Mathematics in the Maritime
In this chapter maritime history is explored in relation to the mathematics that arose from solving basic problems of determining ones location on the ocean, viz., latitude and longitude. Celestial navigation and GPS navigation techniques arose as a resul
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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculating Latitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculating Longitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Map Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Global Positioning Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Least Squares Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Advent of Insurance and Actuarial Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Abstract In this chapter maritime history is explored in relation to the mathematics that arose from solving basic problems of determining ones location on the ocean, viz., latitude and longitude. Celestial navigation and GPS navigation techniques arose as a result of the need to accurately travel from one point to another and determine locations in transit. Oceans cover over 70% of the earth’s surface, and its exploration is traced back to ancient civilizations attempting to travel upon the water. Over time, different devices were invented for navigation across the ocean, each device becoming more sophisticated but using similar mathematical themes. Navigation on the ocean also presented new risks to safety and marked the advent
K. Mycroft () University of Montana, Missoula, MT, USA e-mail: [email protected] B. Sriraman Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA e-mail: [email protected] © Springer Nature Switzerland AG 2020 B. Sriraman (ed.), Handbook of the Mathematics of the Arts and Sciences, https://doi.org/10.1007/978-3-319-70658-0_137-1
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of insurance and actuarial science. These secondary aspects of maritime history are also discussed.
Keywords Latitude · Longitude · Map making · Navigation · Least squares · Global positioning systems · Insurance · Risk
Introduction Humanity has often struggled with finding its way, philosophically and realistically. Navigating within one’s comfort zone is done with ease and familiarity. People may be tempted to remain within their comfort zone, but our collective history indicates that there have alway
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