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the (31), band (15), wikipedia (9), geometry (9), model (7), this (5), edit (5), hyperbolic (5), and (4), page (4), line (4), about (3), links (3), pdf (3), article (3), #navigation (3), conformal (3), org (3), geodesics (3), middle (3), boundaries (3), are (3), displaystyle (3), portion (3), view (2), contact (2), privacy (2), policy (2), terms (2), you (2), upload (2), file (2), related (2), changes (2), tools (2), help (2), search (2), talk (2), categories (2), all (2), stub (2), retrieved (2), from (2), https (2), band_model (2), models (2), along (2), lines (2), parallel (2), through (2), shown (2), plane (2), given (2), sec (2), operatorname (2), jump (2), web (2), 2022 (2), cookie, statement, statistics, developers, mobile, disclaimers, text, available, under, additional, may, apply, using, site, agree, registered, trademark, non, profit, organization, wikimedia, foundation, inc, use, creative, commons, attribution, sharealike, license, was, last, edited, july, 2020, utc, add, languages, printable, version, download, print, export, wikidata, item, cite, information, permanent, link, special, pages, what, here, recent, community, portal, learn, contribute, donate, random, current, events, contents, main, more, history, read, views, english, namespaces, log, create, account, contributions, not, logged, personal, menu, hidden, articles, stubs, index, php, title, oldid, 970081188, can, expanding, external, bowman, joshua, 2018, august, 612, class, lecture, ithaca, matrix, editions, 57965863, oclc, 9780971576629, isbn, teichmüller, theory, applications, topology, dynamics, hubbard, john, references, mercator, projection, see, also, include, any, open, segment, perpendicular, connecting, sides, have, ends, with, either, orthogonal, which, approach, within, whose, centers, hypercycles, infty, employs, euclidean, between, two, distance, preserved, one, assuming, metric, mathbb, left, right, order, rhombic, tiling, free, encyclopedia, wayback, machine, http, archive, 20221114064747, wiki, timestamps, capture, fail, success, 2023, 2021, dec, nov, oct, apr, jul, 2026, captures,

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band model wikipedia 9 captures 19 apr 2022 31 jul 2026 oct nov dec 14 2021 2022 2023 success fail about this capture timestamps the wayback machine http web archive org web 20221114064747 https en wikipedia org wiki band_model band model from wikipedia the free encyclopedia jump to navigation jump to search the order 7 3 rhombic tiling shown in a portion of the band model in geometry the band model is a conformal model of the hyperbolic plane the band model employs a portion of the euclidean plane between two parallel lines 1 distance is preserved along one line through the middle of the band assuming the band is given by z c im z π 2 displaystyle z in mathbb c left operatorname im z right pi 2 the metric is given by d z sec im z displaystyle dz sec operatorname im z geodesics shown in a portion of the band model geodesics include the line along the middle of the band and any open line segment perpendicular to boundaries of the band connecting the sides of the band all geodesics have ends with either are orthogonal to the boundaries of the band or which approach displaystyle pm infty 2 lines parallel to the boundaries of the band within the band are hypercycles whose centers are the line through the middle of the band see also edit mercator projection references edit hubbard john h 2 pdf teichmüller theory and applications to geometry topology and dynamics ithaca ny matrix editions p 25 isbn 9780971576629 oclc 57965863 bowman joshua 612 class lecture hyperbolic geometry pdf retrieved august 12 2018 external links edit models of hyperbolic geometry conformal models of the hyperbolic geometry this geometry related article is a stub you can help wikipedia by expanding it v t e retrieved from https en wikipedia org w index php title band_model oldid 970081188 categories conformal geometry hyperbolic geometry geometry stubs hidden categories all stub articles navigation menu personal tools not logged in talk contributions create account log in namespaces article talk english views read edit view history more search navigation main page contents current events random article about wikipedia contact us donate contribute help learn to edit community portal recent changes upload file tools what links here related changes upload file special pages permanent link page information cite this page wikidata item print export download as pdf printable version languages add links this page was last edited on 29 july 2020 at 03 51 utc text is available under the creative commons attribution sharealike license 3 0 additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia mobile view developers statistics cookie statement