb.edu/~dai/meeting/meeting.html

Participants

Schedule

Accommodations

Transportation
...
E-mail

University of California
International Conference on Geometry and Analysis on Manifolds
Santa Barbara March 14-20, 2008
The conference theme is the Atiyah-Singer index theory and related topics. The conference will start on the 15th and end on the 19th. Sopported in part by the NSF, the College of Letters and Science, UCSB, and the Division of Mathematical, Life, and Physical Sciences, UCSB.
The first day of the conference will be held at the Cliff House, see a map of the location of the Cliff House here ; and also here for a local area map. For the rest of the days, it will be held at South Hall 6635, see the map of UCSB here
Here
are some information on restaurants. More information and reviews
can be found at Santa Barbara.com Organizing Committee Xianzhe Dai, UCSB Xiaonan Ma, Paris VII Weiping Zhang, Chern Institute

54. Regularized Principal Manifolds
Your browser may not have a PDF reader available. Google recommends visiting our text version of this document.
http://www.springerlink.com/index/88tufxjbfmbyvrd7.pdf

55. 250A Differentiable Manifolds
250A is roughly vector calculus on manifolds. An example of a manifold is a surface in space when you ignore the rigid structure of space.
http://math.ucsd.edu/~lindblad/250a/250a.html
Math 250A: Differentiable Manifolds - Fall 04 - Hans Lindblad
250A is roughly vector calculus on manifolds. An example of a manifold is a surface in space when you ignore the rigid structure of space. Many things in geometry and physics, such as Einstein's equations of general relativity, are best stated independent of a particular coordinate system. A manifold together with invariantly defined differential operators is the natural setting for many nonlinear equations of physics. Applications include general relativity, fluid mechanics, electromagnetism, Hamiltonian mechanics, dynamical systems and control theory. The core topics in the course are:
  • Differentiability. Inverse and implicit function theorem. Submanifolds of Euclidean space.
  • Topological and smooth manifolds. Tangent space and bundle. Vector bundles.
  • Vector fields, existence for ODE, Lie bracket and derivative, Frobenius theorem.
  • Tensors and differential forms. Tensor bundles and cotangent bundle.
  • Integration, partition of unity, orientation, Poincare lemma, Stokes formula, De Rham
Additional topics that we might cover:
  • Applications to Hamiltonian Mechanics and Electromagnetism
  • Connections and covariant derivatives. Parallel transport.

56. Gas Handling Equipment: Gas Cylinder Enclosures, Source Manifolds, And Panels
Gas Handling Equipment. •, Gas Purification Systems. •, SEMIGAS® Special Delivery Equipment. •, Gas Cylinder Enclosures, Source manifolds, and Panels
http://www.mathesontrigas.com/gas-cylinder-enclosures-source-manifolds-and-panel
Specialty Gases, Semiconductor Gases, Industrial Gases, Gas Handling Equipment Home
Gases Equipment MSDS Literature Corporate Info myMTGOL Log In Product Search Online Store Matheson Tri-Gas Products Specialty Gases Specialty Gases - Pure Specialty Gas Mixtures Specialty Gas Applications ... Cutting/Welding/Industrial Gases Matheson Tri-Gas Programs FIRST-MATE Supply Chain Excellence ENABLE Distributor Development Program Tri-Tech Taiyo Nippon Sanso Group
Gas Handling Equipment: Gas Cylinder Enclosures, Source Manifolds, and Panels
The links below are PDFs and require Adobe Acrobat Reader to view. Click on the icon to download the latest FREE version. If you are experiencing slow downloads of the PDFs, installing the latest version of Adobe Acrobat Reader may increase performance. SEMI-GAS® Centurion™ Cylinder Enclosures Gas Source Panels and Cylinder Enclosure Systems Specialty Gases, Semiconductor Gases, Industrial Gases, Gas Handling Equipment Home Specialty Gases Semiconductor Gases ... Online Store

57. Positech Manifolds
company profile For over 30 years, Positech fluid power products have been employed worldwide. Transfer fluids (liquids and/or gases) when 360° continuous
http://www.positechmanifolds.com/
AC_FL_RunContent( 'codebase','http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=8,0,0,0', 'width','170', 'height','226', 'src','menu', 'quality','high', 'pluginspage','http://www.macromedia.com/go/getflashplayer', 'allowScriptAccess','sameDomain', 'movie','menu' ); //end AC code
Cancel Subscription
company profile
For over 30 years, Positech fluid power products have been employed worldwide. Transfer fluids (liquids and/or gases) when 360° continuous or oscillating rotation between two machine members is required. Custom designed with multiple circuits for various port and mounting arrangements. For mobile and in-plant equipment. Custom Tailored to your Specifications
Quality Design and Construction Hydraulic or pneumatic. Personal attention to your needs. Fast, efficient service. 100% hydraulically tested during rotation. Full In-House Capabilities All manufacturing processes are performed in our own facilities: machining, grinding, honing, chrome plating, assembly and testing. Cases are made from steel, are bored, drilled, welded, stress relieved, honed, milled and deburred - oil seals are cut into the spool. Almost any kind of port can be put into the spool or case. Chrome plating of the case ID is available. AC_FL_RunContent( 'codebase','http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=8,0,0,0', 'width','19', 'height','19', 'src','sound', 'quality','high', 'wmode','transparent', 'pluginspage','http://www.macromedia.com/go/getflashplayer', 'allowScriptAccess','sameDomain', 'movie','sound' ); //end AC code

58. Geometric Inequalities On Locally Conformally Flat Manifolds
17 M. J. Gursky and J. A. Viaclovsky, Fully nonlinear equations on Riemannian manifolds with negative curvature, Indiana Univ. Math.
http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.dmj/1091217478?abstract=

59. Headers & Manifolds - PriceGrabber.com
Compare prices for Headers manifolds from top brands such as Moroso, GReddy, Bassani, PaceSetter, Doug Thorley, FlowTech, SSR and more
http://autoparts.pricegrabber.com/headers-manifolds/p/3325/
Go back to home page Login Register SHOP FOR IN Search Current Results All Products Appliances Auto Parts Books Cameras Clothing Computers Electronics Furniture Indoor Living Industrial Equipment Magazines Movies Music Musical Instruments Office Outdoor Living Software Sporting Goods Toys Video Games SEARCH Auto Parts Exhaust
(6072 Matches)
Filters: Basic Advanced Click to Add a Filter: Top Manufacturers Price Range
  • Set Price Range
to
  • Hide Price Range

Sort by Rating
Sort by Price from (2 Sellers) Hooker 6914-1HKR Competition Ceramic Header Hooker 6914-1HKR Competition Ceramic Header
Hooker - 69141
Rating: Write a Review
from (2 Sellers) from (2 Sellers) Hooker 2151HKR Super Comp. Header 84-96 Corvette Hooker 2151HKR Super Comp. Header 84-96 Corvette With Hooker Super Competition the objective has always been to make the maximum horsepower and to put it at the optimum point in the power curve. It takes a lot of time and money to do the jo... Hooker 2151HKR Super Comp. Header 84-96 Corvette

60. Manifold - Wikipedia, The Free Encyclopedia
A manifold is an abstract mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may
http://en.wikipedia.org/wiki/Manifold
Manifold
From Wikipedia, the free encyclopedia
Jump to: navigation search On a sphere, the sum of the angles of a triangle is not equal to 180° (see spherical trigonometry ). A sphere is not a Euclidean space, but locally the laws of Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is very nearly 180°. A sphere can be represented by a collection of two dimensional maps, therefore a sphere is a manifold. For other uses, see Manifold (disambiguation) A manifold is an abstract mathematical space in which every point has a neighborhood which resembles Euclidean space , but in which the global structure may be more complicated. In discussing manifolds, the idea of dimension is important. For example, lines are one-dimensional, and planes two-dimensional. In a one-dimensional manifold (or one-manifold), every point has a neighborhood that looks like a segment of a line. Examples of one-manifolds include a line, a circle , and two separate circles. In a two-manifold, every point has a neighborhood that looks like a disk . Examples include a plane, the surface of a

Page 3     41-60 of 65    Back | 1  | 2  | 3  | 4  | Next 20

free hit counter