Flattening the Earth: Mathematical and historical aspects of Mercator projection

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Wlodek Proskurowski
Keyword(s):  
Historical Aspects ◽  
The Earth ◽  
Mercator Projection

UNIVERSAL METRIC BASE (RUMB), UNITS OF ANGLE MEASUREMENT IN GEODESY AND CARTOGRAPHY

2020 ◽  
pp. 53-63
Author(s):  
Nikola Ryazantsev ◽  
◽  
Alexander Nosach
Keyword(s):  
Angle Measurement ◽  
The Earth ◽  
Units Of Measurement ◽  
Mercator Projection ◽  
Rectangular Coordinates ◽  
Measurement Metric ◽  
First Time ◽  
Cylindrical Axis ◽  
Practical Implications ◽  
Objective Study

Objective. Study of ancient cartographic documents in order to clarify the principle of working with a portolan map based on the RUMB metric base. Methodology. Analytical, graphic, mathematical, geodesic. Scientific novelty. For the first time, a table of interrelation of units of measurement of time, angles and distances in the metric base of RUMB is shown. It was found that the so-called portolan maps were built on the basis of RUMB, and their projection is similar to the oblique Mercator projection with a cylindrical axis oriented along the earth’s magnetic axis, with an additional network of rhomb rectangular coordinates, which allows the map to be used at any position of the poles. The Mercator projection is a simplified version of it with one coordinate system. Practical implications. It is shown that dividing the clock face, equator and meridians of the Earth into the same number of parts allows determining the coordinates of points on the Earth’s surface using any of the known parameters, which greatly simplifies the solution of geodetic and navigation problems. Key words: units of measurement, metric base, degree, bearing, portolan map, rose card, projection, coordinate.

Introduction to Systematics

2021 ◽  
pp. 3-34
Author(s):  
Andrew V. Z. Brower ◽  
Randall T. Schuh
Keyword(s):  
Biological Sciences ◽  
Earth Sciences ◽  
Evolutionary Process ◽  
Historical Aspects ◽  
The Earth ◽  
Comparative Framework ◽  
Historical Geology ◽  
Patterns And Processes ◽  
Evolutionary Taxonomy

This introductory chapter provides an overview of systematics, which is the science of biological classification. It embodies the study of organic diversity and provides the comparative framework to study the historical aspects of the evolutionary process. The chapter then explores the nature of systematics as an independent discipline and briefly surveys the literature sources most frequently used by systematists. It differentiates between evolutionary taxonomy, phenetics, and phylogenetics (cladistics). Ultimately, systematics is the most strongly comparative of all of the biological sciences, and its methods and principles transcend the differences between botany and zoology. It is also the most strongly historical field within biology, and as such provides the basis for nearly all inferences concerning historical patterns and processes. Among the earth sciences, systematics is directly comparable to historical geology, and indeed the two fields find integration in paleontology.

Historical Aspects of Agassiz's Lectures on Glacial Geology (1860-61)

1989 ◽  
Vol 8 (1) ◽  
pp. 75-79 ◽  
Author(s):  
Ralph Dexter
Keyword(s):  
Harvard University ◽  
Ice Age ◽  
Glacial Geology ◽  
Historical Aspects ◽  
The Earth ◽  
Comparative Zoology ◽  
Class Room ◽  
Louis Agassiz

Louis Agassiz (1807-1873) is regarded as one of the founders of glacial geology and the originator of the ice-age theory. His public lectures and popular writings included those topics. In 1860-61 he gave a series of class-room lectures on glacial geology to his students at the Museum of Comparative Zoology at Harvard University. Excerpts have been made to show his explanation for the formation of glaciers, their movements, seasonal advancement and retreat, and their eventual covering of much of the earth. Also included were the structure of the glacier, its production of moraines, and its action on bedrocks and the landscape. He gave credit to his predecessors and colleagues, especially de Saussure, Venetz, and de Charpentier, for their pioneering work on glaciers. Brief attention was given to the effect of glaciers on the fauna, according to his interpretation, following the catastrophism theory of Cuvier.

Revisiting the Mercator World Map of 1569: an Assessment of Navigational Accuracy

2016 ◽  
Vol 69 (6) ◽  
pp. 1183-1196 ◽  
Author(s):  
Joaquim Alves Gaspar
Keyword(s):  
New World ◽  
The Novel ◽  
Square Grid ◽  
The Earth ◽  
Mercator Projection

An assessment of the navigational accuracy of the Mercator world map of 1569 is made, aimed at better understanding how the information was adapted from the contemporary cartography. At the time the map was engraved, navigational charts were constructed on the basis of astronomically-observed latitudes, magnetic courses and estimated distances between places. Before this information could be incorporated into the new world map it should be first transformed in such a way that the longitudinal spacings between places were restored to their correct values, as defined on the surface of the Earth. The question of whether Mercator performed such transformations or just considered that the positions were approximately correct has hitherto never been addressed in the literature. It is demonstrated in this article that Mercator was not fully aware of the complexity of the contemporary charts – which he considered to implicitly comprise a square grid of meridians and parallels – and that all planimetric information was directly imported to the novel world map without correction. It is further shown that the Mercator projection was not compatible with the navigational methods of the time.

scholarly journals Interference Identification for Time-Varying Polyhedra

2021 ◽  
Author(s):  
Adam Bienkowski
Keyword(s):  
Traffic Control ◽  
Potential Conflict ◽  
Linear Projection ◽  
The Earth ◽  
Large Numbers ◽  
Mercator Projection ◽  
Maritime Operations ◽  
Conflict Identification ◽  
Polygon Intersection ◽  
Straight Lines

Identification of when and where moving areas intersect is an important problem in maritime operations and air traffic control. This problem can become particularly complicated when considering large numbers of objects, and when taking into account the curvature of the earth. In this paper, we present an approach to conflict identification as a series of stages where the earlier stages are fast, but may result in a false detection of a conflict. These early stages are used to reduce the number of potential conflict pairs for the later stages, which are slower, but more precise. The stages use R-trees, polygon intersection, linear projection and nonlinear programming. Our approach is generally applicable to objects moving in piece-wise straight lines on a 2D plane, and we present a specific case where the Mercator Projection is used to transform objects moving along rhumb lines on the earth into straight lines to fit in our approach. We present several examples to demonstrate our methods, as well as to quantify the empirical time complexity by using randomly generated areas.

scholarly journals A historical account of how continental drift and plate tectonics provided the framework for our current understanding of palaeogeography

2018 ◽  
Vol 156 (2) ◽  
pp. 182-207 ◽  
Author(s):  
G. MEINHOLD ◽  
A. M. CELÂL ŞENGÖR
Keyword(s):  
Earth Sciences ◽  
Plate Tectonics ◽  
Continental Drift ◽  
Historical Aspects ◽  
The Past ◽  
The Earth ◽  
Mountain Belts ◽  
State Of Research ◽  
Analytical Tools ◽  
Shallow Seas

AbstractPalaeogeography is the cartographic representation of the past distribution of geographic features such as deep oceans, shallow seas, lowlands, rivers, lakes and mountain belts on palinspastically restored plate tectonic base maps. It is closely connected with plate tectonics which grew from an earlier theory of continental drift and is largely responsible for creating and structuring the Earth's lithosphere. Today, palaeogeography is an integral part of the Earth sciences curriculum. Commonly, with some exceptions, only the most recent state of research is presented; the historical aspects of how we actually came to the insights which we take for granted are rarely discussed, if at all. It is remarkable how much was already known about the changing face of the Earth more than three centuries before the theory of plate tectonics, despite the fact that most of our present analytical tools or our models were unavailable then. Here, we aim to present a general conspectus from the dawn of ‘palaeogeography’ in the 16th century onwards. Special emphasis is given to innovative ideas and scientific milestones, supplemented by memorable anecdotes, which helped to advance the theories of continental drift and plate tectonics, and finally led to the establishment of palaeogeography as a recognized discipline of the Earth sciences.

scholarly journals Interference Identification for Time-Varying Polyhedra

2021 ◽  
Author(s):  
Adam Bienkowski
Keyword(s):  
Traffic Control ◽  
Potential Conflict ◽  
Linear Projection ◽  
The Earth ◽  
Large Numbers ◽  
Mercator Projection ◽  
Maritime Operations ◽  
Conflict Identification ◽  
Polygon Intersection ◽  
Straight Lines

Identification of when and where moving areas intersect is an important problem in maritime operations and air traffic control. This problem can become particularly complicated when considering large numbers of objects, and when taking into account the curvature of the earth. In this paper, we present an approach to conflict identification as a series of stages where the earlier stages are fast, but may result in a false detection of a conflict. These early stages are used to reduce the number of potential conflict pairs for the later stages, which are slower, but more precise. The stages use R-trees, polygon intersection, linear projection and nonlinear programming. Our approach is generally applicable to objects moving in piece-wise straight lines on a 2D plane, and we present a specific case where the Mercator Projection is used to transform objects moving along rhumb lines on the earth into straight lines to fit in our approach. We present several examples to demonstrate our methods, as well as to quantify the empirical time complexity by using randomly generated areas.

Mathematical Theory of the Mercator Map

1943 ◽  
Vol 36 (8) ◽  
pp. 351-353
Author(s):  
Nelson B. Conkwright
Keyword(s):  
Mathematical Theory ◽  
Large Section ◽  
The Public ◽  
The Earth ◽  
Straight Line ◽  
Mercator Projection ◽  
The Press ◽  
Line Direction

Because of the attention which the Mercator projection has recently received in the press, the manner in which this map is used by the navigator is doubtless familiar to a large section of the public. The projection owes its importance to the fact that the rhumb line direction between two points on the earth can be found by drawing a straight line between the corresponding points on the map, and measuring the angle at which the line intersects the meridians of the map.

scholarly journals "One belt – one road": historical aspects development and regulation of trade

2021 ◽  
Vol 7 (3) ◽  
pp. 79-89
Author(s):  
Mingjun He
Keyword(s):  
World Economy ◽  
Silk Road ◽  
Economic Evolution ◽  
Historical Aspects ◽  
The Past ◽  
The Earth ◽  
One Belt One Road ◽  
The World ◽  
Analysis And Synthesis ◽  
Ancient Silk Road

The article is devoted to a topic that has been significantly updated in the last 5 years – the study of the ancient Great Silk Road as the historical predecessor of the Chinese initiative "One Belt – One Road". This initiative has involved dozens of countries on all continents of the Earth in its sphere. Many of them continue to wonder about the effectiveness of this project for China, other countries, the world economy and trade in general. The purpose of the article is to study the deep historical roots and significance for the socio-economic evolution in the past – with an emphasis on foreign trade aspects-and their role in general economic and humanitarian processes. The historical objectivity and validity of both the ancient Silk Road and the modern "One Belt, One Road" initiative are shown. The author comes to the conclusion that the ancient Great Silk Road played an extremely important role in the socio-economic development of China and other countries along the way, and at the same time provided the opportunity for intercivilizational communication, which together is extremely important in the conditions of the modern unstable world. The following research methods were used in the article: historical and economic analysis, induction and deduction, analysis and synthesis.

The Visual Conquest of International Law: Brute Boundaries, the Map, and the Legacy of Cartogenesis

2018 ◽  
Vol 31 (2) ◽  
pp. 267-288 ◽  
Author(s):  
NIKOLAS M. RAJKOVIC
Keyword(s):  
Social Science ◽  
International Relations ◽  
International Law ◽  
Earth Space ◽  
Spatial Literacy ◽  
The Earth ◽  
Mercator Projection ◽  
International Authority ◽  
Geometric Mapping ◽  
Material Power

AbstractThe late critical geographer Brian Harley forewarned that modern cartography had come to control and even ‘imprison’ spatial understandings of the earth. Where does this leave international lawyers when they encounter a quintessential ‘World Map’? Quite bluntly: tied to an inscriptive institution that has embodied the modern legibility and visualization of earth space. When speaking about the global arrangements of economic and political power constituted through law, what emerges, therefore, is the need for an expanded spatial literacy among international lawyers that critically engages the graphic legacy and influence of the geometric map. To enhance that literacy, I reach beyond the doctrinal field to engage a powerful spatial critique that has thus far encompassed scholarship across geography, international relations (IR) and sociology. A critique that took impetus over 20 years ago with John Agnew's assertion that modern social science had become captured by a ‘territorial trap’. The article attempts to enrich that critique with Mark Salter's insight on material power, Marshall McLuhan's emphasis on the medium of communication, and Bruno Latour's critique of cartographic naturalism. Specifically, I introduce the concept of cartogenesis as a way of underlining the deeper legacy and consequence of modern cartography, and specifically how the map medium should be grasped as a historical actant that has inscribed a particular ‘ground map’ of international authority. Lastly, the article looks at how geometric mapping now confronts new inscriptive ordering in the forms of transnational lists and contracts, which assert a growing scale of authority over earth space to an extent not seen since the Mercator Projection was recognized as an overriding geographic model.

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