This post is also available in: हिन्दी (Hindi)

Some numbers, such as your phone number or your ID number, are decidedly more important than others. But the numbers on this list are of cosmic importance—they are the fundamental concepts that define our universe, that make the existence of life possible and that will decide the ultimate fate of the universe.

## Most Important Numbers in The World

We bring you a list of the 10 most important numbers in the world.

### 1. Avogadro’s Number

**Avogadro’s number** is the number of units of any substance in one mole. It is also called **Avogadro’s constant**. Despite the name, Amedeo Avogadro did not discover or describe Avogadro’s number. Instead, it’s named in honor of Avogadro’s contributions to the field of chemistry.

**Avogadro’s number is a defined value that is exactly 6.02214076×10 ^{23}.** When used as a constant proportionality factor (NA), the number is dimensionless (no units). However, usually Avogadro’s number has units of a reciprocal mole or 6.02214076×10

^{23}mol

^{-1}. Although all of the digits of the number are known, students usually use either 6.02 × 10

^{23}or 6.022 × 10

^{23}, to keep consistent significant digits in chemistry calculations.

#### How Big is Avogadro’s Number?

Avogadro’s number is one mole, so basically this is the same as asking how big a mole is. You can apply Avogadro’s number to *anything*:

- Avogadro’s number of softballs would fill a sphere the size of the Earth.
- One mole of red blood cells is more than all the red blood cells of every person alive right now.
- Avogadro’s number of donuts would cover the Earth with a layer 5 miles deep.
- A mole of moles (the animal) would weigh about half the mass of the Moon.
- If you were given Avogadro’s number of pennies at birth, spent a million dollars every second of every day, and lived to age 100, you’d still have 99.99% of the pennies left.
- It’s 18 milliliters of water molecules.

#### Importance of Avogadro’s Number

The reason Avogadro’s number is important is that it serves as a bridge between the very large numbers and familiar, manageable units. For example, because of Avogadro’s number we calculate the mass of one mole of water to be 18.015 grams. Without this proportionality constant giving us the mole, we’d have to write out “6.02214076×10^{23} water molecules with a mass of 18.015 grams”.

Basically, Avogadro’s number lets us write the mass of one mole of a substance in small numbers (the molecular weight). It also lets us write the ratios between reactants and products in a chemical equation. This greatly simplifies calculations.

### 2. Gravitational Constant

Curiously, though the gravitational constant, G, was the first constant to be discovered, it is the least accurately known of all other constants. That is because of the extreme weakness of the gravitational force when compared with the other basic forces. Its smallness accounts for the fact that the force of gravitational attraction is only appreciable for objects with large mass. While two students will indeed exert gravitational forces upon each other, these forces are too small to be noticeable. Yet if one of the students is replaced with a planet, then the gravitational force between the other student and the planet becomes noticeable.

The **gravitational constant** (also known as the **universal gravitational constant**, the **Newtonian constant of gravitation**, or the **Cavendish gravitational constant**), denoted by the letter *G*, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton’s law of universal gravitation and in Albert Einstein’s general theory of relativity.

In Newton’s law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance. In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor (also referred to as the stress–energy tensor).The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately 6.674×10^{−11} m^{3}⋅kg^{−1}⋅s^{−2}.

#### Importance of Gravitational Constant

Gravitational constant find applications in many areas such as

- The gravitational force of earth ties the terrestrial objects to the earth.
- Explains the attractive force between any two objects having a mass.
- The formation of tides in the ocean is due to the force of attraction between the moon and ocean water.

- All planets make an elliptical revolution with the sun.
- The rotation of the earth around the sun.
- The rotation of the moon around the earth.

### 3. Boltzmann’s Constant

We all know that water flows downhill, not uphill, because that’s the way gravity works. Gravity is a force, and the gravitational pull of the earth acts as if it were concentrated at the center of the earth, and pulls the water downhill. However, there isn’t a similar explanation for why we see ice cubes melt when placed in a glass of hot water but never see ice cubes form spontaneously in a glass of tepid water. This has to do with the way heat energy is distributed, and the solution to this problem was one of the great quests of 19th-century physics.

The solution to this problem was found by the Austrian physicist Ludwig Boltzmann, who discovered that there were many more ways for energy to be distributed throughout the molecules of a glass of tepid water than in a glass of hot water with ice cubes. Nature is a percentage player. It goes most often with the most likely way to do things, and Boltzmann’s constant quantifies this relationship.

Disorder is much more common than order—there are many more ways for a room to be messy than clean (and it’s much easier for an ice cube to melt into disorder than for the ordered structure of an ice cube to simply appear).

The Boltzmann constant (kB) relates temperature to energy. It is an indispensable tool in thermodynamics, the study of heat and its relationship to other types of energy. It’s named for Austrian physicist Ludwig Boltzmann (1844–1906), one of the pioneers of statistical mechanics. Statistical mechanics expands upon classical Newtonian mechanics to describe how the group behavior of large collections of objects emerges from the microscopic properties of each individual object.

The **Boltzmann constant** (*k*_{B} or *k*) 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. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy.

It is named after the Austrian scientist Ludwig Boltzmann.As part of the 2019 redefinition of SI base units, the Boltzmann constant is one of the seven “defining constants” that have been given exact definitions. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly 1.380649×10^{−23} J⋅K^{−1}.

#### Importance of Boltzmann Constant

The Boltzmann Constant is used in diverse disciplines of physics. Some of them are listed below-

- In classical statistical mechanics, Boltzmann Constant is used to express the equipartition of the energy of an atom.
- It is used to express the Boltzmann factor.
- It plays a major role in the statistical definition of entropy.
- In semiconductor physics, it is used to express thermal voltage.

### 4. Imaginary Unit (*i*)

The **imaginary unit** or **unit imaginary number** (** i**) is a solution to the quadratic equation x

^{2}+ 1 = 0. Although there is no real number with this property,

*i*can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of

*i*in a complex number is 2 + 3

*i*, where

*i*= √-1

Imaginary numbers are an important mathematical concept, which extend the real number system R to the complex number system C, in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term “imaginary” is used because there is no real number having a negative square.

There are two complex square roots of −1, namely *i* and −*i*, just as there are two complex square roots of every real number other than zero (which has one double square root).

In contexts in which use of the letter *i* is ambiguous or problematic, the letter *j* or the Greek *ι* is sometimes used instead.For example, in electrical engineering and control systems engineering, the imaginary unit is normally denoted by *j* instead of *i*, because *i* is commonly used to denote electric current.

#### Importance of Imaginary Unit

Some of the common applications of imaginary numbers are

- Signal Processing
- AC Circuit Analysis
- Quantum Mechanics

### 5. Archimedes’ Constant (Pi)

For centuries, ancient mathematicians and engineers would attempt to build and construct using circles, and they found they needed to accurately calculate the relationship (or ratio) between the distance around the outside of a circle (its circumference) and the distance directly across it through the middle (its “diameter”). The relationship seemed to repeat itself in a pattern, no matter the size of the circle, and there were multiple attempts to pinpoint the exact number that represented the ratio.

Ancient Egyptians used a rough approximation between 3.12 and 3.16. Ancient Hebrews estimated at 3. But it was the ancient Chinese mathematicians, and later those in India, who were able to calculate the ratio up to an accuracy of 7 digits.

In Europe, Greek mathematician Archimedes in the 3rd century BCE proved the upper limit of the ratio as 22/7, and this value became the commonly accepted number to calculate the circumference to diameter relationship for over 1,000 years. In 1630, the number was expanded to 39 digits, getting closer to its more commonly accepted modern form. It is now understood as an irrational number, which does not end or fall into a repeating pattern.

In the 18th century the Greek letter pi (π) came to signify the relationship and is common in calculations not only of circles, but of ellipses and cosmological curvilinear shapes as well. In common schoolhouse geometry, pi is generally taught as 3.14159 to introductory students. For advanced calculations requiring the utmost precision, values of pi may be taken to hundreds of places in statistics, thermodynamics, cosmology, and electromagnetism.

#### Importance of Archimedes’ Constant

Some of the applications of Archimedes’ Constant (PI) are:

- Electrical engineers used pi to
**solve problems for electrical applications** - Statisticians use pi to
**track population dynamics** - Medicine benefits from pi when
**studying the structure of the eye** - Biochemists see pi when
**trying to understand the structure/function of DNA** - Physicists looking into the
**behavior of fluid ripples**see pi and use it in their**calculations** - Clock designers use pi when
**designing pendulums for clocks** - Aircraft designers use it to
**calculate areas of the skin of the aircraft** **Signal processing and spectrum analysis**(finding out what frequencies are in the wave you are using) uses pi since the fundamental period of a sine wave is 2*pi.**Navigation**, such as global positioning (GPS)**Calculating the number of death in a population****Solving Mathematics problems in Geometry like finding the area of a circle etc.**

### 6. Euler’s Number (*e*)

The number *e*, sometimes called the natural number, or Euler’s number, is an important mathematical constant approximately equal to 2.71828…When used as the base for a logarithm, the corresponding logarithm is called the natural logarithm, and is written as *ln(x)*. Note that *ln*(*e*) = 1 and that *ln*(1) = 0.

There are a number of different definitions of the number *e*. Most of them involve calculus. One is that *e* is the limit of the sequence whose general term is (1 + 1/*n*)* ^{n}*. Another is that

*e*is the unique number so that the area under the curve

*y*= 1/

*x*from

*x*= 1 to

*x*=

*e*is 1 square unit.

Another definition of *e* involves the infinite series 1/1! + 1/2! + 1/3! + 1/4! + … It can be shown that the sum of this series is *e*.

The story of *e* is a bit convoluted and includes the contributions of three mathematicians: John Napier, Jacob Bernoulli, and Leonard Euler. In the 17th century, Napier, a Scottish mathematician, physicist, and astronomer, began looking for a simpler way to multiply very large numbers. Specifically, he wanted to find a shortcut for exponents. While Napier didn’t discover the number *e*, he did come up with a list of logarithms that he unknowingly calculated with the constant.

It would be about another 70 years before this list of logarithms became associated with exponents. In 1683, Swiss mathematician Jacob Bernoulli discovered the constant* e* while solving a financial problem related to compound interest. He saw that across more and more compounding intervals, his sequence approached a limit (the force of interest). Bernoulli wrote down this limit, as *n* keeps growing, as *e*.

Finally, in 1731, Swiss mathematician Leonhard Euler gave the number *e* its name after proving it’s irrational by expanding it into a convergent infinite series of factorials.

#### Importance of Euler’s Number

Some of the applications of Euler’s number are:

- Computation of compound interest
- Addition of signals using Phasor theorem
- Solving first order differential equations
- Growth and depreciation problems

### 7. The Golden Ratio

In mathematics, two quantities are in the **golden ratio** if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, (a + b)/a = φ (Golden Ratio). It is an irrational number that is a solution to the quadratic equation x^{2} – x – 1 = 0 with a value of φ = (1 + √5)/2 = 1.618033988749…

The golden ratio is also called the **golden mean** or **golden section**. Other names include **extreme and mean ratio**, **medial section**, **divine proportion,** **divine section,** **golden proportion**, **golden cut**,^{ }and **golden number**.

Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which may be cut into a square and a smaller rectangle with the same aspect ratio.

The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts.

Some twentieth-century artists and architects, including Le Corbusier and Salvador Dalí, have proportioned their works to approximate the golden ratio, believing this to be aesthetically pleasing. These often appear in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio.

The golden ratio is best approximated by the famous “Fibonacci numbers.” Fibonacci numbers are a never-ending sequence starting with 0 and 1, and continuing by adding the previous two numbers. The next numbers in the Fibonacci sequence, for instance, are 1,2,3, 5, 8, 13, ….

The ratios of sequential Fibonacci numbers (2/1, 3/2, 5/3, etc.) approach the golden ratio. In fact, the higher the Fibonacci numbers, the closer their relationship is to 1.618.

The golden ratio is sometimes called the “divine proportion,” because of its frequency in the natural world. The number of petals on a flower, for instance, will often be a Fibonacci number. The seeds of sunflowers and pine cones twist in opposing spirals of Fibonacci numbers. Even the sides of an unpeeled banana will usually be a Fibonacci number—and the number of ridges on a peeled banana will usually be a larger Fibonacci number.

#### Importance of Golden Ratio

While the Golden Ratio doesn’t account for *every* structure or pattern in the universe, it’s certainly a major player. Here are some examples.

**Flower petals:**The number of petals in a flower consistently follows the Fibonacci sequence. Famous examples include the lily, which has three petals, buttercups, which have five (pictured at left), the chicory’s 21, the daisy’s 34, and so on. Phi appears in petals on account of the ideal packing arrangement as selected by Darwinian processes; each petal is placed at 0.618034 per turn (out of a 360° circle) allowing for the best possible exposure to sunlight and other factors.**Seed heads:**In some cases, the seed heads are so tightly packed that total number can get quite high — as many as 144 or more. And when counting these spirals, the total tends to match a Fibonacci number. Interestingly, a highly irrational number is required to optimize filling (namely one that will not be well represented by a fraction). Phi fits the bill rather nicely.**Pinecones:**Similarly, the seed pods on a pinecone are arranged in a spiral pattern. Each cone consists of a pair of spirals, each one spiraling upwards in opposing directions. The number of steps will almost always match a pair of consecutive Fibonacci numbers. For example, a 3-5 cone is a cone which meets at the back after three steps along the left spiral, and five steps along the right.**Fruits and Vegetables:**Likewise, similar spiraling patterns can be found on pineapples and cauliflower.**Tree branches:**The Fibonacci sequence can also be seen in the way tree branches form or split. A main trunk will grow until it produces a branch, which creates two growth points. Then, one of the new stems branches into two, while the other one lies dormant. This pattern of branching is repeated for each of the new stems. A good example is the sneezewort. Root systems and even algae exhibit this pattern.**Snail shells:**Snail shells and nautilus shells follow the logarithmic spiral, as does the cochlea of the inner ear. It can also be seen in the horns of certain goats, and the shape of certain spider’s webs.**Spiral galaxies:**Not surprisingly, spiral galaxies also follow the familiar Fibonacci pattern. The Milky Way has several spiral arms, each of them a logarithmic spiral of about 12 degrees.**Faces:**Faces, both human and nonhuman, abound with examples of the Golden Ratio. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. Similar proportions can be seen from the side, and even the eye and ear itself (which follows along a spiral).**Fingers:**Looking at the length of our fingers, each section — from the tip of the base to the wrist — is larger than the preceding one by roughly the ratio of phi.**Animal bodies:**Even our bodies exhibit proportions that are consistent with Fibonacci numbers. For example, the measurement from the navel to the floor and the top of the head to the navel is the golden ratio. Animal bodies exhibit similar tendencies, including dolphins (the eye, fins and tail all fall at Golden Sections), starfish, sand dollars, sea urchins, ants, and honey bees.**DNA molecules:**Even the microscopic realm is not immune to Fibonacci. The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. These numbers, 34 and 21, are numbers in the Fibonacci series, and their ratio 1.6190476 closely approximates Phi, 1.6180339.**Animal fight patterns:**When a hawk approaches its prey, its sharpest view is at an angle to their direction of flight — an angle that’s the same as the spiral’s pitch.

### 8. Speed of Light

The speed of light denoted by *c* is 186,282 miles per second, or 299,792,458 meters per second. A meter is defined from this constant. (**a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1/299792458 second**) Understanding the speed of light is both one of physics’ proudest accomplishments, and understanding what it really pimples is one of its most dizzying questions.

According to special relativity, *c* is the upper limit for the speed at which conventional matter, energy or any signal carrying information can travel through space.

Though this speed is most commonly associated with light, it is also the speed at which all massless particles and field perturbations travel in vacuum, including electromagnetic radiation (of which light is a small range in the frequency spectrum) and gravitational waves.

Such particles and waves travel at *c* regardless of the motion of the source or the inertial reference frame of the observer. Particles with non zero rest mass can approach *c*, but can never actually reach it, regardless of the frame of reference in which their speed is measured.

In the special and general theories of relativity, *c* interrelates space and time, and also appears in the famous equation of mass–energy equivalence, *E* = *mc*^{2}, In some cases objects or waves may appear to travel faster than light (e.g. phase velocities of waves, the appearance of certain high-speed astronomical objects, and particular quantum effects).

The expansion of the universe is understood to exceed the speed of light beyond a certain boundary.The speed at which light propagates through transparent materials, such as glass or air, is less than *c*; similarly, the speed of electromagnetic waves in wire cables is slower than *c*.

The ratio between *c* and the speed *v* at which light travels in a material is called the refractive index *n* of the material *n* = *c*/*v*, For example, for visible light, the refractive index of glass is typically around 1.5, meaning that light in glass travels at *c* / 1.5 ≈ 200000 km/s (124000 mi/s); the refractive index of air for visible light is about 1.0003, so the speed of light in air is about 90 km/s (56 mi/s) slower than *c*.

### 9. Absolute Zero

**Absolute zero** is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvins. The fundamental particles of nature have minimum vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion.

The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as −273.15 degrees on the Celsius scale (International System of Units), which equals −459.67 degrees on the Fahrenheit scale (United States customary units or Imperial units). The corresponding Kelvin and Rankine temperature scales set their zero points at absolute zero by definition.

It is commonly thought of as the lowest temperature possible, but it is not the lowest *enthalpy* state possible, because all real substances begin to depart from the ideal gas when cooled as they approach the change of state to liquid, and then to solid; and the sum of the enthalpy of vaporization (gas to liquid) and enthalpy of fusion (liquid to solid) exceeds the ideal gas’s change in enthalpy to absolute zero. In the quantum-mechanical description, matter (solid) at absolute zero is in its ground state, the point of lowest internal energy.

The laws of thermodynamics indicate that absolute zero cannot be reached using only thermodynamic means, because the temperature of the substance being cooled approaches the temperature of the cooling agent asymptotically, and a system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state at absolute zero. The kinetic energy of the ground state cannot be removed.

Scientists and technologists routinely achieve temperatures close to absolute zero, where matter exhibits quantum effects such as Bose–Einstein condensate, superconductivity and superfluidity.

### 10. The Schwarzschild Radius

How far can you compress something before you reach nature’s ultimate breaking point—that is, before you create a black hole?

Inspired by Einstein’s theory of general relativity and its novel vision of gravity, the German physicist Karl Schwarzschild took on this question in 1916. His work revealed the limit at which gravity triumphs over the other physical forces, creating a black hole. Today, we call this number the Schwarzschild radius. The Schwarzschild radius is the ultimate boundary.

The **Schwarzschild radius** (sometimes historically referred to as the **gravitational radius**) is a physical parameter in the Schwarzschild solution to Einstein’s field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic radius associated with any quantity of mass. The Schwarzschild radius was named after the German astronomer Karl Schwarzschild, who calculated this exact solution for the theory of general relativity in 1916.

The Schwarzschild radius is given as *r** _{s}* = (2

*GM*)/

*c*

^{2}, where

*G*is the gravitational constant,

*M*is the object mass, and

*c*is the speed of light. In natural units, the gravitational constant and the speed of light are both taken to be unity, so the Schwarzschild radius is

*r*

*= 2*

_{s}*M*.

Schwarzschild showed that any mass could become a black hole if that mass were compressed into a sufficiently small sphere—a sphere with a radius R, which we now call the Schwarzschild radius. To calculate the Schwarzschild radius of any object—a planet, a galaxy, even an apple—all you need to know is the mass to be compressed.

The Schwarzschild radius for the Earth is approximately one inch, meaning that you could squish the entire mass of the Earth into a sphere the size of a basketball and still not have a black hole: light emitted from that mass can still escape the intense gravitational pull. However, if you squeeze the mass of the Earth into a sphere the size of a ping-pong ball, it becomes a black hole.

The Schwarzschild radius for the Earth is approximately one inch, meaning that you could squish the entire mass of the Earth into a sphere the size of a basketball and still not have a black hole: light emitted from that mass can still escape the intense gravitational pull. However, if you squeeze the mass of the Earth into a sphere the size of a ping-pong ball, it becomes a black hole.