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

But that is only the beginning. There are at least two, to as many as ten, illustrations on each page, half being scientific, the other half artistic. My favorite combination is the splash crater of a milk drop on p. 11 and the Hindu deity Shiva Nataraj on p. 4. They form a complimentary pair visually and philosophically, both illustrating the monad, a generating center with a resultant circle of generated objects.

In the next two chapters, two intersecting circles lead to the tension-filled dyad whose resolution is in the triad, which breaks the tension by allowing expansion to another dimension.

In my words, this sounds a bit mystical and foggy, but Schneider provides just the right amount of background which carries you into the heart of the world of numbers, showing how they reflect both the scientific construction of the universe as well as artistic human creations.

The longest chapter is on the number five, which remarkably leads to the spiral, and to the generation of life. These are very valuable insights, much to be pondered. This chapter also contains an excellent discussion of the Golden Mean, the number 1.618..., which is often found in nature as well as in human expeience.

Just pick the book up sometime and glance at the quotations and illustrations. If you can resist buying it, you are a better man than I am.


Resource for integrating geometry with other subjects   December 22, 2000
John R. Snyder (Austin, TX USA)
10 out of 11 found this review helpful

I am using this book to great effect in my Montessori elementary class with 9-12 year olds. Geometry is an important part of the Montessori elementary curriculum, but it is not very well integrated with the other subjects. Schneider's book is just the thing I needed to create those links to history, art, religion, literature, architecture, music, arithmetic and algebra. This allows me to turn almost any lesson into a geometry lesson on the spur of the moment and vice versa, which means that whatever the child is interested in can be their individual path to geometry. The children love repeating the constructions of the various geometrical figures, embellishing them, and discovering their own new patterns and methods. Montessori emphasizes story-telling as a core teaching strategy, and Schneider's book is a treasure trove of great vignettes, intriguing historical facts, and surprising developments with which to spice up the more formal lessons. The girls especially seem to benefit by a multi-disciplinary approach to geometry, which typically strikes them as cerebral and irrelevant to their lives. I would never have had the time to do the research to uncover all these stories and interconnections for myself. Thanks, Michael Schneider!


Mathemagical!   December 10, 1999
D. Page (Loudonville, NY USA)
4 out of 4 found this review helpful

I have to agree with the other reviewers who said they had a hard time putting this book down. So did I, even after I finished it! In fact, I loved this book so much, one year I bought 4 extra copies as Christmas presents. Without a doubt the most amazing book you will ever read. If you have lost touch with the awe and majesty of the universe, look no further, this is the book for you.


thoroughly enjoyable and engaging   May 20, 2003
Robert Andrews (Florence, MS United States)
7 out of 7 found this review helpful

It's a good thing they bound the book well, because I have put it to a good deal of use over the last few years, as have the numerous people who have come over to read it (because I won't let them leave my house with it!).

The author manages to get me to pull out my compass and actually draw geometrical patterns and explore the often-unexpected relationships between different shapes & patterns. And his joy in the subject inspires me to see nature's patterns and relationships as well, which seems to be the main point of the book.

A few reviewers seem to take at least some issue with some of the author's colorful ideas and statements, but I don't feel that they detract from the book in any powerful way, considering the author's intent to inspire fresh thinking in the student. Sometimes the best way to do this is to point to some unusual connections and coincidences. It's not a book about theorem and proof, but about falling in love with geometry (and in this it excels).