Caldecott Honor winner Grace Lin celebrates math for every kid, everywhere! Manny and his friends Olivia and Mei blow bubbles in this playful introduction to geometry. Manny's wand is a circle. Olivia's wand is a square. Mei's wand is a heart. What shape will their bubbles be? (Surprise! They're all spheres.) Storytelling Math celebrates children using math in their daily adventures as they play, build, and discover the world around them. Joyful stories and hands-on activities make it easy for kids and their grown-ups to explore everyday math together. Developed in collaboration with math experts at STEM education nonprofit TERC, under a grant from the Heising-Simons Foundation.
For thousands of years, people believed the Earth was flat. Similarly, everything we believe about hell, the devil and karma is based on centuries of dogma, illogical beliefs and foolish theories. In this book, Samael Aun Weor demonstrates how to confirm for yourself the reality of the inferior levels of life, and how to avoid them. Although modern culture laughs at the mere mention of the devil and hell while simultaneously indulging deeply in them via popular music, movies, and television, the practical reality remains completely unknown to the general public. Samael Aun Weor discusses his personal, conscious experiences of the inferior worlds and the beings who reside there. By application of ancient techniques preserved by the Gnostic tradition, anyone can confirm with certainty what exists in the subtle dimensions of nature, whether above or below. Learn the true identity of both the Devil and Lucifer, and how to harness the forces of nature in order to be propelled towards a higher way of life. Dispels centuries of beliefs and theories, while explaining the essential truths hidden in ancient symbols Provides practical steps towards acquiring your own experience of the truth Supported by solid science and authentic spiritual traditions
This new revision of a standard work gives a general but comprehensive introduction to positional astronomy. Useful for researchers as well as undergraduates.
Caldecott Honor winner Grace Lin celebrates math for every kid, everywhere! Mei explores measurement as she plants a sunflower seed and watches it grow. The plant starts off as tall as her toe, but soon it's up to her knees, then her waist, then her shoulders. How tall will it get? Storytelling Math celebrates children using math in their daily adventures as they play, build, and discover the world around them. Joyful stories and hands-on activities make it easy for kids and their grown-ups to explore everyday math together. Developed in collaboration with math experts at STEM education nonprofit TERC, under a grant from the Heising-Simons Foundation.
Praise for the previous edition [. . .] Dr. Popko’s elegant new book extends both the science and the art of spherical modeling to include Computer-Aided Design and applications, which I would never have imagined when I started down this fascinating and rewarding path. His lovely illustrations bring the subject to life for all readers, including those who are not drawn to the mathematics. This book demonstrates the scope, beauty, and utility of an art and science with roots in antiquity. [. . .] Anyone with an interest in the geometry of spheres, whether a professional engineer, an architect or product designer, a student, a teacher, or simply someone curious about the spectrum of topics to be found in this book, will find it helpful and rewarding. – Magnus Wenninger, Benedictine Monk and Polyhedral Modeler Ed Popko's comprehensive survey of the history, literature, geometric, and mathematical properties of the sphere is the definitive work on the subject. His masterful and thorough investigation of every aspect is covered with sensitivity and intelligence. This book should be in the library of anyone interested in the orderly subdivision of the sphere. – Shoji Sadao, Architect, Cartographer and lifelong business partner of Buckminster Fuller Edward Popko's Divided Spheres is a "thesaurus" must to those whose academic interest in the world of geometry looks to greater coverage of synonyms and antonyms of this beautiful shape we call a sphere. The late Buckminster Fuller might well place this manuscript as an all-reference for illumination to one of nature's most perfect inventions. – Thomas T. K. Zung, Senior Partner, Buckminster Fuller, Sadao, & Zung Architects. This first edition of this well-illustrated book presented a thorough introduction to the mathematics of Buckminster Fuller’s invention of the geodesic dome, which paved the way for a flood of practical applications as diverse as weather forecasting and fish farms. The author explained the principles of spherical design and the three classic methods of subdivision based on geometric solids (polyhedra). This thoroughly edited new edition does all that, while also introducing new techniques that extend the class concept by relaxing the triangulation constraint to develop two new forms of optimized hexagonal tessellations. The objective is to generate spherical grids where all edge (or arc) lengths or overlap ratios are equal. New to the Second Edition New Foreword by Joseph Clinton, lifelong Buckminster Fuller collaborator A new chapter by Chris Kitrick on the mathematical techniques for developing optimal single-edge hexagonal tessellations, of varying density, with the smallest edge possible for a particular topology, suggesting ways of comparing their levels of optimization An expanded history of the evolution of spherical subdivision New applications of spherical design in science, product design, architecture, and entertainment New geodesic algorithms for grid optimization New full-color spherical illustrations created using DisplaySphere to aid readers in visualizing and comparing the various tessellations presented in the book Updated Bibliography with references to the most recent advancements in spherical subdivision methods
