Math.pdf

Math behind Sri Yantra

These nine triangles are of various sizes and intersect with one another. In the middle is the power point (bindu), visualizing the highest, the invisible, elusive center from which the entire figure and the cosmos expand. The triangles are enclosed by two rows of (8 and 16) petals, representing the lotus of creation and reproductive vital force. The broken lines of the outer frame denote the figure to be a sanctuary with four openings to the regions of the universe. There are Nine Mandalas to Shri Yantra: The Earth Square or Bhupura, Sixteen Petals, Eight Petals, Fourteen Triangles, Outer 10 Triangles, Inner 10 Triangles, Eight Triangles, The Four Weapons, Central Triangle, Bindu. Each Mandala corresponds to specific deities/functions in the human body, symbolizing the openings in the body, different types of prana, the tanmantras (related to the five sense organs), and other forces/functions of the body. On the Sri Yantra there are marmas where three lines intersect, and there are 54 such intersections. Each intersections has masculine and feminine, shiva and shaktiqualities. 54 x 2 equals 108. Thus, there are 108 points that define the Sri Yantra as well as the human body.

The Sri Yantra is a series of interlocking triangles with a perfect ratio of 3.14 or the divine number, Pi. Triangles The sri yantra consists of nine interwoven isosceles triangles: four point upwards (Shrikantha or Shiva), and five point downwards (Shivayuvati). The triangles are arranged in such a way that they produce 43 konas (subsidiary triangles), at the center of the smallest of which there is a big dot (known as the bindu). These smaller triangles are supposed to form the abodes of different gods, whose names are sometimes entered in their respective places. The Shri Chakra is also known as the nav chakra or navayoni chakra because it can also be seen as having nine levels. "Nine" comes from "Nau or Nava" of Sanskrit. Each level corresponds to a mudra, a yogini, and a specific form of the deity Tripura Sundari along with her mantra. They correspond to the nine openings in the body The base angle of a properly done Sri Chakra is 51. In 1997, RKS Muthukrishanan discovered that the base triangles of the pyramids of Egypt are equal in angle measurement to Sri Chakra. This strengthens the possibility that the great civilization shared a common science of measurement and mathematics. Lotus petals A Lotus represents the 5 natural elements of the universe; Earth, Fire, Water, Air and Ether in its purest form. The lotus petals in a Yantra usually appear in a circle, which itself is inside a square. These lotus petals are known as the lunar mansion or Chandra (Moon) Mandala and the circle outside is known as the Solar Mansion or the Surya (Sun) Mandala. The circle with eight lotus petals is called Vasudalam. The Surya Mandala is portrayed by 12 lotus petals. This represents the twelve signs of the zodiac that the Sun will move through during the year. The Lunar mansion is shown with sixteen petals (Kalasram). The Moon has 16 phases or 16 kalas during its cycle from new moon to full moon. The 16 yoginis are associated with

the attainment of desires by the cultivation or strengthening of power over mind, ego, sound, touch, sight, taste, smell, intellect, steadiness, memory, name, growth, etheric body, revivification, and physical body. If the petals do not represent either solar or lunar mansions in the Yantra, then it refers to the manifested reality; which is eight fold. This eight fold manifested energy is the phenomenal world consists of five elements of Universe. Earth, Fire, Water, Air and Ether together with mind, intellect and ego. A Lotus represents these elements in its pure form. These are surrounded by two circles of lotuses, one with eight petals (Vasudalam) and the other with sixteen petals (Kalasram). The whole mandala of 16 petals is called 'Fulfiller of Desire'. Bhupara (Square) A square is made of four lines, two of which are vertical lines representing movement and two are horizontal lines representing stability. Together it creates a balance. Thus the confined space inside the square represents our materialistic need in life, stability, solidity and contentment. Bindu A point, called Bindu in Tantra, holds a very significant position in the Yantra and is the center of the geometrical structure. It represents the Shiva-Shakthi in Union in the casual state from which all other parts of the diagram, representing the cosmos, are evolved. At the heart of the Bindu is Kamakala with three bindus – red (ova), white (semen), and mixed. Said to be root potential of sun, moon and fire (Also seen as: face of devi and her two breasts; prakasha/vimarsha; anusvara/visarga breathing). It is like sun and moon coming together in an eclipse, or the seed from which the plant human being grows. A complete individual grows within nine months to be born as a Sri Yantra or plant. Flowering of plant – 24 petals of the yantra. This forms the structure of Sri Yantra.

The 15 Nitya Devis

These 15 Nityas rule the famous 15 letters Devi mantra known as Panchadasakshari Mantra: Ka E Aie La Hreem Ha Sa Ka Ha La Hreem Sa Ka La Hreem. They form the 15 Tithis (Phases) have two aspects each – Prakashamsa, which rules the day portion of the Tithi, and Vimarshamsa, which rules the night part of the Tithi. At night they collect the divine nectar and during the day they release it. On Poornima or full moon day all the 15 Nityas are in the moon and the moon is shining brightly. On the 1st Thithi after the Poornima, one Nitya leaves the moon and goes to the sun and the moon is reduced slightly in size. On the next Dwiteeya Tithi another Nitya leaves the moon and goes to the sun and the moon is further reduced in size. This way they leave one by one till the moon becomes totally dark on the 15th day, which is called Amavasya or the new moon day. This is known as Krishna Paksha or the waning phase. After Amavasya they return one by one on each Tithi and the moon starts shining again until it is full on the Poornima when the last Nitya returns to it. This is called Shukla Paksha. Kameswari to Chitra are the Nityas ruling the Krishna Paksha Tithis from Pratipada to Amavasya. In Shukla Paksha the order of the Nityas is reversed, i.e., Chitra to Kameswari. One Krishna Paksha and one Shukla Paksha form a 30-day lunar month. 12 such months form a 360-day lunar year. Multiplied by 2 (the day and night aspects of theNityas/Tithis) we have 720 aspects of the Nitya Devis in a year. This way, they rule the day, the night, the days, months, seasons and the years. Furthermore, each aspect

of a Nitya rules 100 Nadis in our body. This way they rule the 72000 Nadis in our body, with ever changing moods and physical results in human lives. The Nityas or Eternities of Lalita represent the fifteen lunar days or tithis of the waxing Moon. Each has her own yantra, mantra, tantra and prayogas or ritual applications. The full circle of the Nityas also represents the 21,600 breaths a human being takes in a full day and night. As such, the Nityas are the Kalachakra, or Wheel of Time. The 15 Nityas are modifications of Lalita with her 3 gunas and her 5 elements(5 x 3) of aether, air, fire, water and earth. As the moon remains itself, though appearing differently according to phase, so too does Lalita. Each Nitya has her own vidya (that is mantra), yantra and group of energies (Shaktis). Hence Lalita or Tripurasundari is the 16th day or full moon, with her 15 digits. Each of the Nityas has a certain number of arms, the totality of arms (= rays) of the whole circle being 108. Because any unit of time is taken as a microcosm or parallel of any other valid unit, each of the fifteen Nityas thus has 1,440 breaths (15 X 1440 = 21,600). This identity between space, time, Tripurasundari and the individual is elaborated at great length in the Tantraraja Tantra. The Nityas are the vowels of the Sanskrit alphabet and are identical with both time and space. For example, if the number of tattvas or consonants (36) are multiplied by the 16 Nityas the number of letters is 576. The multiples of this number provide the number of years in the different Yugas. So the circle of the matrikas and the Nityas is identical with the sidereal zodiac as well as mantra. The ancient scriptures Nitya Shodasarnava Tantram, Srividya Vilasam, Vamakeswara Tantram, Tantraraja Tantra and Mantra Ratnakaram have specified that the 15 Nityas must be worshiped in the Srichakra central triangle, anticlockwise, and the 16th Nitya, Maha Tripura Sundari must be worshiped in the Bindu.

Merkabah/Merkavah mysticism or chariot mysticism: Jewish mysticism, c. 100 BCE – 1000 CE, centered on visions such as those found in the Book of Ezekiel Sri Yantra and Human physiology

Drunvalo Melchizedek in his work on the flower of life geometry has mentioned that there is a field of energy around the body in the shape of a star tetrahedron. It is called a Merkaba which translates as vehicle of light.

A Star Tetrahedron is made up of two interlocking tetrahedrons. The two interlocking tetrahedrons represent male and female energy in perfect balance. The tetrahedron facing up is male, and the one facing down is female. There is a Star Tetrahedral field around everything, not just our bodies. There is also a tube that runs through the body. It connects the apexes of this Star Tetrahedral field. Learning how to breathe through this tube, combined with rotating the fields, produces the merkaba, a vehicle of ascension. We have a physical body, a mental body, and an emotional body, and they all have Star Tetrahedral shapes. These are three identical fields superimposed over each other, the only difference among them being that the physical body alone is locked—it does not rotate. The merkaba is created by counter-rotating fields of energy. The mental Star Tetrahedral field is electrical in nature, male, and rotates to the left. The emotional Star Tetrahedral field is magnetic in nature, female, and rotates to the right. It is the linking together of the mind, heart, and physical body in a specific

geometrical ratio and at a critical speed that produces the merkaba The word "Mer" denotes counter-rotating fields of light, "Ka" Spirit, and "Ba" body, or reality.

Clockwise/anticlockwise and Zero • Electrons can spin clockwise/anti clockwise in an atom. Two electrons in an orbital can never have the same direction of spin, they are always opposite. • Most left-handed people prefer to draw circles clockwise and circulate in buildings clockwise, and most right-handed people prefer to draw circles counterclockwise and circulate in buildings counterclockwise. It is believed that this can be attributed to dominant brain hemispheres • Coriolis effect- physics term to describe a certain force which acts perpendicular to the direction of a rotating object. In northern hemisphere it makes moving objects go to the right and in the southern hemisphere it makes objects go to the left. This plays a role in cyclonic weather systems. Though it behaves like a real force, it is a consequence of inertia, not like nuclear or electromagnetic forces. •

“Labyrinth” – found in Rome, Italy, Native American tribes, It is held as a symbol of the Divine Feminine. They are ancient spiral patterns representing the cyclical nature of life. The lines and plans are said to be the plan of the Creator. Made for people to repetitively trace with eyes or fingers, dance on it, or walk on it. Cultures hold the labyrinths like a deity and are encouraged to connect with it in all ways - physically, emotionally, and spiritually

Medieval labyrinths were constructed to embody arithmetic and geometric principles of sacred geometry. Similar to Tibetan Mandala making where clockwise/anti movements are made and then meditated upon. Use of labyrinths have found to be beneficial for psychological ailments and also for healing, few trying to incorporate methods into medical system.

Chartres labyrinth: six petaled rose “rosette” – symbolizes 6 stages of creation

Native American Labyrinth “man in the maze” (11 concentric circles / rings and 16

spokes):

Creten Labyrinth (can also be made to have a right hand entrance):

• Sufi Dancers use repetitive, rhythmic, intense clockwise and anticlockwise whirling and spiraling movements to raise consciousness. These spins around ones own axis is believed to invoke a stillness of heart and connection to the Divine source. Connection between Devi and Friday. Kolams, bhajans, and new sarees. Friday = shukra, most feminine out of the seven days. Pre-pubescent girls are involved in such activities to develop femininity about themselves. - Usage of 11, 33 in the construction of Linga Bhairavi and its similarity in the human body – vertebral column, number of rib bones 22, number of bones in skull - 11 Always the karmic residue or the past memory which makes this life process happen, controls these 112 chakras. There are a few of them which will allow you an access to the beyond but most of them function within the framework of the karmic influence. But there are other two chakras which are 113 and 114 which are outside the physical framework of the body which generally remain very... very minimal or almost dormant in most people, but if you have done enough sadhana it becomes active. And this was a kind of... this happened in a certain way, I will not go into the detail but the 114th chakra pulsates in a certain way which is... right from ancient times has been described as the ouroboros. ouroboros is the symbol of a snake eating its own tail, that is, it's trying to swallow itself. Have you seen this symbol? Almost every ancient culture - in India it's been plenty, all over the temples you can see them - you can see this in Greece, you can see this in Egypt, you can see this in Mesopotamian temples almost

everywhere. Ancient cultures which were focused more upon the beyond than what is here, in all those cultures you will see the symbol of ouroboros where a snake is trying to eat its own tail. So the 114th chakra pulsates in the form of an ouroboros and today, I don't know how they arrived at this, the modern mathematics uses ouroboros as the sign of infinity So the 14th chakra pulsates in the form of the infinite and if one's energies touch this dimension within you, then every action, whatever you do is a process of liberation. If it's within the 112, every action that you do has a residue, so it is best that you do the right kind of action so that it leaves a pleasant residue, not an unpleasant residue upon you. But if one's energy transcends the 112 and resides mostly in those two chakras which are beyond the physical framework, then he need not bother about his actions. He can act whichever way he wants. Whichever way he acts, it only leads to his liberation because action is not his anymore, it is of infinite nature. The sign of Kirtimukha in every temple, where he is eating himself up, is the sign of infinite because in eating up the physical, in dissolving the physical is the infinite possible and this is the natural movement of the 114th chakra or the 8th dimension as it is referred. So people tried to create structures and instruments through which we can take them... we can take another human being to that experience. These instruments, very ambitious projects, not always successful, sometimes successful, sometimes not. It took us three lifetimes to put this up. Continuously been a failure, only now enjoying success. (Laughs) Though came with enormous power, continuous failure. ___________________________________________ Ouroboros The Ouroboros or Uroboros (tail-devouring snake) is an ancient symbol depicting a serpent or dragon eating its own tail. While first emerging in Ancient Egypt, the Ouroboros has been important in religious and mythological symbolism, but has also been frequently used in alchemical illustrations, where it symbolizes the circular nature of the alchemist's opus. It is also often associated with Gnosticism, and Hermeticism. Ancient Egypt

The first known appearance of the ouroboros motif is in the Enigmatic Book of the Netherworld, an ancient Egyptian funerary text in KV62, the tomb of Tutankhamun, in the 14th century BC. Some Hindu folk-myths have a snake (Adisesha) circling the tortoise Kurma that supports the eight elephants which support the world on their backs. It is a common belief among the native people of the tropical lowlands of South America that watersat the edge of the world-disc are encircled by a snake, often an anaconda, biting its own tail. Indian mythology and tradition – variations - Single snake on deity in various locations of body, feet (karthikeya), Stomach (Ganesha), Neck and above head (Shiva) - Intertwined snakes – three and half and seven intersection snakes - Seven headed hooded snake – Dhyanalinga Srinivasa Ramanujam December 22 is the 125th anniversary of the birth of Srinivasa Ramanujan, an Indian mathematician renowned for somehow intuiting extraordinary numerical patterns and connections without the use of proofs or modern mathematical tools. A devout Hindu, Ramanujan said that his findings were divine, revealed to him in dreams by the goddess Namagiri. While on his death-bed in 1920, Ramanujan wrote a letter to his mentor, English mathematician G. H. Hardy. The letter described several new functions that behaved differently from known theta functions, or modular forms, and yet closely mimicked them. No one at the time understood what Ramanujan was talking about. “It wasn’t until 2002, through the work of Sander Zwegers, that we had a description of the functions that Ramanujan was writing about in 1920,” Ono says. “We proved that Ramanujan was right,” Ono says. “We found the formula explaining one of the visions that he believed came from his goddess.”

“No one was talking about black holes back in the 1920s when Ramanujan first came up with mock modular forms, and yet, his work may unlock secrets about them,” Ono says. Only in 2010 did they find out that this theorem describes various behaviors of black holes. (Not the black hole itself.) “So much of what Ramanujan offers comes from mysterious words and strange formulas that seem to defy mathematical sense,” Ono says. “Although we had a definition from 2002 for Ramanujan’s functions, it was still unclear how it related to Ramanujan’s awkward and imprecise definition.” Ono and his students finally saw the meaning behind the puzzling paragraph, and a way to link it to the modern definition. “We developed a theorem that shows that the bizarre methodology he used to construct his examples is correct,” Ono says. “For the first time, we can prove that the exotic functions that Ramanujan conjured in his deathbed letter behave exactly as he said they would, in every case.” Although Ramanujan received little formal training in math, and died at the age of 32, he made major contributions to number theory and many other areas of math. Ono says. “The pages were yellow and falling apart, but they are filled with formulas and class invariants, amazing visions that are hard to describe, and no indication of how he came up with them.” _______________________________________________________

Sadhguru on Devi The original word to describe the feminine was “re.” The word “re” refers to the Mother Goddess of the existence and is the basis of the more recent word “stree.” “Stree” literally means a woman. The word “re” means movement, possibility, or energy. In terms of creation, how did the feminine happen, first of all? The story goes like this. The forces which were detrimental to the existence rose and started threatening the very existence which was still in an infant state. So the three main gods, Brahma, Vishnu and Mahesh, met. These three gods signify three different qualities. Today, according to modern physical sciences, it is clearly understood that the proton, neutron and electron

are the basic building blocks for the existence. They are in place the way they are, and they are in movement. The dynamism in them is only because of an electrical charge which is outside of these three forces. Without that electrical or electromagnetic charge, these three cannot be in any state of dynamism. Without the dynamic movement of these three, there is no such thing as creation. It is this aspect of science that the story is trying to propound in a very dialectical way. It says that these three gods met because the forces of destruction had risen, and they did not know how to handle it. They had three stellar qualities within them, but they found these three qualities were not enough. They understood that a combination of these three qualities was needed. So all of them exhaled powerfully, letting out the best of what they were. This exhalation from these three forces merged and became the feminine, or the Devi. The word “Devi” comes from the word “Dev.” “Dev” means “the space.” So Devi is not a particle – she is the space which holds the three fundamental forces in the existence. It is this that we refer to as “De-vi.” ___________________________________________________________________ Fibonacci Fibonacci numbers are 0 1 1 2 3 5 8 13 21 34 55 89 144 .......... (*) They belong to the infinite Fibonacci series generated by the following simple rule: given the first two numbers in the series 0 and 1, every other number is the sum of the preceding two (e.g. 1 = 0 + 1, 3 = 2 + 1, 5 = 3+2 .........144 = 89 +55...). Fibonacci numbers are pervasive in all areas of science. In geometry they are related to pentagons, decagons and 3-dimensional Platonic solids. The ratio of the sides approaches a limiting value denoted by φ = (1+√5)/2 = 1.61803.... called the Golden Ratio. This ratio is ubiquitous in nature: in the branching of trees, arrangement of flower petals, seeds and leaves, spiral patterns of florets in sun flowers, spiral shapes of seashells, cones of pine tree etc. It appears to be closely related to growth processes in nature. The Golden Ratio is also believed to figure prominently in Western art: in architecture (pyramids, Parthenon), paintings (Leonardo da Vinci), sculpture, poetry (Virgil) and music. There is a vast literature on the subject and many claims are controversial.

A Sanskrit grammarian, Pingala, is credited with the first mention of the sequence of numbers, sometime between the fifth century B.C. and the second or third century A.D. Since Fibonacci introduced the series to Western civilization, it has had a high profile from time to time. Recently, in The Da Vinci Code , for example, the Fibonacci sequence is part of an important clue. Another application, the Fibonacci poem , is a verse in which the progression of syllable numbers per line follows Fibonacci's pattern. Kolam Kolams have been found to also follow the Fibonacci number patterns. • • •

Algorithms for drawing kolams are used in development of Picture drawing Computer software.[10] Kolams are also used to simplify the representation of complex protein structures for easy understanding.[13] Kolam drawing is said to stimulate the right side of the brain and has been done by women for thousands of years.

Scientists’ predicament: “Google” and Infinity • A google – 1 followed by a hundred zeros – in an attempt to reach the largest number. • This is more than the number of atoms in a human being, on planet earth, or in the universe • Stepping stone on the way to a larger number – google plex (10 ^google) – one followed by a google of zeros. Not enough space in the universe to write the number down – even if we can write each zero on an atom. • Graham’s number was discovered by mathematician and former circus performer Ronald Graham – o Received record in 1980 guiness book- highest number ever used in a mathematical proof. He says he himself doesn’t know anything about the number

• To most people infinity is not real, but mathematics cannot be done without infinity. Infinity is the landscape in which you work and do mathematics • Infinity- paradoxical. For every infinite number there is a bigger one (infinity +1) • Theory: Infinity of Infinities – Georg Cantor o Died in an asylum • Cosmology has come to this: there are “Infinitely many infinite universes” Other experimental findings • Solidity of matter is a mirage – just a result of frequency. If the frequency is altered, the structure of the matter will change. • Experiments done to see what is the inside of an atom- shocked to see entirely empty space. How can an empty atom make a solid world? • Cymatics- vibrations which go thru media, a set pattern follows. Higher frequency- more complex pattern. This is happening to earth and humanity. • 64 possible codes of amino acids form helical structure from four elements – carbon, oxygen, hydrogen and nitrogen. Out of this, only 20 are on. They say emotion is a switch which is directly related to genetic coding. o Fear- creates a ‘long, slow wave’ which touches few sites in the DNA. Fearful people have limited access to dna coding. Love- a higher frequency, shorter wavelength- touches more sites in the DNA strand. • Experiment: Russian researcher Dr.Vladimir Poponin put DNA in a Vacuum tube and put light through it. When the DNA was removed, the particles of light (photons) continued spiraling on its own in the same form of the DNA even if no DNA strands were present. This effect is called ‘Phantom DNA Effect’. o Bridges gap between physical/ethereal