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A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science

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The Universe May Be a Mystery,But It's No Secret Michael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through ten to explore the mathematical principles made visible in flowers, shells, crystals, plants, and the human body, expressed in the symbolic language of folk sayings and fairy tales, myth and religion, art and architecture. The Universe May Be a Mystery,But It's No Secret Michael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through ten to explore the mathematical principles made visible in flowers, shells, crystals, plants, and the human body, expressed in the symbolic language of folk sayings and fairy tales, myth and religion, art and architecture. This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round.Why one and two weren't considered numbers by the ancient Greeks.Why squares show up so often in goddess art and board games.What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster a cathedral, and much more.


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The Universe May Be a Mystery,But It's No Secret Michael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through ten to explore the mathematical principles made visible in flowers, shells, crystals, plants, and the human body, expressed in the symbolic language of folk sayings and fairy tales, myth and religion, art and architecture. The Universe May Be a Mystery,But It's No Secret Michael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through ten to explore the mathematical principles made visible in flowers, shells, crystals, plants, and the human body, expressed in the symbolic language of folk sayings and fairy tales, myth and religion, art and architecture. This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round.Why one and two weren't considered numbers by the ancient Greeks.Why squares show up so often in goddess art and board games.What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster a cathedral, and much more.

30 review for A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science

  1. 5 out of 5

    David

    I have just finished reading this book, and I like some parts of it. After getting over my initial disappointment, I realized that I had expectations from its title, and the title simply is misleading. The book is really about geometric patterns in our culture and in ancient and other modern cultures. Where do these patterns come from, and how do they manifest in art, in symbology, in philosophy. Many of the geometric patterns--maybe all of them--come from nature, and that is where the author ti I have just finished reading this book, and I like some parts of it. After getting over my initial disappointment, I realized that I had expectations from its title, and the title simply is misleading. The book is really about geometric patterns in our culture and in ancient and other modern cultures. Where do these patterns come from, and how do they manifest in art, in symbology, in philosophy. Many of the geometric patterns--maybe all of them--come from nature, and that is where the author ties in to nature. The problem with the book, is that the author himself does not really understand what his book is really about. It's not about science. While the book asks science-related questions, (why do we see a spiral shape in shells, galaxies, hurricanes, and watery whirlpools), there are no science answers. And when the book does reflect on an interesting science question, like how does light penetrate through glass, the author says "E=mc2" as if the formula offers an explanation. The author seems truly ignorant of science, but I think he states Einstein's formula as a symbolic triad that pervades many cultures, rather than as a scientific explanation. The author has tried to organize the material in 10 chapters devoted, each in turn, to the numbers 1-10. But in so doing, he makes a mistake; in each chapter he tries to come up with all the examples he can think of, where that number appears in everyday life. Some of the examples are absolutely banal. For example, in Chapter 8 he mentions that in an octagon, there are 8 corner angles each covering 135 degrees, so the total angle adds up to 1080 degrees, which is the same as the radius of the moon, expressed in miles. Like this explains anything? Don't look to this book for a better understanding of nature or science. Instead, (once you get past the New Age banalities) look at this book to understand a little better, the subtle forms in which geometric patterns manifest themselves in cultures, in art, philosophy, and spiritualism, and where people copied them out of nature.

  2. 5 out of 5

    Ami

    I just can't slog through this book anymore. It was another book I really wanted to like. I read some reviews that warned me that it was less "Math, Nature, Art & Science" and more "New Age hoo-hah" and unfortunately that turned out to be the case. I can't verify that the connections the author is making are not true, just like I can't verify that they're not, because everything is written in that completely unsourced manner. But not only is it unsourced, it's also unexplained thoroughly, and sor I just can't slog through this book anymore. It was another book I really wanted to like. I read some reviews that warned me that it was less "Math, Nature, Art & Science" and more "New Age hoo-hah" and unfortunately that turned out to be the case. I can't verify that the connections the author is making are not true, just like I can't verify that they're not, because everything is written in that completely unsourced manner. But not only is it unsourced, it's also unexplained thoroughly, and sort of glossed over until there is just a vomited pile of stuff about whatever number/shape/idea the author is on, lying at my feet, about which I am dubious. Maybe I'm being too harsh, and I know that I have enjoyed many a feel-good yet unsourced pseudoscientific book before, but this one just rubbed me the wrong way. Around the first chapter, I encountered this pivotal rambling sentence: "In Hindu mythology, the dimensionless Brahma speaks aloud the word aham, 'I Am,' a word made of the first, middle, and final letters of the Sanskrit alphabet, which represents the circle's three parts; the center, the radius, and the cicumference, and our own spiritual center, psychological reaches, and outer material form". I decided then that this book is a skimmer, and that I would mostly look at the photos and read their captions. But by the time I got to the number 3, the author had started doing things like drawing triangles over pictures of thiings that did not really have triangular shapes, so that we could see how the "pattern" shows up again & again. Like, a butterfly, do you see how it looks like a triangle, man? Except I think it looks more like a pentagram shape, but then he draws a pentagram over a bat that is shaped more like a triangle in chapter 5. And by then he's got calipers next to every photo and I've given up.

  3. 4 out of 5

    Bruce

    This is a wonderfully accessible book that takes each of the numbers from one to ten and devotes a chapter to the symbology and geometry behind it. The author does an amazing job condensing a vast amount of historical and mathematical information into a concise and highly readable text. He is a professional educator and it shows (in a good way) Contemplating/meditating on the concepts in this book has been very conducive to some powerful experiences*. This book is a real keeper and I go back to i This is a wonderfully accessible book that takes each of the numbers from one to ten and devotes a chapter to the symbology and geometry behind it. The author does an amazing job condensing a vast amount of historical and mathematical information into a concise and highly readable text. He is a professional educator and it shows (in a good way) Contemplating/meditating on the concepts in this book has been very conducive to some powerful experiences*. This book is a real keeper and I go back to it for reference from time to time. Highly recommended. If you are more of a multi media person you can get a DVD containing some of the same (and some additional) information presented in more of a slide show format-- just google for the author's web site. To get technical, in the introduction the author discusses the differences between symbolic and sacred geometry, and says the book is mostly about symbolic. But the sacred aspect of it oozes out of every word. A great reference for those seeking enlightenment :-)

  4. 4 out of 5

    Rebekah

    I was lucky enough to chance upon a free copy of this book. It's amazing and wonderful. It takes you through the basic numbers, showing you how to construct a regular polygon using only a compass and straight edge to emphasize how everything emerges from one. Everything is connected in that way. Everything emerges from the same place. It goes on to discuss the importance of that particular number, shape or related sequence in how nature is constructed, and what that number has symbolized histori I was lucky enough to chance upon a free copy of this book. It's amazing and wonderful. It takes you through the basic numbers, showing you how to construct a regular polygon using only a compass and straight edge to emphasize how everything emerges from one. Everything is connected in that way. Everything emerges from the same place. It goes on to discuss the importance of that particular number, shape or related sequence in how nature is constructed, and what that number has symbolized historically. If I had read this years earlier, maybe I would have paid a bit more attention in math classes.

  5. 4 out of 5

    Fayren

    Whoever thinks our world is just full of chaos should read this book! It's all actually magically organized.

  6. 5 out of 5

    Janet

    This is an excellent, almost magical book about how the essential nature of numbers, their relationship with each other, and the patterns that arise from them shape the foundation of our world. It is also very dense, and the larger the numbers got the harder it was for me to read. (Your mileage may vary.) Eventually I realized I was not going to finish it, but it's going to stay on my shelves as an inspirational resource. I would recommend it to parents of young children as a way of inspiring you This is an excellent, almost magical book about how the essential nature of numbers, their relationship with each other, and the patterns that arise from them shape the foundation of our world. It is also very dense, and the larger the numbers got the harder it was for me to read. (Your mileage may vary.) Eventually I realized I was not going to finish it, but it's going to stay on my shelves as an inspirational resource. I would recommend it to parents of young children as a way of inspiring your kids to look at and interact with numbers in a new way. You wouldn't give this book to a child, but if you glean the essence of it and share it, it could be great. It would be great for middle readers as well, although -- again -- with the caveat that they wouldn't necessarily want to read every word, but to get the basic ideas, which would open up their experience and understanding of numbers, geometry, biology, and etc.

  7. 5 out of 5

    Camille

    Wow! This book is about more than math. It connects science, literature, philosophy,religion, art and architecture. I plan on using this as our core book for our homeschool studies in the fall. I was hooked from the very first page, and kept thinking how much I would have loved math in school, if I'd had a teacher like Michael Scneider.

  8. 5 out of 5

    Jenny

    FASCINATING read on sacred geometry and the archetypes of the numbers 1-10: where they show up in nature, language, history and architecture, and how they inform every aspect of our own being/consciousness/transformation. Definitely esoteric and not for everyone, but I loved it. Recommended by my teacher at Katonah Yoga, Nevine Michaan.

  9. 4 out of 5

    Evan

    This book is amazing!!!!

  10. 4 out of 5

    Debbie

    I wish they would teach geometry like this in school!

  11. 4 out of 5

    Haley

    I've read this book many times over, one of my very favorite books on numbers. Instructions for making the platonic solids out of paper and golden calipers too.

  12. 4 out of 5

    Gavin White

    I have mixed feelings in regard to this book. It took me three goes to finish it and it ended up being a bit of a struggle. On the positive side I have learnt many interesting nuggets of geometric and mathematical lore and some new graphic procedures. On the other hand, it was very 'New Age' in its approach and the terms of its narrative. I would have preferred a more classical philosophical approach in line with the Neo-Platonists rather than a load of Jungian psycho-babble about personal growt I have mixed feelings in regard to this book. It took me three goes to finish it and it ended up being a bit of a struggle. On the positive side I have learnt many interesting nuggets of geometric and mathematical lore and some new graphic procedures. On the other hand, it was very 'New Age' in its approach and the terms of its narrative. I would have preferred a more classical philosophical approach in line with the Neo-Platonists rather than a load of Jungian psycho-babble about personal growth, saving the planet and raising one's consciousness etc. I also noticed several factual errors in the text, and given that there are no footnotes it is impossible to check sources - so I reckon there are plenty more errors dotted around. At the end of the day, what you get here is one person's synthesis of the geometric cannon set out around the numbers 1 to 10. This is just one way, often adopted by the Greek writers, to approach the subject. As you may guess, this approach lends an inherent bias towards a cabbalistic view of mythical traditions and the interpretation of geometric forms and configurations. Getting through this book and confronting my own issues with it made me think about geometry and what I am interested in learning about. The basic numbers (and their roots - which are hardly discussed) are certainly powerful metaphors for understanding form, and nature does indeed use a myriad of geometric structures in her creations. This seems to be the solid, even scientific, basis upon which the art of geometry is founded. But beyond this point it all starts to get rather diffuse and analogical, by which I mean: disparate phenomenon get lumped together as a 'family' because they all exhibit some type of five-fold geometry in their form for instance. This approach is nothing more than the dead-end dialectics of two or more things having an 'affinity', 'resonance' or 'correspondence'. This is not what I am looking for! I am seeking something more rational and scientific in its approach. There are many potential areas of exploration - the symmetries found in the properties of sub-atomic particles, an exploration of how sound and vibration manifest as visual patterns, the symmetries and dynamics of fields, how our brain structures our perceptions. Even if such a study cannot answer so many questions it at least asks them and that can help to lead geometry away from its speculative past into a more relevant and instructive future. This book gives you an endless array of disconnected facts, which can provide a springboard for one's intuition but I believe that the subject of geometry demands and requires much more than that.

  13. 4 out of 5

    Stan

    This is a fantastic book about mathematics! The most frequently asked question students in the public education system have of their math teachers is 'When am I ever going to use this (math concept) in my life?' And it is a valid question. So much of what is taught in math classes has no practical value for most people; the few things that are taught in math classes that have practical value are not presented in the context of here is how this relates to everyday life; and much of math that has This is a fantastic book about mathematics! The most frequently asked question students in the public education system have of their math teachers is 'When am I ever going to use this (math concept) in my life?' And it is a valid question. So much of what is taught in math classes has no practical value for most people; the few things that are taught in math classes that have practical value are not presented in the context of here is how this relates to everyday life; and much of math that has practical every-day value is not taught in common core math classes for who knows what reason. A Beginner's Guide looks at numbers from a different perspective. Numbers matter in the real world because they are symbolic representations of the very essence of what makes up the universe. Numbers are everywhere, working behind the scenes whether we appreciate them or not! When you finish this book you won't be any better at balancing your check book, but you will never look at the world or the universe the same way. Another book that zeros in on how numbers relate to the world is Stephen Wolfram's A New Kind of Science. It's a very different book than Beginner's, but is also fascinating.

  14. 4 out of 5

    Avi Love

    This book by Michael Schneider is a wonderful in-depth introduction to a wide range of subjects. Michael himself is an incredible resource. Find him online sharing amazing and wondrous things, in a way both adults and children can receive. Michael's enthusiasm for sacred geometry found in every day life is contagious. I am blessed to have been in many of his classes over the past several years in Northern California. Whenever he has new material -- in person, in print, or online with articles, i This book by Michael Schneider is a wonderful in-depth introduction to a wide range of subjects. Michael himself is an incredible resource. Find him online sharing amazing and wondrous things, in a way both adults and children can receive. Michael's enthusiasm for sacred geometry found in every day life is contagious. I am blessed to have been in many of his classes over the past several years in Northern California. Whenever he has new material -- in person, in print, or online with articles, interviews or video links -- I am there in a flash. IMHO it is a privilege to be on the planet at the same time as this man.

  15. 4 out of 5

    Kenzie

    This book was a lovely tour of numbers 1-10 via a combination of geometry, myth, art, and science. The main thesis: the universe follows particular geometric/numerical patterns, and by recognizing those patterns, we can live harmoniously within creation. I sometimes wondered whether the facts were being oversimplified in order to support the thesis, and the connections between patterns and nature frequently seemed tenuous. Nevertheless, I really enjoyed learning to draw polygons with nothing but This book was a lovely tour of numbers 1-10 via a combination of geometry, myth, art, and science. The main thesis: the universe follows particular geometric/numerical patterns, and by recognizing those patterns, we can live harmoniously within creation. I sometimes wondered whether the facts were being oversimplified in order to support the thesis, and the connections between patterns and nature frequently seemed tenuous. Nevertheless, I really enjoyed learning to draw polygons with nothing but a compass and straight edge, and I thought it was overall a fun read that made great connections to biology, music, architecture, symbolism in world religions, and a lot more.

  16. 4 out of 5

    Melissa

    I love, love, love this book! It's so amazing to learn how mathematical principles surround us in every day life. The principle of symmetry alone is astounding. It's fascinating to see how the universe was created from a blueprint that is based on math. Every math class can become more interesting and worthwhile if one can see how math appears in the world rather than just on paper. Real math is exciting. I think a teacher would be able to break down the themes in this book to add some magic to I love, love, love this book! It's so amazing to learn how mathematical principles surround us in every day life. The principle of symmetry alone is astounding. It's fascinating to see how the universe was created from a blueprint that is based on math. Every math class can become more interesting and worthwhile if one can see how math appears in the world rather than just on paper. Real math is exciting. I think a teacher would be able to break down the themes in this book to add some magic to a child's world that will leave them loving math rather than relegating it to the most dreaded subject.

  17. 4 out of 5

    Brian

    This is a GREAT book for any one learning introductory geometry. I am using it in my geometry classes. It shows tons of examples of geometry in nature and art; it opens your eyes to see the geometric relationships and patterns that surround us. There are a couple problem points. He gets a little over-the-top philosophical some times and I have found errors, not typos but mistakes in math or physics, in several places. Despite these I’d say its well worth reading, even if only for the pictures!

  18. 5 out of 5

    Alexander McLeese

    A genuinely awesome read and a book which you can read again and again. Great for anyone who likes things of an esoteric nature, sacred geometry, sacred mathematics, numerology, the teachings of Pythagoras etc

  19. 5 out of 5

    Verena

    Fascinating concept

  20. 4 out of 5

    Leah Douglas

    “Both Pythagoras and Plato suggested that all citizens learn the properties of the first ten numbers as a form of moral instruction.” P. xxiii “Mythmatics” ❤️ p xxvii “...perhaps instead of teaching science to youngsters in separate pigeonholes of biology, chemistry, physics, and so on, science courses could investigate the principles that run through each of them, such as wholeness, polarity, balance, pattern, and harmony.” P 28 “Unlike any other shape, the three sides of a triangle resolve opposi “Both Pythagoras and Plato suggested that all citizens learn the properties of the first ten numbers as a form of moral instruction.” P. xxiii “Mythmatics” ❤️ p xxvii “...perhaps instead of teaching science to youngsters in separate pigeonholes of biology, chemistry, physics, and so on, science courses could investigate the principles that run through each of them, such as wholeness, polarity, balance, pattern, and harmony.” P 28 “Unlike any other shape, the three sides of a triangle resolve opposite tensions into one solid, stable whole needing no support from without. A triangle is self-sufficient.” P 46 “Four shows up wherever there is reference to earth and matter.” P 68 (four footed animals, four elements, four phases of matter, four corners of the earth. 40 is a passing beyond material/wordly phase or leveling up. Aristotle: “The aim of art is to represent not the outward appearance of things, but their inward significance.” Five: ability to regenerate another whole like itself. Excellence, brilliance, authority. Pentagram is the first shape to have a correct or incorrect orientation. Fibonacci sequence and the golden ratio. Six: structure, function, order, efficiency, a glorified triangle, leaving no wasted space. Seven: Virgin, untouched, a complete yet ongoing process, connection to Athena is fascinating p 225-228, the Sabbath, with six days of work whirling round it continuously. Musical scale, actually inexact, we tune our instruments slightly off in order to make equally tempered, 7 colors in rainbow spectrum “Natural expressions of the Heptad are not as obvious as the results of other Archetypal numbers and shapes because they must be seen as a sequence of relationships.” P 250 Eight: periodic renewal, new creation, glorified number 4, special relationship btwn 8 and 1 (Jesus 8th day, new creation) Octave, 8 same as 1, but completes the scale. Mitosis, 7 steps, step 8 is two separate cells. Nine: horizon, final step, the end, nine rings of hell, Abraham’s 99 years, 9 months pregnancy Ten: beyond, final, heaven, opening to all the rest of the numbers to infinity (I wish he talked about zero itself and how big a deal it’s “discovery” was)? Ten words genesis 1, Ten Commandments, ten plagues, ten strings, 100 years old, tithe, string theory (!!!), *** “The Decad is the recurrence of the Monad, unity at another level. With this new beginning we are back where we began, although the better for having gone through the experience of which the Decad is the summit.” P 346 Plato’s academy door: “Let none ignorant of geometry enter here.”

  21. 5 out of 5

    Jessica

    Welp, looks like we aren't going to finish this K-choice read aloud. We started out strong, really liked the idea of it...but there is just too much woo and illogic. Archetypes and symbolism are interesting and the history of numbers is foundational, but this author needed to lose at least 50% of this text--tighten it up and find the facts, and much more clearly delineate the supposition and pie-in-the-sky arm waving. We got almost halfway through on the strength of the historical bits and the f Welp, looks like we aren't going to finish this K-choice read aloud. We started out strong, really liked the idea of it...but there is just too much woo and illogic. Archetypes and symbolism are interesting and the history of numbers is foundational, but this author needed to lose at least 50% of this text--tighten it up and find the facts, and much more clearly delineate the supposition and pie-in-the-sky arm waving. We got almost halfway through on the strength of the historical bits and the fun of sifting the wheat from the chaff, but ultimately became too frustrated. I'll keep it on the shelf for casual browsing and future endeavors in critical thinking, but as a history and influence of math and numbers book? Not what we'd hoped. Moving on.

  22. 5 out of 5

    Jenny

    This book was not what I expected. I was thinking it was about physics but it’s really about numbers, patterns, geometry and the application and discovery of all three. It was not an easy read by any means but very interesting, when I could understand it. I heard someone say that there is something to offend everyone in it. So true. I’ve seen lots of reviews calling it New Age nonsense. I didn’t always agree with Schneider but there was enough that I liked that I would read it again. Hopefully I This book was not what I expected. I was thinking it was about physics but it’s really about numbers, patterns, geometry and the application and discovery of all three. It was not an easy read by any means but very interesting, when I could understand it. I heard someone say that there is something to offend everyone in it. So true. I’ve seen lots of reviews calling it New Age nonsense. I didn’t always agree with Schneider but there was enough that I liked that I would read it again. Hopefully I can glean more in future readings.

  23. 4 out of 5

    Ethan Chappell

    This book took math and helped me learn how to apply it to the real world. It went through all the shapes from the circle to the decagon and showed how they all link together to make the world around us. It introduced me to so much and I really enjoyed learning about he golden mean. It's a fairly long book and I would totally read it again just so I can do all the projects and research in depth the history of mathematics.

  24. 5 out of 5

    Blake Paine

    This book has been a golden thread, tying so many ideas together for me! It is an inward thread and this book is just mind blowing! If you are trying to recover from a scientific materialist hangover this is a good place to start. This book offers a new freedom to explore the Cosmo's and what universal archetypes have to teach us about what it means to be human.

  25. 4 out of 5

    Cheeseo

    This book is about math and how it has influenced the world. It shows how nature uses math to create harmony. Really intersting to learn about. If you read it, take it with a grain of salt- I'm pretty sure many parts are opinion stated as fact. Would recomended it.

  26. 4 out of 5

    Stephanie

    Fascinating! I enjoyed how Schneider explores the world using geometric principles. Geometry was always my least favorite part of math, but after reading this it’s now one of the most interesting. Math needs to be taught more often by using real world connections!

  27. 5 out of 5

    Mark

    I had to zoom through this book after having allowed it to languish until the library due date was upon me. Every chapter was faacinating and intriguing. I just didn’t know—until now. I’ve had to set this aside until I can get my hands upon another copy. I’ll be watching!!

  28. 4 out of 5

    Manish Katyal

    An atypical book. Very new-agey, light on the math but still engaging.

  29. 5 out of 5

    Stephen Cranney

    A lot of interesting points and connections throughout nature, but it got a little too much into mumbo jumbo.

  30. 4 out of 5

    Sjj

    Although I did not find this an easy book to read, I did learn enough facts about numbers and geometry to put it in my "worth reading" category.

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