Geometry in Nature

In nature, there are some of the most beautiful patters, designs, and structures from the most miniscule particles and organisms, such as phytoplankton, to large expressions of life in the greater cosmos. Many of these structures are geometrical - symmetrical by design - and were used by humans in the early Greek, Egyptian, Roman and ancient Indians for architecture construction. Most humans used the Pythagorean Theorem by measurements of the human body, but this is only one of nature's form of geometrical archetypes. There are many other forms of archetypal expressions in nature, including vibrational resonance. However, an underlying law of nature is the inseparable relationship of the part to the whole, and thus brings a sense of interconnectedness and inseparability for all things created. Some people call this the "Golden Ratio" that is related to "Sacred Geometry".

Source: http://media-cache-ec0.pinimg.com/736x/2b/54/dd/2b54ddc1258231e27a61414f2e5eb5ea.jpg

According to Wikipedia:

"Sacred geometry is used as a religious, philosophical, and spiritual term to explain the fundamental laws of the universe covering Pythagorean geometry and the perceived relationships between geometrical laws and quantum mechanical laws of the universe that create the geometrical patterns in nature. Many Gothic cathedrals were built using proportions derived from the geometry inherent in the cube and double-cube; this tradition continues in modern Christian churches to the present time.[4] churches, temples, mosques, religious monuments, altars, tabernacles; as well as for sacred spaces such as temenoi, sacred groves, village greens and holy wells, and the creation of religious art.

Source: https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLcjVlOMpJdvS_nQQAPkfTJYMSUHk1cYtANIk4QjicLmvMKn6BllUXiLeQV0-aC-qqHM9hCxS2aIyD1A99LE-NoQM0BAh1CuGFUJaeGHYL12slE0uLau83unL4-aN6FYsxnxmLKXTJSLo/s640/parthenongoldenratio.png

Source: http://hoffnermath.files.wordpress.com/2009/03/pythagoreansnail2.jpg

According to Stephen Skinner, the study of sacred geometry has its roots in the study of nature, and the mathematical principles at work therein.^[3] Many forms observed in nature can be related to geometry, for example, the chambered nautilus grows at a constant rate and so its shell forms a logarithmic spiral to accommodate that growth without changing shape. Also, honeybees construct hexagonal cells to hold their honey. These and other correspondences are sometimes interpreted in terms of sacred geometry and considered to be further proof of the natural significance of geometric forms."

The image below is a diatom... a phytoplankton that displays it's natural geometric form in a delicate, yet robust structure.  How fascinating it is, that life is surrounded by geometry; nature is geometry!

Source: http://fineartamerica.com/featured/73-diatom-sem-steve-gschmeissner.html