Fields Book 
Store - Soulful and scholarly books from the world's spiritual traditions

Projective Geometry (New)

by Edwards, Lawrence

Publisher: Steiner Books

Binding: Paperback

Book ID: 9780863153938, 0863153933


Usually available in 1-2 weeks


Projective geometry is a non-metrical form of geometry that emerged in the early nineteenth century. It originated from the principles of perspective art. Here, he presents a clear and artistic understanding of the intriguing qualities of projective geometry.

Projective geometry formalizes a central principle of perspective art -- that parallel lines meet at infinity and, therefore, should be drawn that way. Essentially, projective geometry may be viewed as an extension of Euclidean geometry -- one in which the "direction" of each line is subsumed within the line as an extra "point," and in which a "horizon" of directions corresponding to coplanar lines is regarded as a "line." Thus, two parallel lines will meet on a horizon because they possess the same direction.

In the spirit of projective geometry’s origins in synthetic geometry, some mathematicians have investigated projective geometry as a useful means to describe natural phenomena. The first research in this direction was stimulated by a suggestion from the philosopher and spiritual teacher Rudolf Steiner.

In the mid-twentieth century, Louis Locher-Ernst explored the tension between central forces and peripheral influences. Lawrence Edwards discovered significant applications of projective geometry (Klein path curves) to organic development. In the spirit of D'Arcy Thompson's On Growth and Form, but with greater mathematical rigor, Edwards demonstrated that forms such as the buds of leaves and flowers, pine cones, eggs, and the human heart can be described simply through the use of certain path curves. Varying a single parameter -- lambda -- transforms the interaction of what projective geometry calls "growth measures" into surprisingly accurate representations of many organic forms, which are otherwise not easily described through mathematics. Moreover, negative values of the same parameter produce inversions representing vortexes of both water and air.

Lawrence Edwards researched and taught projective geometry for more than forty years. His book will reveal the secrets of space to those who work through its more than two hundred instructive diagrams and exercises. Projective Geometry is an essential resource for teachers of Waldorf education or for those who wish to strengthen their thinking and expand their view of mathematics.

Lawrence Edwards (1911–2004) studied the work of Rudolf Steiner and, until he retired, was a Waldorf class teacher and an upper school mathematics teacher at the Edinburgh Rudolf Steiner School. He was inspired toward scientific research after studying projective geometry with George Adams and, following a "second career," researching whether the path curves he had learned about applied also to forms in nature. He confirmed this and discovered important rhythmic processes in earthly nature that correlate with celestial rhythms. He lectured widely all over the world.

Deconstructing Gurdjieff: Biography of a Spiritual Magician Deconstructing Gurdjieff: Biography of a Spiritual Magician
Churton, Tobias
Inner Traditions / Bear & Company

In November 1949, architect Frank Lloyd Wright announced the death of "the greatest man in the world," yet few knew who he was talking about. Enigmatic, misunderstood, declared a charlatan, and recently dubbed "the Rasputin who inspired Mary Poppins," Gurdjieff's life has become a legend. But who really was George Ivanovich Gurdjieff?

Employing the latest research and discoveries, including previously unpublished reminiscences of the real man, Tobias Churton investigates the truth beneath th...

Price: $29.95

The Complete Mystical Records of Dr. John Dee: Transcribed from the 16th-Century Manuscripts Documen The Complete Mystical Records of Dr. John Dee: Transcribed from the 16th-Century Manuscripts Documen
Klein, Kevin
Llewellyn Worldwide, Ltd.

A lavishly packaged, two-volume box set containing the most faithful and accurate versions of John Dee's journals ever published. This is a must-have treasure for Dee aficionados and esoteric scholars who absolutely need the most meticulously detailed version of these highly influential works. A labor of love twenty years in the making, these volumes include transcripts of four manuscripts from the British Library and one from the Bodleian Library in Oxford. Two of these manuscripts have never b...

Price: $200.00

Tarot Sola Busca: Ferrara XV Century Tarot Sola Busca: Ferrara XV Century
Lo Scarabeo
Lo Scarabeo

One of the oldest tarot decks ever created, the Tarot Sola Busca is known for its alchemical symbolism and for having inspired many of the minor arcana of the Rider Waite Smith deck. The first entry in Lo Scarabeo's new Anima Antiqua series (Ancient Soul), this deck has been lovingly printed with great care from originals found in the greatest collections of rare tarot decks. This is a limited-edition, numbered deck printed on the highest quality stock.

The companion booklets f...

Price: $34.95

Treading the Mill: Workings in Traditional Witchcraft (Revised and expanded) Treading the Mill: Workings in Traditional Witchcraft (Revised and expanded)
Pearson, Nigel G
Troy Books

In Treading the Mill, Suffolk witch Nigel Pearson presents an extensive and thorough exploration of the working ways of the modern traditional witch, including Compass rites, directional virtues, tools & their hallowing, spellcrafting, wortcunning, transvection, spirit familiars, faerie lore, the old gods, self-dedication and much more.

Price: $20.95

Jim Maynard's Celestial Influences 2018: Pacific Time (9" x 12") Jim Maynard's Celestial Influences 2018: Pacific Time (9" x 12")
Maynard, Jim
Quicksilver Productions

Celestial Influences is an essential astrological reference. It is the best astrological calendar available. It opens to 12 x 18 inches. The zodiac months are highlighted with a colored tint and the zodiac illustrations are in full color.

12 x 9 inches, 48 pages, full-color cover, full-color illustrations.

Price: $13.95