ABSOLUTE CONSTANT: CONCEPT AND EXPLANATION, EXAMPLES - MATHS - 2024

The absolute constants are constants those always keep their value during a calculation process. All absolute constants are numerical values, and in some cases they are represented by letters that make up the Greek alphabet.

The concept of constant magnitude refers to one whose value remains fixed; This means that its value does not change and always remains the same. This value does not change as long as the situation or process for which this quantity is being used lasts.

Concept and explanation

Constants are absolute because their value never changes when a calculation procedure is performed. These are also known as numeric constants because, as their name implies, they are values ​​represented by numbers and, in some cases, by letters, such as:

- In the equation: y = 4x + 1, the absolute constants are 4 and 1.

There are many areas where absolute constants are implemented; for example, in areas such as physics, chemistry and mathematics, their use is very important because they help to solve infinities of problems.

There are many values ​​of constants that serve as a reference in the different alternatives to solve exercises; Absolute constants such as area and volume are one of the most used in disciplines such as engineering.

Applications and examples

Applications in mathematics

In this area there are several numbers that represent absolute constants, which historically have helped in the resolution of many problems that have helped in the evolution of humanity.

Pi (π)

One of the constants that has been very important is pi (π), which has been studied since Antiquity (1800 BC).

Many centuries later it was Archimedes who determined its value, which is an irrational number that reflects the relationship that exists between the length of a circumference and its diameter.

This has been calculated based on different approximations, its numerical value is: 3.1415926535… and it consists of approximately 5000 * 10 ⁹ decimal places.

From the constant π, it was possible to deduce in geometry the area and volume of conic sections and bodies in revolution, such as the circle, the cylinder, the cone, the sphere, among others. It is also used to express equations in radians.

Golden number (φ)

Another very important constant used or found in various areas is the golden number (φ), also called the golden number or golden mean. It is a relationship or proportion between two segments of a line, expressed by the equation:

It was discovered in ancient times and studied by Euclid. This relationship is represented not only in geometric figures such as pentagons, but also in nature, such as in the shell of a snail, in seashells, in the seeds of sunflowers and in leaves. It can also be found in the human body.

This relationship is known as divine proportion, because it attributes an aesthetic character to things. Due to this, it has been used in architectural design and various artists such as Leonardo Da Vinci have implemented it for their works.

Other constants

Other absolute constants that are widely recognized and of equal importance are:

- Pythagoras constant: √2 = 1.41421…

- Euler's constant: γ = 0.57721…

- Natural logarithm: e = 2.71828…

Physics applications

In physics, an absolute constant is that magnitude whose value, expressed in a system of units, remains unchanged in physical processes over time.

They are known as universal constants because they have been fundamental for the study of different processes ranging from the simplest to the most complex phenomena. Among the best known are:

Constant of the speed of light in vacuum (c)

Its value is approximately 299 792 458 m _* s ^-1. It is used to define the unit of length that light travels in a year, and from this the measurement of length meter is born, which has been essential for measurement systems.

Universal constant of gravitation (G)

This determines the intensity of the force of gravity between bodies. It is part of the studies of Newton and Einstein, and its approximate value is 6.6742 (10) _* 10 ^-11 N _* m ² / kg ².

Permittivity constant in vacuum (ε

This constant is equal to 8.854187817… _* 10-12 F _* m ^-1.

Magnetic permeability constant in vacuum (μ

Which it equals 1.25566370 _* 10 ^-6 N . A ^-2.

Applications in chemistry

In chemistry, as in other areas, an absolute constant is that data, principle or fact that is not subject to changes or variations; refers to the constants of a body or to a set of characters that allow us to differentiate one chemical species from another, such as, for example, the molecular and atomic weight of each element.

Among the main absolute chemical constants are:

Avogadro's number (N

It is one of the most important constants. With this it is possible to count microscopic particles to determine the weight of an atom; Thus, the scientist Amedeo Avogadro established that 1 mol = 6.022045 _* 10 ²³ mol ^-1.

Electron mass (m

It is equal to 9, 10 938 _* 10 ⁻³¹

Proton mass (m

This constant is equal to 1.67262 _* 10 ⁻²⁷

Neutron Mass (m

Equal to 1.67492 _* 10 ⁻²⁷

Radio Bohr (a

Equivalent to 5.29177 _* 10 ⁻¹¹

Electron radius (r

Which is equal to 2.81794 _* 10 ⁻¹⁵

Gas constant (R)

Constant that is equal to 8.31451 (m ² _* kg) / (K _* mol _* s ²)

Applications in programming

The absolute constant is also used in the area of ​​computer programming, in which it is defined as a value that cannot be modified when a program is being executed; that is, in this case it is a fixed length, which is reserved from the computer's memory.

In different programming languages, constants are expressed through commands.

Example

- In the C language, absolute constants are declared with the command "#define". That way, the constant will keep the same value during the execution of a program.

For example, to indicate the value of Pi (π) = 3.14159, we write:

#include

#define PI 3.1415926

int main ()

{

printf ("Pi is worth% f", PI);

return 0;

}

- In both C ++ and Pascal languages, constants are commanded with the word "const".

References

1. Anfonnsi, A. (1977). Differential and Integral Calculus.
2. Arias Cabezas, JM, & Maza Sáez, I. d. (2008). Arithmetic and Algebra.
3. Harris, DC (2007). Quantitative chemical analysis.
4. Meyer, MA (1949). Analytic geometry. Editorial Progreso.
5. Nahin, PJ (1998). An Imaginary Tale. Princeton University Press;.
6. Rees, PK (1986). Algebra. Reverte.