## Cartographic Science: A Compendium of Map Projections, with DerivationsGeographic books routinely introduce map projections without providing mathematical explanations of projections and few delve into complex mathematical development or cover the breadth of projections. From basic projecting to advanced transformations, Cartographic Science: A Compendium of Map Projections, with Derivations is a comprehensive reference that offers an explanation of the science of cartography. The book is a compilation of more than a hundred map projections, from classic conics to contemporary transformations using complex variables. Starting from widely described geometric projecting onto flat paper, cylinder, and cone and then progressing through several layers of mathematics to reach modern projections, the author maximizes the application of one layer of complex mathematics before continuing on to the next. He also supplies numerous one-page tutorials that review terms and methodologies, helping minimize the challenges of unfamiliar mathematical territory. Divided into four parts, the first section examines the shape and size of the Earth, then proceeds to investigate the means for relating the curved surface to a flat surface, and addresses scaling. It goes on to cover pertinent principles of projection including literal projecting, true but synthetic projections, secantal projections, pseudocylindrical projections, and pseudoconical projections, as well as the other variants of more serious projections. The book concludes by looking at factors influencing Mean Sea Level and notes the cartographic aspects of current developments. Cartographic Science: A Compendium of Map Projections, with Derivations explains the mathematical development for a large range of projections within a framework of the different cartographic methodologies. This carefully paced book covers more projections, with gentle and progressive immersion in the mathematics involved, than any other book of its kind. |

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### Contents

THE CURVED WORLD | 1 |

Tutorial number and title | 2 |

Curved Earth to flat map | 3 |

A globe as model and intermediary | 25 |

A SPHERICAL WORLD | 37 |

Literal projections | 39 |

Equidistant and other algebraic variants | 65 |

Secantal projections | 101 |

More conformal projections | 347 |

Novelty projections | 363 |

AN ELLIPSOIDAL WORLD | 377 |

Location Page number | 378 |

Ellipses and ellipsoids | 379 |

UTM and UPS | 411 |

THE REAL WORLD | 431 |

The geoid and geodesy | 433 |

Pseudo projections | 125 |

Interrupted and composite maps | 167 |

At oblique aspect | 187 |

Globular projections | 221 |

Extension by arithmetic tricks | 239 |

Twopoint and nonazimuthal Azimuthals | 261 |

Differential geometry | 277 |

Of scales and distortion | 293 |

Optimizing distortion | 323 |

APPENDICES | 447 |

A Greek letters and words | 448 |

B Glossary of symbols | 450 |

Glossary of terms | 456 |

Index to projections | 460 |

E Historical bibliography | 470 |

487 | |

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### Common terms and phrases

3-dimensional angle applied authalic auxiliary axes axis Azimuthal Azimuthal projection Bonne projection cartographic central meridian centre Chapter circle circular arcs co-ordinates complex numbers cone conformal map conformal projections Conical projection cos0 curvature curved Cylindrical projection defined denote derived developable surface developed differential Earth ellipse ellipsoid equal Equal-area Azimuthal Equatorial aspect Exhibit factor flat-polar formulae function geometry gives globe Gnomonic graticule great-circle distance grid Grinten hemisphere hence identical illustrated intermediate parameters intersection Lambert length longitude and latitude loxodrome mathematical Mercator Mercator projection Mollweide multiplier Obliq Oblique aspect orthogonal Orthographic Perspective plane Plate-Carree plotting equations Polyconic Polyconic projection projection at Simple provides Pseudocylindricals Putnins radial radians radius secantal Simple aspect sin0 Sinusoidal Sinusoidal projection spacing of parallels sphere spherical standard parallels Stereographic projection straight lines Substituting from Equation surface tangential transformation triangle true scale Tutorial variable vector whole world zero zone

### Popular passages

Page 479 - Elements of Map Projection, with Applications to Map and Chart Con-struction.— Charles H. Deetz, Cartographer, and Oscar S.