## Geometry made easy!

The two are similar in size but of very different ages: Plato was carved out by a small asteroid 3. Erosion occurs on the moon over the eons as micrometeorites "sandpaper" its surface. Moonquakes, temperature extremes, the solar wind and the slumping of crater walls through gravity and settling contribute as well. Copernicus left shows many terraces due to slumping of its walls.

The crater is 2. No doubt it too had central mountains, now submerged beneath dark, smooth lava flows.

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Skip to content. Opens in new window Click to print Opens in new window. These inevitably follow geometrical archetypes, which reveal to us the nature of each form and its vibrational resonances. They are also symbolic of the underlying metaphysical principle of the inseparable relationship of the part to the whole. It is this principle of oneness underlying all geometry that permeates the architecture of all form in its myriad diversity. This principle of interconnectedness, inseparability and union provides us with a continuous reminder of our relationship to the whole, a blueprint for the mind to the sacred foundation of all things created.

Starting with what may be the simplest and most perfect of forms, the sphere is an ultimate expression of unity, completeness, and integrity. There is no point of view given greater or lesser importance, and all points on the surface are equally accessible and regarded by the center from which all originate.

Atoms, cells, seeds, planets, and globular star systems all echo the spherical paradigm of total inclusion, acceptance, simultaneous potential and fruition, the macrocosm and microcosm. The circle is a two-dimensional shadow of the sphere which is regarded throughout cultural history as an icon of the ineffable oneness; the indivisible fulfillment of the Universe. All other symbols and geometries reflect various aspects of the profound and consummate perfection of the circle, sphere and other higher dimensional forms of these we might imagine.

The ratio of the circumference of a circle to its diameter, Pi, is the original transcendental and irrational number. Pi equals about 3. Our holistic perspectives, feelings and intuitions encompass the finite elements of the ideas that are within them, yet have a greater wisdom than can be expressed by those ideas alone.

At the center of a circle or a sphere is always an infinitesimal point.

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The point needs no dimension, yet embraces all dimension. Transcendence of the illusions of time and space result in the point of here and now, our most primal light of consciousness. Life itself as we know it is inextricably interwoven with geometric forms, from the angles of atomic bonds in the molecules of the amino acids, to the helical spirals of DNA, to the spherical prototype of the cell, to the first few cells of an organism which assume vesical, tetrahedral, and star double tetrahedral forms prior to the diversification of tissues for different physiological functions.

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## THE ARK OF MATHEMATICS PART 1: GEOMETRY MADE SIMPLE, FUN, AND EASY by Chad Clawitter

Our human bodies on this planet all developed with a common geometric progression from one to two to four to eight primal cells and beyond. Almost everywhere we look, the mineral intelligence embodied within crystalline structures follows a geometry unfaltering in its exactitude. The lattice patterns of crystals all express the principles of mathematical perfection and repetition of a fundamental essence, each with a characteristic spectrum of resonances defined by the angles, lengths and relational orientations of its atomic components.

The square root of 2 embodies a profound principle of the whole being more than the sum of its parts.

The square root of two equals about 1. The new generation possesses the capacity for synthesis, growth, integration and reconciliation of polarities by spanning both perspectives equally.

### Qui sommes nous

The root of two originating from the square leads to a greater unity, a higher expression of its essential truth, faithful to its lineage. John, Chapter 1, verse 5. By the same token, we have the capacity to surpass the genetically programmed limitations of our ancestors, if we can shift into a new frame of reference i.

Our dictionary refers to the word matrix both as a womb and an array or grid lattice. Our language has some wonderful built-in metaphors if we look for them! The golden ratio a. The golden ratio is about 1. As such, it symbolically links each new generation to its ancestors, preserving the continuity of relationship as the means for retracing its lineage.

## Intermediate algebra and analytic geometry made simple

The mathematician credited with the discovery of this series is Leonardo Pisano Fibonacci and there is a publication devoted to disseminating information about its unique mathematical properties, The Fibonacci Quarterly. Fibonacci ratios appear in the ratio of the number of spiral arms in daisies, in the chronology of rabbit populations, in the sequence of leaf patterns as they twist around a branch, and a myriad of places in nature where self-generating patterns are in effect.

The sequence is the rational progression towards the irrational number embodied in the quintessential golden ratio. This most aesthetically pleasing proportion, phi, has been utilized by numerous artists since and probably before!

As scholars and artists of eras gone by discovered such as Leonardo da Vinci, Plato , and Pythagoras , the intentional use of these natural proportions in art of various forms expands our sense of beauty, balance and harmony to optimal effect. Leonardo da Vinci used the Golden Ratio in his painting of The Last Supper in both the overall composition three vertical Golden Rectangles, and a decagon which contains the golden ratio for alignment of the central figure of Jesus.

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The Vesica Piscis is formed by the intersection of two circles or spheres whose centers exactly touch.