# Flat Maps that improve on the Winkel Tripel

@inproceedings{Gott2021FlatMT, title={Flat Maps that improve on the Winkel Tripel}, author={J. Richard Gott and David M. Goldberg and Robert J. Vanderbei}, year={2021} }

Goldberg & Gott (2008) developed six error measures to rate flat map projections on their verisimilitude to the sphere: Isotropy, Area, Flexion, Skewness, Distances, and Boundary Cuts. The first two depend on the metric of the projection, the next two on its first derivatives. By these criteria, the Winkel Tripel (used by National Geographic for world maps) was the best scoring of all the known projections with a sum of squares of the six errors of 4.563, normalized relative to the…

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## References

SHOWING 1-10 OF 21 REFERENCES

A map of the universe

- Physics, Geology
- 2003

We have produced a new conformal map of the universe illustrating recent discoveries, ranging from Kuiper Belt objects in the solar system to the galaxies and quasars from the Sloan Digital Sky…

Part 2: Distortion-Spectrum Applications Projection Cross-breeding

- Computer Science
- 1997

The concept of projection cross-breeding is introduced as a technique of mixing two or more 'parent' MCME projections selected from the MCME Atlas in order to produce an 'offspring' projection that minimizes cartographic distortions and inherits the most desirable cartographic characteristics for the specific data-mapping task.

ANALYSIS OF THE KOREAN CELESTIAL PLANISPHERE

- Physics
- 1996

We have analyzed the content of the Korean stone star chart. Ch'on-Sang-Yul-Cha-Bun-Ya-Ji-Do(here-after Ch'on-Sang-Do). In the star map we have found 1468 stars, 4 more than the Chinese star catalog…

Part 1: Distortion-Spectrum Fundamentals A New Tool for Analyzing and Visualizing Map Distortions

- Computer Science
- 1997

The basic techniques for calculating map distortions are reviewed, and several new concepts in analytic cartography are introduced together with the pertinent terminology: standardization of…

The Cosmic Web: Mysterious Architecture of the Universe

- Physics
- 2016

It is fair to say that Edwin Hubble discovered the universe. Leeuwenhoek peered into his microscope and discovered the microscopic world; Hubble used the great 100inchdiameter telescope on Mount…

Three-dimensional nets and polyhedra

- Mathematics
- 1977

In a storage room of the University of Minnesota, there used to be (and probably still are) four large isosceles triangular mirrors, with edges proportional to 2 : y/3 : y3 , relics of an abandoned…

Motives for Patenting a Map Projection: Did Fame Trump Fortune?

- Economics
- 2018

ABSTRACT John Parr Snyder claimed that patenting a map projection was largely pointless because essentially similar transformations are readily available in the public domain. Map projection patents…

The Sponge-like Topology of Large-Scale Structure in the Universe

- Physics
- 1986

We describe and apply a quantitative measure of the topology of large scale structure: the genus of density contours in a smoothed density distribution. For random phase (gaussian) density fields,…

Calculation and Visualization of Flexion and Skewness

- PhysicsKartografija i geoinformacije
- 2018

A recent study on map projections expanded two new measures of distortion, namely flexion and skewness. However, it introduced them only for the unit sphere. The present paper derives formulas for…

REFLECTIONS ON REFLECTION IN A SPHERICAL MIRROR

- Mathematics, Physics
- 1998

(1998). Reflections on Reflection in a Spherical Mirror. The American Mathematical Monthly: Vol. 105, No. 6, pp. 523-528.