Mathematics & Physical Constants

mathematical constants

Math, like music is a universal language. Perhaps Math is the word of GOD.
Laws of physics are UNiversal Laws. Perhaps the laws of physics are the manifestation of GOD's work.
Nmbers system with 0 and Infinity as boundaries

Pi - Tau

PI: The ratio of the circumference of a circle to its diameter.
Pi is an irrational number. It can’t be expressed as a fraction; it doesn’t end with a repeating pattern (like the decimal expression of 1/3, 0.33333…, in which the threes repeat forever), or terminate after a certain number of decimal places (like 3/4, or .75). While we know pi to more than a trillion places, we really don’t need them. Scientists can determine the spherical volume of the entire universe using just 39 places past the decimal, according to NASA’s Jet Propulsion Laboratory only uses pi up to 15 decimal places for its robotic space and earth science missions. “For JPL’s highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793,” explains engineer Marc Rayman. “There are no physically realistic calculations scientists ever perform” that would require more decimal points than that.

Welsh mathematician William Jones in a 1706 work called Synopsis Palmariorum Matheseos, in which he abbreviated the Greek περιϕέρεια, (meaning “circumference,” or “periphery”) to its first letter: π.3.

Convergents of the pi continued fractions are the simplest approximants to pi. The first few are given by 3, 22/7, 333/106, 355/113, 103993/33102, 104348/33215, . pi (100 digits) = 3.141592653589793238462643383279502884197169399375105820974944 5923078164 0628620899 8628034825 3421170679

Tau is simply 2pi = 6.283185...

e Euler’s Number

Euler’s Number = 2.71828182845904523536... e= 1 + 1/1 + 1/2! + 1/3! + 1/4! + 1/5!) e: Base of the exponential function which equals its own derivative.


Golden Ratio = 1.61803398874989484820

Other Useful Constants

Square Root of 2 = 1.41421356237309504880

Log(2)= 0.69314718055994530941
Log(10) = 2.30258509299404568401
ln(2):  The alternating sum of the reciprocals of the integers.

Euler-Mascheroni Constant  g :  Limit of   [1 + 1/2 + 1/3 +...+ 1/n] - ln(n).
Euler-Mascheroni Constant = 0.57721566490153286060

Catalan's Constant  G :  The alternating sum of the reciprocal odd squares.
Catalan's Constant = 0.91596559417721901505

Apéry's Constant  z(3) :  The sum of the reciprocals of the perfect cubes.
Zeta(3) - Apery's Constant = 1.20205690315959428539
Zeta(5)	1.03692775514336992633

Imaginary  i:  If "+1" is a step forward, "+ i" is a step sideways to the left. 

Delian constant:  21/3  is the solution to the  duplication of the cube.

Rayleigh factor  for the diffraction limit of angular resolution.
Mertens constant:  The limit of   [1/2 + 1/3 + 1/5 +...+ 1/p] - ln(ln p)

Artins's constant  is the proportion of long primes in decimal or binary.

Ramanujan-Soldner constant (m):  Positive root of the logarithmic integral.
The Omega constant:  W(1) is the solution of the equation   x exp(x) = 1.
Feigenbaum constant (d) and the related reduction parameter (a). 

Gelfond's Constant  raised to the power of  i  is  -1.

Brun's Constant:  A standard uncertainty  (s)  means a 99% level of  ±3s

Prévost's Constant:  The sum of the reciprocals of the Fibonacci numbers.

Grossman's Constant:  One recurrence converges for only one initial point.

Ramanujan's Number:   exp^(Pi*SQRT(163))   is almost an integer.

Ramanujan-Soldner constant (m):  Positive root of the logarithmic integral.

Viswanath's Constant:  Mean growth in random additions and subtractions.

Copeland-Erdös Number:  Almost all numbers are  normal,  like this one.

Lemniscate Constant = 5.24411510858423962092

Gauss's constant:  Reciprocal of the arithmetic-geometric mean of 1 and Ö2.
Rayleigh factor  for the diffraction limit of angular resolution.

Mertens constant:  The limit of   [1/2 + 1/3 + 1/5 +...+ 1/p] - ln(ln p)

The Omega constant:  W(1) is the solution of the equation   x exp(x) = 1.

Feigenbaum constant (d) and the related reduction parameter (a). 

Gelfond's Constant  raised to the power of  i  is  -1.

Grossman's Constant:  One recurrence converges for only one initial point.

List of numbers Irrational numbers
ζ(3) √2 √3 √5 φ ρ δS e π

Physical Constants

  1. The Universal Gravitational Constant = 6.67408 × 10-11 m^3 kg^-1 s^-2
  2. Speed of Light in a Vacuum: c = 299,792,458 m/s.
  3. Avogadro's number: The number of things per mole of stuff.
  4. Planck's constant h: The ratio of a photon's energy to its frequency.
    h=6.62607004*10^(−34) m^2 kg/s
  5. Boltzmann constant = 1.38064852 * (10^-23) m^2 kg s^-2 K^-1
    The Boltzmann constant is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula

Additional Notes

The Pythagorean Theorem (by Euclid?) is now attributed to Pythagoras. However studies show that this theorem was found 1000 years before Pythagoras. The square of a hypotenuse is always equal to the sum of the squares of its other two lines.

Logarithm: Numbers can be multiplied by adding two related numbers, discovered by Laird John Napier. With time, this method got easier and faster and was further refined by Henry Briggs.

Calculus is the calculation of instantaneous rates of change. Having been first described in the 17th century, the method has served as a foundation for many natural laws.

The Law of Gravitation involves controversy of Newton having it borrowed from Johannes Kepler and Robert Hooke. Known to many ancient cultures. In fact this famous law is known for being later supplanted by Einstein in his theory of relativity.

Imaginary numbers (SQRT(-X)) were first formed by Girolamo Cardano, later expanded by Raphael Bambelli and John Wallis, before being described by William Hamilton. Until its description, Imaginary numbers have always existed as a peculiar problem in math. Complex Numbers are extension.
The square of any imaginary number will always result in a negative number. Today this formula is broadly used in complex mathematical theory apart from electrical engineering.

Formula for Polyhydra by Euler, describes the shape or structure of a particular space regardless of its alignment. The method has been a very fundamental one in the development of topography. It has extended geometry and has proved as a useful tool to biologists and engineers. Today it is very important inI understanding the functioning of a particular DNA. The formula was first described by Descartes before Euler had refined, proved and finally published it.

Normal Distribution: When you observe a point on a curve you will notice that the probability is greatest at the average. This is a discovery mainly by Blaise Pascal. It later came into distribution with Bernoilli. This equation has been very useful in the foundation of modern statistics, science and social science. Today it is very useful in determining the effectiveness of a particular drug and is thus very helpful in clinical trials.

Wave Equation has been very useful in discovering how sound works, how earthquakes happen and the way oceans behave.

Fourier Transform describes patterns as a function of frequency in time. Discovered by Joseph Fourier, the equation has proved very important today in compressing information in JPEG format and the discovery of the structure of molecules. It has also proved essential in the analysis of signals. Complex patterns can be broken, cleaned up and analyzed with the use of this equation.

Novier Strokes was developed by Leonhard Euler, for modeling the movement of fluids. It states that while the left side accelerates a small amount, the right indicates the forces acting on that amount of fluid. This equation has been very helpful in making vehicles more aerodynamic apart from leading to the development of modern passenger jets.

The Equations of Maxwell map out relationships between electric and magnetic fields, this equation, developed by Michael Faraday, has led to the creation of most of the technologies that we use today by aiding us in the understanding of electromagnetic waves.

Thermodynamics Second Law: This law that proves the dissipation of energy and heat over time, has been very essential in understanding energy and the universe through the concept of entropy. Based on the idea that nature has no reversible processes, by Sadi Carnot, which was later extended by Ludwig Boltzman, the equation was formally stated by Wiliiam Thomson.

Relativity: This theory by Einstein has proved to be the most famous equation in history. The theory states that energy is always equal to mass times the speed of light squared and has been a useful method in changing our view of matter and reality to this day. In modern times it has helped in the use of nuclear weapons.

Schrodinger equation founded by Louis Victor de Broglie, states that models matter not as a particle but a wave, reveals to us the dual nature of matter. It has helped revolutionize at small scales, our view of physics. This equation has been extremely helpful in modern computer technology, by being of use to transistors and semiconductors.

Information Theory Developed by Claude Shannon for estimating how much data exists in a piece of code using the probabilities of its components symbols. This equation has in fact helped in ushering the age of information where engineers no longer have to seek codes that are too efficient. It has established the boundaries for the making of almost everything from CDs to digital communications.

Logistic Model has been very useful in estimating changes in population with limited resources across all generations. It led to realization that chaos is a result of differential equations helping change our understanding of natural systems with the development of the chaos theory. It is very useful in weather forecast and the modeling of earthquakes.

Omega is the ratio of the total amount of matter in the universe divided by the minimum amount of matter needed to cause the big crunch. If Omega is less than one, the galaxies will fly apart forever. If it's more than one, then sometime in the far-distant future the big crunch will happen. Our best estimate at the moment is that Omega lies somewhere between 0.98 and 1.1. So the fate of the universe is still unknown. if there were approximately five atoms of hydrogen per cubic meter of space, that would be just enough matter for gravitational attraction to bring the galaxies back together in a big crunch. That tipping point is called Omega; it'

In Quantum Physics, to bring something into the physical world requires focusing not on what you see, but on what you want to see.

Einstein said, "Matter is formed out of energy". The very substance of what we see and feel came from someone’s thoughts or energy.

Ergo, not only do our thoughts impact matter, our thoughts are vibrational energy that manifest in what we see in our lives.