That is because every natural pattern of growth or movement conforms to one or more geometric shapes like the sphere, circle, spiral, triangle, hexagon and square among others. For instance, the simplest of geometric forms, the sphere, is reflected in atoms, cells, seeds, planets, and globular star systems.
These naturally occurring geometric shapes and patterns were believed to be the starting alphabets of everything in the universe. Sacred geometry was broken down further into numbers, mathematical formulas and symbols. Man then cleverly employed this geometry from nature and reproduced it in art, architecture, music and meditation throughout history. In architecture, sacred geometry finds ample expression.
Yantras are beautiful art, the original Vedic sacred geometry. These cosmic diagrams generate nourishing, life-supporting energies. Yantras embody the energy of particular sacred archetypal energies, such as deities and planets or grahas. Yantras are especially useful in buildings that were not Vastu-designed.
The Yantra, used in meditation by Hindus is a classic example of sacred geometry. This is a geometrical pattern made of several concentric figures (squares, circles, lotuses, triangles and a point or bindu at the centre). The Mantra Sloka and Strotra were often related with numbers. The vedi for worship had a definite structures (mostly squires).
These shapes are believed to have a powerful quieting effect on the mind. A lotus flower symbolises the chakra energy centres; a bindu (dot) signifies both the point of creation and the infinite cosmos; a triangle with an upward point, denotes masculinity; with a downward point, the triangle becomes a symbol of femininity.
They protect from negative, disruptive energies in the environment. The directions, elements, and planets exert powerful vibratory effects on our bodies, minds, and emotions. Yantras help us have the support of nature rather than resistance from nature. There are mantras, or sacred sound vibrations, associated with most yantras. There are both two- and three-dimensional yantras.
Temples designed on the basis of sacred geometry include the Madurai Meenakshi Temple, the Maha Meru Sri Yantra Temple in Amarkantak, Madhya Pradesh, Mahabodhi Temple in Bodh Gaya, Mahadev Temple in Khajuraho, Nashik’s Trimbakeshwar temple, Borobudur temple, Indonesia, Hindu temples in Angkor Wat, and the Bahai Temple in Delhi (based on lotus geometry).
Fractal Geometry; Ancient India offer a sentiment, full of harmony with nature, of equality with and love for all her innumerable creations. To want to describe or suggest aspects of nature is a sign of dissociation of nature from consciousness.
But India lives in nature, thus she does not observe it, but realises it. The metaphysics here is that the part cannot be separate from the whole. Just like a seed carries the blueprint of a grown tree. People have understood the spiritual significance of geometry for ages, from the ancient Vedic India to till date. The ancient belief held that God created the universe according to a geometric plan. Thus this geometry became sacred. Also, man read a deeper meaning in these oft-repeated growth patterns of life.
Symbolism is an artistic and poetic movement using symbolic images and indirect suggestion to express mystical ideas, emotions, and states of mind. It is the use of symbols to represent meta-physical ideas or qualities. When architectural forms become the vehicles of content-in plan, elevation, and ornamentation-they become symbolic.
Their symbolism can be understood consciously or unconsciously, by association to a building one has seen before and by the fact that it suggests certain universal experiences. Symbolism was largely a reaction against naturalism and realism, anti-idealistic styles which were attempts to represent reality in its gritty particularity, and to elevate the humble and the ordinary over the ideal.
The roots of sacred geometry are found in nature. Sacred Geometry is a series of geometric shapes that have deeper metaphysical meaning. These shapes offer insights into the basis of the world around us. Sacred geometry makes us believe that the idea behind the creation of the entire cosmos was according to a specific geometric plan. Spiritually, Sacred Geometry is just one component in a vast concept of synchronicity.
Symbolism was a reaction in favour of spirituality, the imagination, and dreams. Symbolism is a field where in a lot of ancient historical texts help in the basic understanding of the field but modern and recent texts have refrained from treading the path. Ideas by their very nature are always changing. Knowledge is a dynamic, cultural and historic process. Symbolism, being subject to these aspects of culture, attains different meanings at different situations and with changing times.
After coining the term ‘fractal’ and setting up some mathematical formulae, it now has great possibility to experiment about the refining of conventional temple-form or searching for new form of complexity related with Hindu cosmology with the consideration of ritual guides. For searching the new, complex, fractal and chaotic forms in contemporary architecture, on the one hand, manual experiments of architectural elements with the fractal geometry are extensively practiced.
On the other hand, by adopting the theories of folds, fractals, complexity and algorithms, ‘computer architecture’ has been developed that translates the theories into architecture. Accordingly, fractal geometry not only analyzes old buildings and existing urban patterns and growth, but also helps to create countless unimaginable forms and patterns for finding new possibilities of space as well as aesthetics in contemporary architecture.
A synchronicity between nature, science, music, math, art, and the physical world. Sacred Geometry is a process of aligning one's heart, mind and spirit in sync with the Source. It is the gateway between the etheric and physical realms. Working with sacred geometry is a mirror of the soul~ it is fundamental to the evolution of consciousness as well as to the existence of life itself. It is this principle of oneness underlying all geometry that permeates the architecture of all forms in its myriad diversity.
This principle of interconnection, 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. It is in the intricate details of the natural world that is astonishing and makes one see the pattern behind life. A popular hexagon from nature is the honeycomb, the geometrically perfect home for bees. Many crystals are hexagonal and so are snowflakes.
For instance the pine cone with its perfect spiral spines has long been a symbol of human enlightenment. The spiral is another universal geometry. You can spot it in a snail’s shell, in the Milky Way which houses our planet Earth, in tornadoes, whirlpools, in the centre of sunflowers which is a mathematical wonder in itself; in the cochlea of the human ear and even our DNA.
The Sulbasutras contain the geometry necessary for construction of the vedi and the agni for the obligatory and votive rites. These in turn are a part of the Kalpasutras , which are attached to the Vedas as one of the six V dangas or limbs of the Vedas. It is likely that the Sulbasutra sections were a part of the Srautasutras of the Yajur Veda, the Veda designed for the performance of sacrifices.
The three most primitive agni, Garhapatya, Aavaniya and Daksinagni, are older than the Rg Veda and the Mahavedi was likely known to the Indus Valley civilisation. It is generally recognised that the Pythagorean theorem was known in India at the latest in the 8th century B.C.E. (Amma 14-15).
The Sulbasutras deal with the correct construction of the vedi and agni including orientation, size, shape and areas and, as such, they are not meant as mathematical theorems or proofs. The geometry in the Sulbasutras can be categorised into that which expressly states theorems, constructions and implicit geometrical truths contained in constructions.
Modern historical research has shown that what is known as Pythagoras’ Theorem was in fact known to the ancient Indians. Whereas Pythagoras (540 B.C.E.) is given credit for this formula in modern western culture, the Vedic priests were using this principle to build their altars. We did it before Pythagoras even had taken birth on this earth, this theorem was discovered by Baudhayana. According to Baudhayana Sulbasutras:
“दीर्घचतुरश्रस्याक्ष्णया रज्जु: पार्श्र्वमानी तिर्यग् मानी च यत् पृथग् भूते कुरूतस्तदुभयं करोति ॥”
A rope stretched along the length of the diagonal produces an aea which the vertical and horizontal sides make together. Well this theorem was later on proved by both Baudhayana and Apstamba.
Baudhayana later on provided a numerical proof of this theorem and Pythagoras (Baudhayana) triplets but it was unfortunately ignored, and Baudhayana was not the single one to prove it was later on proved by apstamba and another ancient mathematicians known as Bhaskaracharya (also known as Bhaskar II ).
The unique proof that Bhaskaracharya provided was geometrical as well as numerical and the best part is that it's truly generalized and works for all sorts of triangles (scalene, isosceles and equilateral) but again it was ignored and Pythagoras was wrongly credited for this theorem by Cicero and the ancient mathematicians / historians of greece.
And the interesting fact is that Bhaskaracharya was the first to conceive differential calculus and differential coefficient and many more discoveries (his discoveries are countless) but we are never taught about these facts (even in n.c.e.r.t) it is clearly stated that “this theorem was earlier discovered by Baudhayan”
Not only Pythagauras theorym in fact there are many important theories and concepts which were discovered by ancient Indian philosophers in the past. Examples : Theory of atom, Gravity, Power, Motion, Velocity, Square formula, Value of Pi, Lunar eclipse, Motion of stars, Motion and size of earth, Theory of earth’s motion by Aryabhatta etc. Its high time we realize the contributions of our ancient sages and rishis. Their work and contribution has constructively affected our lives in ways we cannot even comprehend.
In the Black Yajur Veda (8th B.C.E.) and the Satapath Brahmana, 36 units is the length of the east-west line or praci or line of symmetry or prsthya of the Mahavedi and 30 units as one of the north-south lines. The praci and half the side make the sides containing the right angle in the triangle with sides 36, 15, and 39 units.
There is a possibility that this theorem was known even earlier by the construction of the three agni, Garhapatya, Ahavaniya and Daksina. Other rational right triangles as well as the irrational right triangle 1,1 √2 and approximate right triangles are also mentioned in the Sulbasutras (Amma 17-18). There are several Vedic proofs for this theorem which are all fairly simple (Tirthaji 349-351).
In fractal geometry, fractal dimension is the quantity which measures the fractal character of an object. For any fractal object fractal dimension is always non-integer, i.e., unlike integer-dimensional objects (Example: zero-dimensional point, one dimensional line, two dimensional square and three dimensional cube) fractal object is a fractional-dimensional which may be in between one dimensional and two dimensional object, or in between two dimensional and three dimensional object.
For in between one-dimensional and two-dimensional fractal object fractal dimension ‘D’ is always more than 1 and less than 2, whereas for in between two- and three-dimensional fractal object the fractal dimension ‘D’ is always more than 2 and less than 3. There are various methods to evaluate the fractal dimension, among which the ‘box counting method’ is suitable for measuring the fractal dimension of the elevation of buildings, mountains, trees or any objects which are not true fractal.
Albeit, ‘self-similarity dimension method’ is very common for calculating the fractal dimension, but the method is only applicable for true mathematical fractals where self-similar structures are found at all zooming scales. Fractal dimension calculated by ‘box counting method’ measures the fractal dimension of an image on the basis of roughness or quality of texture or the amount of details. In fact, feng shui, astrology, numerology and tarot all begin with a fundamental faith in sacred geometry. The Mandala, the most admired symbol of Buddhist religion and art is another instance of sacred geometry.
Authored by Anadi Sahoo
