In A Beginner's Guide to Constructing the Universe: Mathematical Archetypes of Nature, Art, and Science, author Michael S. Schneider takes his readers beyond the basic understanding of numbers as taught by mathematics education. The average person understands that numbers represent quantities we can calculate and count. However, Schneider teaches that numbers are so much more. Numbers represent abstract ideas of balance, structure, opposing forces, oneness, and so much more. Numbers are also archetypes, or models, seen repeatedly all throughout nature. His 10 chapters speak of 10 different numbers and their geometric shapes.
Starting with the Monad, meaning the number one, he equates the number one with the circle. The circle, he explains, as a never-ending line of perfection, is a "reflection of the world's--and our own--deep perfection, unity, design excellence, wholeness, and divine nature" (p. 2). He further explains that the Greeks saw it as the shape from which all other shapes are formed, "the womb in which all geometric patterns develop" (p. 2). Among his other arguments are the points that the Monad represents power and motivation.
In his chapter "Dyad," he explains how we can come to see unity as becoming many. Unity becomes many when it is reproduced. Using mirrors and circles, we can see an endless reproduction of many circles and draw a line connecting these circles. The word Dyad means "twoness" or "otherness," and just like the circle represents unity, the line connecting circles represents otherness, the Dyad, the number two. He further describes the Dyad as representing polarity because a line has opposing parts. Yet, since the line is connected with unity, "its opposite poles remember their source and attract each other in an attempt to merge and return to that state of unity" (p. 24).
In other chapters, he explains the Triad, the Tetrad, the Pentad, the Hexad, the Heptad, the Octad, the Ennead, and finally the Decad. He concludes by describing two digit numbers as a brand new reality and gives pointers on seeing geometry within our everyday environment.