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Fibonacci & Pythagoras Help save a beautiful discovery from oblivion

This is another brillian video from Mathologer. In 2007 a simple beautiful connection Pythagorean triples and the Fibonacci sequence was discovered. This video is about popularising this connection which previously went largely unnoticed. If you want more details go to the video on Mathologer.

Pascal’s Triangle

  • One of the most interesting Number Patterns is Pascal’s Triangle (named after Blaise Pascal, a famous French Mathematician and Philosopher). …
  • Diagonals. …
  • Symmetrical. …
  • Horizontal Sums. …
  • Exponents of 11. …
  • The same thing happens with 116 etc.
  • Squares. …
  • Fibonacci Sequence.

The Coefficients of the Binomia Theorem from Pascal’s Triangle

Pascal’s triangle formula is (n+1)C(r) = (n)C(r – 1) + (n)C(r). It means that the number of ways to choose r items out of a total of n + 1 items is the same as adding the number of ways to choose r – 1 items out of a total of n items and the number of ways to choose r items out of a total of n items.

The Fibonacci sequence with Pythagorean triples

The sum of the squares of consecutive Fibonacci numbers is another Fibonacci number. Specifically we have the following right triangle. The hypotenuse will always be irrational because the only Fibonacci numbers that are squares are 1 and 144, and 144 is the 12th Fibonacci number.

Pascal’s triangle is commonly used in probability theory, combinatorics, and algebra. In general, we can use Pascal’s triangle to find the coefficients of binomial expansion, the probability of heads and tails in a coin toss, the probability of certain combinations of things, and so on


About Mathologer

Enter the world of the Mathologer for really accessible explanations of hard and beautiful math(s). In real life the Mathologer is a math(s) professor at Monash University in Melbourne, Australia and goes by the name of Burkard Polster. These days Marty Ross another math(s) professor, great friend and collaborator for over 20 years also plays a huge role behind the scenes, honing the math(s) and the video scripts with Burkard. And there are Tristan Tillij and Eddie Price who complete the Mathologer team, tirelessly proofreading and critiquing the scripts and providing lots of original ideas. If you like Mathologer, also check out years worth of free original maths resources on Burkard and Marty’s site

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Tesla’s 3-6-9 and Vortex Math – Is this really the key to the universe

“If you only knew the magnificence of 3, 6 and 9, you would have a key to the universe”.
If you want to find the secrets of the universe, think in terms of energy, frequency and vibration”.
“My brain is only a receiver, in the Universe there is a core from which we obtain knowledge, strength and inspiration. I have not penetrated into the secrets of this core, but I know that it exists.”

Nikola Tesla

Tesla did countless mysterious experiments, but he was a whole other mystery on his own. As a famous saying goes “The greatest minds are always curious”, this goes well for Nikola Tesla. He also had an eidetic — photographic — memory, which he used to craft his ideas and inventions in his head before setting out to create them in reality.

Patterns involving 3

  • Walk around a block 3 times before entering a building
  • Chose only those Hotel’s rooms, which had their room number divisible by 3
  • He would wash his dishes with 18 napkins only (18 is divisible by 9, 6, and 3)

In addition, the number three holds significance not only for Tesla, but for many people throughout history. Examples include the three subatomic particles of an atom (proton, neutron, and electron), the Holy Trinity in Christianity (God, Jesus, and the Holy Spirit), and the three Egyptian gods representing heaven, earth, and the abyss. Furthermore, the concept of time in the Sanskrit language is divided into three parts: the past, present, and future, known as “Kaal.” This demonstrates that the number three has been significant across various cultures and fields of knowledge.

Vortex Math

Another extraordinary video by Mathologer. Vortex math is a system of numbers which explains the essence of form as a sphere with a vortex. The numbers reveal a spiral line and a curved plane. The numbers in this spiral line describe the form of a vortex , the vortex describes an inward contraction with its equal expansion which is the inner form of a torus . Vortex math numbers illustrate the contracting and the expanding elements of the external physical plane and they also illustrate the internal and subtle aspect of consciousness.

Essentially, according to vortex math, that repeated pattern of numbers defines a “vortex”, which is the deepest structure in the universe, and it’s the key to understanding all of math, all of physics, all of metaphysics, all of medicine. It’s the fundamental pattern of everything, and by understanding it, you can do absolutely anything.

Giza – Orion Correlation Theory

We find lots of evidence that nature uses threefold and sixfold symmetry, including the hexagonal tile shape of the common honeycomb. Interestingly not just in nature but also the ancient establishments have this symmetry. One of the greatest of them all is the Giza – Orion correlation theory.

According to this, there is a correlation between the location of the three largest pyramids of Giza and Orion’s Belt of the constellation Orion, and this correlation was intended as such by the original builders of the Giza pyramid complex. The stars of Orion were associated with Osiris, the god of rebirth and the afterlife by the ancient Egyptians. Depending on the version of the theory, additional pyramids can be included to complete the picture of the Orion constellation, and the Nile river can be included to match with the Milky Way galaxy.

pyramids od Giza

The Ten Emanations of God

With the zero being regarded as Heaven and the all or nothing this now leaves us 9 numbers within our base-ten system. 1, 2, 3, 4, 5, 6, 7, 8 and 9. These nine gods were celebrated by the Greeks and Egyptians in the Ennead.

The Ennead was nine gods that represented the archetypal principles that regulated and ruled the cosmos through the laws of number. This company of nine has shown its face many times throughout the world.

In Norse mythology, the god Odin hung on the Yggradsil tree for nine days. Benjamin Franklin was Grand Master of the charitable Nine Sisters Lodge. In the European Middle ages we see the Nine-Worthies, semi-legendary figures who personified the ideas of chivalry. We have all heard of Cloud Nine, being dressed to the nines, the nine lives of a feline and a stitch in time saves nine. The Christian’s mythologized the power of these nine numbers in the Christian Angelic hierarchy with those angels being the (9) Seraphim, (8) Cherubim, (7) Thrones, (6) Dominions, (5) Virtues, (4) Powers, (3) Principalities, (2) Archangels and (1) Angels.

Even the ancient Mayan venerated the principles of nine. One of the most well-known Mayan pyramids is the pyramid at Chichen Itza. Chichen Itza is nine-level pyramid with a celestial observatory at the top. For a few moments on the solstices and equinoxes, the light and shadows on this pyramid forms a snake that travels down the side of the pyramid to the base, where the head of this great snake, called Quetzacoatal or Kukulcan is carved into stone. The Hebrew letter “Teth”, transcribed as a “T”, meant serpent, or the secret intelligence of all spiritual activities, and was designated by the number nine.

The number 9 shows up quite often in the metrology of our universal architecture as well. The diameters of the Moon, the Sun and the Earth using decimal parity all reduce down to this number of spirit.

Nikola Tesla’s Wardenclyffe wireless station

Nikola Tesla’s Wardenclyffe wireless station, located in Shoreham, New York, seen in 1904. The 187 foot (57 m) transmitting tower appears to rise from the building but actually stands on the ground behind it. Built by Tesla from 1901 to 1904 with backing from Wall Street banker J. P. Morgan, the experimental facility was intended to be a transatlantic radiotelegraphy station and wireless power transmitter, but was never completed. The tower was torn down in 1916 but the lab building, designed by noted New York architect Stanford White remains.

Nikola Tesla’s Wardenclyffe wireless station, located in Shoreham, New York, 1904.

Human’s Plexus Systems and “Nikola Tesla’s 369 Theory” for Forming Universe and God

All activities which are taking place in the Cosmos also exist in a human body in subtle micro-scale. Plexuses centers in a human body are the most mysterious kinds of energies. The six-center plexus system is the path of the Kundalini shakti, the primordial cosmic energy of a person. Each plexus has its own propensities (vibrating words/dimensions/vritti) and an acoustic root. These plexuses control some cluster of words of sounds and corresponding physical organs in human body. The 50 main propensities of the human’s unit mind are expressed through the vibration-expression of these plexuses. These vibrations cause hormones to secrete from the corresponding glands of the human’s body. These plexuses can play very important roles in curing the diseases. According to the Theory of Nikola Tesla’s 369, there are all together 1 to 9 digital root numbers exist. All other higher or lower numbers are the combination of those digital root numbers. This statement seems quite true when we compare it with Theory of Absolutivity. If 3, 6, 9 numbers are arranged together it makes a letter Ohm (AUM) which represents actually a Sagun Bramh/Nikola Tesla’s 369 triangle which is a part of NirgunBramh having  higher dimensions. Number zero is the NirgunBramh (having all the qualities but in dormant form) which does not possess any quality in action. Number 3, 6, 9 forming as an equilateral triangle of static, mutative and sentient forces representing the Black-hole which is a part of Sagun Bramh projecting Himself as a Visible World through Big-bang along with forming five basic elements such as Ethereal, Areal, Fire, Liquid and Solid. According to the biological science, life emerged in this planet from matter about four billion years ago in the form of DNA that carried the software for the development of billion of species on the way to its final destination in humans. These facts also fully support the above hypothesis of universe formations.


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Thermodynamics – Explaining the Triple Point

The triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. As a result, at the triple point of water, the entropy is constant. Therefore, the entropy is constant at the triple point of water. The triple point of water is used to define the Kelvin(K), the base unit of thermodynamic temperature in the International System of Units (SI).  

The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero. The entropy of a system at absolute zero is typically zero, and in all cases is determined only by the number of different ground states it has.

The single combination of pressure and temperature at which liquid water, solid ice, and water vapor can coexist in a stable equilibrium occurs at exactly 273.1600 K (0.0100 °C; 32.0180 °F) and a partial vapor pressure of 611.657 pascals (6.11657 mbar; 0.00603659 atm).