This book is about exploring the tetrahedron by using only the nine creases generated by folding the tetrahedron into a paper circle. It has more mathematical and educational information than The Wholemovement of Geometry: folding the circle for information book. At the same time the tetrahedron folds takes the circle folding process to a deeper level, folding forms observed in the natural world, making stronger connections to art and mathematics, and demonstrating algebraic functions experientially appropriate for 5 and 6 years old students. A hands-on ethics is observed and discussed that only occurs with folding the circumference. Most of the folding and information in this book is new, and what is carried over is different in presentation. It stands on its own without any prerequisite. This makes it a good companion to The Wholemovement of Geometry.

In a broad sense Design Science is the grammar of a language of images rather than of words. Modern communication techniques enable us to transmit and reconstitute images without the need of knowing a specific verbal sequential language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multidimensional. Architectural renderings commonly show projections onto three mutually perpendicular planes, or consist of cross sections at differ ent altitudes representing a stack of floor plans. Such renderings make it difficult to imagine buildings containing ramps and other features which disguise the separation between floors; consequently, they limit the creativity of the architect. Analogously, we tend to analyze natural structures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures.

Integrate practical insights from modern physics, ancient Hermetic Laws, non-dual meta-physics, transpersonal psychology, and humor, as tools for undoing conflicting beliefs we've dreamed ourselves into. The seven Hermetic laws are explored in depth and demonstrate how a mindfulness that embraces 'other' as 'self' can reverse the typical misapplication of these inescapable laws of Mentalism, Correspondence, Vibration, Polarity, Rhythm, Cause & Effect and Generation. Ubiquitous geometric symbols, paired to each of these laws - the circle, vesica piscis, sine wave, line, spiral, fractal and yin-yang - and their countless commonplace variations, seen from the vantage point of shared interests, reflect these ideas. The inspired use of natural law restores attributes of life, love, strength, purity, beauty, perfection and gratitude to our awareness.

Synergetics 2 contains a ninety-page index to both volumes. They comprise a single work with the sequence of paragraphs numbered to dovetail in a single integrated narrative. They should eventually be published as a single work eliminating the artificial division into two volumes resulting from the chronology of their composition. E. J. Applewhite, courtesy of the Estate of R. Buckminster Fuller

This 256 page resource has 221 full page black and white "line art" graphic images. The ready-to-use templates teach by "whole brain" play and creative exploration, with over 1300 smaller images surrounding the central full page image on each page, providing examples of countless variations for the creative explorer of this art form and science. In addition to a large collection of 2-dimensional patterns, a "coloring book for kids of all ages", there are 27 3-dimensional "fold-up" patterns which make it easier than ever before to create exquisite shapes revered by pioneers such as Plato, Pythagoras, and Leonardo daVinci. There is a brief introductory section on the philosophical perspective of universal proportions and symbols. The book also has extensive tables, World Wide Web links and bibliographic references for those whose interest and curiosity has been sparked by the hands-on, experiential majority of the book. It is a reference for serious students of geometry and its omnipresent purpose. This is a newer, perfect bound version of the book which has also been available in a spiral-bound version since 1997.

This volume contains the papers presented at the International Conference on Challenges in Mathematics Education for the Next Decade held from September 10-15, 2017 in Balatonfüred, Hungary. The Conference was organized by The Mathematics Education for the Future Project – an international edu­cational project founded in 1986.