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												  Nicolas-Auguste Tissot: a Link Between Cartography and Quasiconformal TheoryNICOLAS-AUGUSTE TISSOT: A LINK BETWEEN CARTOGRAPHY AND QUASICONFORMAL THEORY ATHANASE PAPADOPOULOS Abstract. Nicolas-Auguste Tissot (1824{1897) published a series of papers on cartography in which he introduced a tool which became known later on, among geographers, under the name of the Tissot indicatrix. This tool was broadly used during the twentieth century in the theory and in the practical aspects of the drawing of geographical maps. The Tissot indicatrix is a graph- ical representation of a field of ellipses on a map that describes its distortion. Tissot studied extensively, from a mathematical viewpoint, the distortion of mappings from the sphere onto the Euclidean plane that are used in drawing geographical maps, and more generally he developed a theory for the distor- sion of mappings between general surfaces. His ideas are at the heart of the work on quasiconformal mappings that was developed several decades after him by Gr¨otzsch, Lavrentieff, Ahlfors and Teichm¨uller.Gr¨otzsch mentions the work of Tissot and he uses the terminology related to his name (in particular, Gr¨otzsch uses the Tissot indicatrix). Teichm¨ullermentions the name of Tissot in a historical section in one of his fundamental papers where he claims that quasiconformal mappings were used by geographers, but without giving any hint about the nature of Tissot's work. The name of Tissot is also missing from all the historical surveys on quasiconformal mappings. In the present paper, we report on this work of Tissot. We shall also mention some related works on cartography, on the differential geometry of surfaces, and on the theory of quasiconformal mappings.
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												  Mercator-15Dec2015.PdfTHE MERCATOR PROJECTIONS THE NORMAL AND TRANSVERSE MERCATOR PROJECTIONS ON THE SPHERE AND THE ELLIPSOID WITH FULL DERIVATIONS OF ALL FORMULAE PETER OSBORNE EDINBURGH 2013 This article describes the mathematics of the normal and transverse Mercator projections on the sphere and the ellipsoid with full deriva- tions of all formulae. The Transverse Mercator projection is the basis of many maps cov- ering individual countries, such as Australia and Great Britain, as well as the set of UTM projections covering the whole world (other than the polar regions). Such maps are invariably covered by a set of grid lines. It is important to appreciate the following two facts about the Transverse Mercator projection and the grids covering it: 1. Only one grid line runs true north–south. Thus in Britain only the grid line coincident with the central meridian at 2◦W is true: all other meridians deviate from grid lines. The UTM series is a set of 60 distinct Transverse Mercator projections each covering a width of 6◦in latitude: the grid lines run true north–south only on the central meridians at 3◦E, 9◦E, 15◦E, ... 2. The scale on the maps derived from Transverse Mercator pro- jections is not uniform: it is a function of position. For ex- ample the Landranger maps of the Ordnance Survey of Great Britain have a nominal scale of 1:50000: this value is only ex- act on two slightly curved lines almost parallel to the central meridian at 2◦W and distant approximately 180km east and west of it. The scale on the central meridian is constant but it is slightly less than the nominal value.
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												  TYPHOONS and DEPRESSIONS OVER the FAR EAST Morning Observation, Sep Teinber 6, from Rasa Jima Island by BERNARDFSEPTEMBER1940 MONTHLY WEATHER REVIEW 257 days west of the 180th meridian. In American coastal appear to be independent of the typhoon of August 28- waters fog was noted on 10 days each off Washington and September 5, are the following: The S. S. Steel Exporter California; on 4 days off Oregon; and on 3 days off Lower reported 0700 G. C. T. September 6, from latitude 20'18' California. N., longitude 129'30'E.) a pressure of 744.8 mm. (993.0 nib.) with west-northwest winds of force 9. Also, the TYPHOONS AND DEPRESSIONS OVER THE FAR EAST morning observation, Sep teinber 6, from Rasa Jima Island By BERNARDF. DOUCETTE, J. (one of the Nansei Island group) was 747.8 mm. (997.0 5. mb.) for pressure and east-northeast, force 4, for winds. [Weather Bureau, Manila, P. I.] Typhoon, September 11-19) 1940.-A depression, moving Typhoon, August %!-September 6,1940.-A low-pressure westerly, passed about 200 miles south of Guam and area far to the southeast of Guam moved west-northwest, quickly inclined to the north, intensifying to typhoon rapidly developing to typhoon intensity as it proceeded. strength, September 11 to 13. It was stationary, Sep- When the center reached the regions about 250 miles tember 13 and 14, about 150 miles west-northwest of west of Guam, the direction changed to the northwest, Guam, and then began a northwesterly and northerly and the storm continued along this course until it reached course to the ocean regions about 300 miles west of the the latitude of southern Formosa.
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												  QUICK REFERENCE GUIDE Latitude, Longitude and Associated MetadataQUICK REFERENCE GUIDE Latitude, Longitude and Associated Metadata The Property Profile Form (PPF) requests the property name, address, city, state and zip. From these address fields, ACRES interfaces with Google Maps and extracts the latitude and longitude (lat/long) for the property location. ACRES sets the remaining property geographic information to default values. The data (known collectively as “metadata”) are required by EPA Data Standards. Should an ACRES user need to be update the metadata, the Edit Fields link on the PPF provides the ability to change the information. Before the metadata were populated by ACRES, the data were entered manually. There may still be the need to do so, for example some properties do not have a specific street address (e.g. a rural property located on a state highway) or an ACRES user may have an exact lat/long that is to be used. This Quick Reference Guide covers how to find latitude and longitude, define the metadata, fill out the associated fields in a Property Work Package, and convert latitude and longitude to decimal degree format. This explains how the metadata were determined prior to September 2011 (when the Google Maps interface was added to ACRES). Definitions Below are definitions of the six data elements for latitude and longitude data that are collected in a Property Work Package. The definitions below are based on text from the EPA Data Standard. Latitude: Is the measure of the angular distance on a meridian north or south of the equator. Latitudinal lines run horizontal around the earth in parallel concentric lines from the equator to each of the poles.
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												  AIM: Latitude and LongitudeAIM: Latitude and Longitude Latitude lines run east/west but they measure north or south of the equator (0°) splitting the earth into the Northern Hemisphere and Southern Hemisphere. Latitude North Pole 90 80 Lines of 70 60 latitude are 50 numbered 40 30 from 0° at 20 Lines of [ 10 the equator latitude are 10 to 90° N.L. 20 numbered 30 at the North from 0° at 40 Pole. 50 the equator ] 60 to 90° S.L. 70 80 at the 90 South Pole. South Pole Latitude The North Pole is at 90° N 40° N is the 40° The equator is at 0° line of latitude north of the latitude. It is neither equator. north nor south. It is at the center 40° S is the 40° between line of latitude north and The South Pole is at 90° S south of the south. equator. Longitude Lines of longitude begin at the Prime Meridian. 60° W is the 60° E is the 60° line of 60° line of longitude west longitude of the Prime east of the W E Prime Meridian. Meridian. The Prime Meridian is located at 0°. It is neither east or west 180° N Longitude West Longitude West East Longitude North Pole W E PRIME MERIDIAN S Lines of longitude are numbered east from the Prime Meridian to the 180° line and west from the Prime Meridian to the 180° line. Prime Meridian The Prime Meridian (0°) and the 180° line split the earth into the Western Hemisphere and Eastern Hemisphere. Prime Meridian Western Eastern Hemisphere Hemisphere Places located east of the Prime Meridian have an east longitude (E) address.
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												  Latitude/Longitude Data StandardLATITUDE/LONGITUDE DATA STANDARD Standard No.: EX000017.2 January 6, 2006 Approved on January 6, 2006 by the Exchange Network Leadership Council for use on the Environmental Information Exchange Network Approved on January 6, 2006 by the Chief Information Officer of the U. S. Environmental Protection Agency for use within U.S. EPA This consensus standard was developed in collaboration by State, Tribal, and U. S. EPA representatives under the guidance of the Exchange Network Leadership Council and its predecessor organization, the Environmental Data Standards Council. Latitude/Longitude Data Standard Std No.:EX000017.2 Foreword The Environmental Data Standards Council (EDSC) identifies, prioritizes, and pursues the creation of data standards for those areas where information exchange standards will provide the most value in achieving environmental results. The Council involves Tribes and Tribal Nations, state and federal agencies in the development of the standards and then provides the draft materials for general review. Business groups, non- governmental organizations, and other interested parties may then provide input and comment for Council consideration and standard finalization. Standards are available at http://www.epa.gov/datastandards. 1.0 INTRODUCTION The Latitude/Longitude Data Standard is a set of data elements that can be used for recording horizontal and vertical coordinates and associated metadata that define a point on the earth. The latitude/longitude data standard establishes the requirements for documenting latitude and longitude coordinates and related method, accuracy, and description data for all places used in data exchange transaction. Places include facilities, sites, monitoring stations, observation points, and other regulated or tracked features. 1.1 Scope The purpose of the standard is to provide a common set of data elements to specify a point by latitude/longitude.
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												  Day-Ahead Market Enhancements Phase 1: 15-Minute SchedulingDay-Ahead Market Enhancements Phase 1: 15-minute scheduling Phase 2: flexible ramping product Stakeholder Meeting March 7, 2019 Agenda Time Topic Presenter 10:00 – 10:10 Welcome and Introductions Kristina Osborne 10:10 – 12:00 Phase 1: 15-Minute Granularity Megan Poage 12:00 – 1:00 Lunch 1:00 – 3:20 Phase 2: Flexible Ramping Product Elliott Nethercutt & and Market Formulation George Angelidis 3:20 – 3:30 Next Steps Kristina Osborne Page 2 DAME initiative has been split into in two phases for policy development and implementation • Phase 1: 15-Minute Granularity – 15-minute scheduling – 15-minute bidding • Phase 2: Day-Ahead Flexible Ramping Product (FRP) – Day-ahead market formulation – Introduction of day-ahead flexible ramping product – Improve deliverability of FRP and ancillary services (AS) – Re-optimization of AS in real-time 15-minute market Page 3 ISO Policy Initiative Stakeholder Process for DAME Phase 1 POLICY AND PLAN DEVELOPMENT Issue Straw Draft Final June 2018 July 2018 Paper Proposal Proposal EIM GB ISO Board Implementation Fall 2020 Stakeholder Input We are here Page 4 DAME Phase 1 schedule • Third Revised Straw Proposal – March 2019 • Draft Final Proposal – April 2019 • EIM Governing Body – June 2019 • ISO Board of Governors – July 2019 • Implementation – Fall 2020 Page 5 ISO Policy Initiative Stakeholder Process for DAME Phase 2 POLICY AND PLAN DEVELOPMENT Issue Straw Draft Final Q4 2019 Q4 2019 Paper Proposal Proposal EIM GB ISO Board Implementation Fall 2021 Stakeholder Input We are here Page 6 DAME Phase 2 schedule • Issue Paper/Straw Proposal – March 2019 • Revised Straw Proposal – Summer 2019 • Draft Final Proposal – Fall 2019 • EIM GB and BOG decision – Q4 2019 • Implementation – Fall 2021 Page 7 Day-Ahead Market Enhancements Third Revised Straw Proposal 15-MINUTE GRANULARITY Megan Poage Sr.
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												  The Leap Minute (Or, Predicting the Unpredictable)The Leap Minute (or, Predicting the Unpredictable) John H. Seago, AGI Leap Minutes – Who Cares? § Former BIPM Director § Specialists in the timekeeping industry § Officials involved with the ITU-R process – Sometimes unnamed § Expert consumers of civil time § General public “Several years ago, some scientists § Technology bloggers suggested scheduling a leap hour § Interested journalists for the year 2600. This idea was abandoned as impractical, given that the instructions would have to be left for people six centuries hence. § Bloomberg editorial: But could there instead be, say, a leap minute every half century?” 2 Perspectives of Experts & Officials § Insertion of a leap minute into UTC suggested by Nelson et al. (2001) – “relatively easy to adopt” § Hudson (1967) “Some Characteristics of Commonly Used Time Scales.” Proceedings of the IEEE, Vol. 55, No. 6, June 1967, p. 820. – “Everyday users would not need to be concerned about the introduction of an occasionally modified, atomic scale of time.” – “approximate epochal coherence with the rising and setting of the sun would be retained, and there need be no fear of a radical departure from solar time for ‘everyday’ purposes.” § 2011 Royal Society Discussion Meeting, UK. 3 Perspectives of Specialist Consumers § “Leap minutes or leap hours would be very disruptive.” § “Perhaps, a ‘leap minute’ once a century might do. That would be better than this silly idea of a ‘leap hour’.” § “Why not introducing leap minutes instead of leap seconds?” [as an alternative proposal] § “I am wondering there has been enough discussion regarding introducing 'leap minute' instead of leap second.” [as an alternative proposal] § “But if we want follow day and night variation, then within decades we'll need a leap minute or within millennia a leap hour..
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												  2020 Last-Minute Year- End General Business Income Tax DeductionsAdvantage Tax and Business Services Tax-Saving Tips November 2020 For a cash-basis taxpayer, qualifying expenses 2020 Last-Minute Year- include lease payments on business vehicles, rent payments on offices and machinery, and business End General Business and malpractice insurance premiums. Income Tax Deductions Example. You pay $3,000 a month in rent and would like a $36,000 deduction this year. So on Your goal should be to get the IRS to owe you Thursday, December 31, 2020, you mail a rent money. Of course, the IRS is not likely to cut you a check for $36,000 to cover all of your 2021 rent. check for this money (although in the right Your landlord does not receive the payment in the circumstances, that will happen), but you’ll realize mail until Tuesday, January 5, 2021. Here are the the cash when you pay less in taxes. results: Here are seven powerful business tax-deduction You deduct $36,000 in 2020 (the year you strategies that you can easily understand and paid the money). implement before the end of 2020. The landlord reports taxable income of 1. Prepay Expenses Using the IRS $36,000 in 2021 (the year he received the Safe Harbor money). You just have to thank the IRS for its tax-deduction You get what you want—the deduction this year. safe harbors. IRS regulations contain a safe-harbor The landlord gets what he wants—next year’s entire rule that allows cash-basis taxpayers to prepay and rent in advance, eliminating any collection problems deduct qualifying expenses up to 12 months in while keeping the rent taxable in the year he expects advance without challenge, adjustment, or change it to be taxable.
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												  Chapter 13.2: Topographic Maps 1Chapter 13.2: Topographic Maps 1 A map is a model or representation of objects and terrain in the actual environment. There are numerous types of maps. Some of the types of maps include mental, planimetric, topographic, and even treasure maps. The concept of mapping was introduced in the section using natural features. Maps are created for numerous purposes. A treasure map is used to find the buried treasure. Topographic maps were originally used for military purposes. Today, they have been used for planning and recreational purposes. Although other types of maps are mentioned, the primary focus of this section is on topographic maps. Types of Maps Mental Maps – The mind makes mental maps all the time. You drive to the grocery store. You turn right onto the boulevard. You identify a street sign, building or other landmark and know where this is where you turn. You have made a mental map. This was discussed under using natural features. Planimetric Maps – A planimetric map is a two dimensional representation of objects in the environment. Generally, planimetric maps do not include topographic representation. Road maps, Rand McNally ® and GoogleMaps ® (not GoogleEarth) are examples of planimetric maps. Topographic Maps – Topographic maps show elevation or three-dimensional topography two dimensionally. Topographic maps use contour lines to show elevation. A chart refers to a nautical chart. Nautical charts are topographic maps in reverse. Rather than giving elevation, they provide equal levels of water depth. Topographic Maps Topographic maps show elevation or three-dimensional topography two dimensionally. Topographic maps use contour lines to show elevation.
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												  The Longitude of the Mediterranean Throughout History: Facts, Myths and Surprises Luis Robles MacíasThe longitude of the Mediterranean throughout history: facts, myths and surprises Luis Robles Macías To cite this version: Luis Robles Macías. The longitude of the Mediterranean throughout history: facts, myths and sur- prises. E-Perimetron, National Centre for Maps and Cartographic Heritage, 2014, 9 (1), pp.1-29. hal-01528114 HAL Id: hal-01528114 https://hal.archives-ouvertes.fr/hal-01528114 Submitted on 27 May 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. e-Perimetron, Vol. 9, No. 1, 2014 [1-29] www.e-perimetron.org | ISSN 1790-3769 Luis A. Robles Macías* The longitude of the Mediterranean throughout history: facts, myths and surprises Keywords: History of longitude; cartographic errors; comparative studies of maps; tables of geographical coordinates; old maps of the Mediterranean Summary: Our survey of pre-1750 cartographic works reveals a rich and complex evolution of the longitude of the Mediterranean (LongMed). While confirming several previously docu- mented trends − e.g. the adoption of erroneous Ptolemaic longitudes by 15th and 16th-century European cartographers, or the striking accuracy of Arabic-language tables of coordinates−, we have observed accurate LongMed values largely unnoticed by historians in 16th-century maps and noted that widely diverging LongMed values coexisted up to 1750, sometimes even within the works of one same author.
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												  Prime Meridian ×This website would like to remind you: Your browser (Apple Safari 4) is out of date. Update your browser for more × security, comfort and the best experience on this site. Encyclopedic Entry prime meridian For the complete encyclopedic entry with media resources, visit: http://education.nationalgeographic.com/encyclopedia/prime-meridian/ The prime meridian is the line of 0 longitude, the starting point for measuring distance both east and west around the Earth. The prime meridian is arbitrary, meaning it could be chosen to be anywhere. Any line of longitude (a meridian) can serve as the 0 longitude line. However, there is an international agreement that the meridian that runs through Greenwich, England, is considered the official prime meridian. Governments did not always agree that the Greenwich meridian was the prime meridian, making navigation over long distances very difficult. Different countries published maps and charts with longitude based on the meridian passing through their capital city. France would publish maps with 0 longitude running through Paris. Cartographers in China would publish maps with 0 longitude running through Beijing. Even different parts of the same country published materials based on local meridians. Finally, at an international convention called by U.S. President Chester Arthur in 1884, representatives from 25 countries agreed to pick a single, standard meridian. They chose the meridian passing through the Royal Observatory in Greenwich, England. The Greenwich Meridian became the international standard for the prime meridian. UTC The prime meridian also sets Coordinated Universal Time (UTC). UTC never changes for daylight savings or anything else. Just as the prime meridian is the standard for longitude, UTC is the standard for time.