﻿ Peirce Projection

# Peirce Projection

Often incorrectly spelled as the "Pierce" projection, this projection is a conformal projection also known as a quincuncial projection. It is a transverse case of the Guyou projection.

Caution: This is a "one-way" projection in terms of accuracy in that once data is projected into the Peirce coordinate system it cannot be re-projected to other systems without some loss of precision. The definition of the projection in common use does not include formulae for the inverse transformation, so projecting from Peirce to latitude / longitude uses iterative approximations and thus can lose precision.

###### Scale

Not true anywhere. Scale is especially false in the corners of the projection, where scale is elongated, and at the poles, where scale is compressed.

###### Distortion

The projection is conformal except at the four "corners" of the Equator. Conformality (and therefore local angle preservation) fails at the corners.

###### Usage

Useful for showing polar regions.

When North Pole and South Pole hemispherical aspects are used as tiles as seen above, may be used to create interesting floors for bathrooms, as they may be tiled infinitely to create a display that allows any point on Earth to be viewed in a direct line from any other point.

###### Limiting Forms

The Guyou and Peirce projections are transverse cases of each other. The Guyou is the equatorial aspect (hence the classification as a psuedocylindrical projection within Manifold) and the Peirce is the polar aspect (hence the classification as an azimuthal projection within Manifold).

The term "quincuncial" refers to a presentation using a whole-Earth form of this projection into a square consisting of a central diamond square and four corner one-fourth squares, thus having five regions (Latin for five is quinque).

###### Options

Specify the center of the projection by setting latitude origin and longitude origin.

###### Origin

Invented by Charles Sanders Peirce in 1879 while he was at the U.S. Coast and Geodetic Survey.

###### Charles Sanders Peirce (1839-1914)

A classic example of a very bright individual who dabbled in many areas but left virtually no enduring mark in history, Peirce was a troublesome employee at the U.S. Coast and Geodetic Survey until eventually resigning in 1891.

He invented a philosophical approach called Pragmatism he hoped would provide a counterpoint to Kant, invented a method of obtaining acetylene, set forth a means for defining the meter by a wavelength of light, was fond of presenting logic using "semiotics" (a theory of signs), observed occultations, obtained a degree in Chemistry at Harvard in 1863 and died mired in poverty and illness in 1914 after being unable to find steady employment after leaving the Survey.

Peirce continues to have his fans, who create websites reprinting his philosophical gems such as: "Thought is what it is only by virtue of its addressing a future thought which is in its value as thought identical with it, though more developed.  In this way, the existence of thought now depends on what is to be hereafter; so that it has only a potential existence, dependent on the future thought of the community." ...Thus speaks a pragmatist!

The Peirce quincuncial projection seems typically Peirce in that its use of elliptical integrals for computation achieves a result through fearsomely complex means when simpler methods would seem to serve as well.

When contemplating Peirce's life one wonders how it is that accidents of history have elevated some would-be philosophers to super stardom while others have been consigned to the dustbin of history. For example, but for an accident of utopian popularity, Marx, too, like Peirce could have ended up as yet another unknown kook beavering away at writings that made sense only to him.