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# Math, physics, chemistry formulas

All exact sciences use formulas that describe processes and phenomena. The equivalence of mass and energy is calculated as E \u003d mc², distance - as S \u003d v ∙ t, and density - as p \u003d m / V. It is enough to replace the variables with specific numbers, substitute their numerical values instead of constants and perform a mathematical calculation to get the desired parameter .

## What is a formula

The word "formula" (formula) comes from the Latin forma (view, image) and is related to all major exact sciences: mathematics, physics and chemistry. In fact, a formula is one of the varieties of a formalized language that expresses phenomena and processes not in words, but in the form of alphanumeric designations. It is opposed to graphs, drawings, diagrams and other graphic ways of expressing information and is often directly or inversely related to them. For example, a parabola can be described as a quadratic function y = ax² + bx + c, a sinusoid can be described as the formula y = sin x, and a molecular model of titanium oxide can be described as TiO2.

If we talk about physical and mathematical formulas, they contain variables, instead of which known values are substituted in real calculations. The simplest example of such a formula is the equation x = y². Knowing what y is equal to, we square it and get x, and if x is known, we extract the square root of it and get y. An equation can contain one or more variables, as well as constants - constant values. For example, the number π, which is 3.1415926535.

In chemical formulas, the arrow "→" is used instead of the equal sign. For example, 3Mg + SeO3 → 3MgO + Se. There are no constants and variables in such formulas, they are made up only of the designations of chemical elements, taking into account their valency and the number of atoms in the compounds.

## Exact sciences using formulas

Today, formulas are used not only in exact sciences, but also in many applied sciences, as well as in computer science, a relatively new scientific discipline. But the main areas of their application were and remain - physics, chemistry and the main branches of mathematics: algebra, geometry and trigonometry. What are they studying?

### Physics

One of the basic sciences of natural science, describing the fundamental patterns of processes and phenomena in nature. Why the sun rises and sets, why the sky is blue, why ships float and planes fly - all these and millions of other questions are answered by physics accurately and comprehensively. Its main sections are mechanics, optics, thermodynamics and electrodynamics, and with the help of physical formulas, you can briefly and accurately describe most processes or phenomena.

### Chemistry

Science that studies substances, their composition and structure, as well as patterns in their interaction. Chemistry predominantly considers matter at the molecular and atomic level, and also takes into account the basic subatomic particles: nuclei and electrons. Chemical formulas describe the processes of transformation of some substances into others: taking into account the number of molecules and atoms. Chemistry cannot exist without mathematics, it is firmly connected with physics, and forms "border" sciences with it: geochemistry, biochemistry, quantum chemistry, and others.

### Math

It is not for nothing that it is called the “queen of sciences”, because without mathematical expressions it is impossible to imagine any other discipline. Biology, astronomy, geography - everywhere mathematical calculations and notation are used to make descriptions as accurate and specific as possible. At the same time, mathematics is not an objective, but a formal science, since it never describes phenomena and processes as a whole, but only their individual properties. For example, in the simplest formula S = v ∙ t, only time, distance and speed of an object are taken into account, but its shape, size, color, purpose and other characteristics are not taken into account, most of which, in principle, cannot be described from a mathematical point of view.

#### Algebra

Along with arithmetic, the basic section of mathematics is algebra. Unlike the first, it is designed to maximally generalize all operations: addition, subtraction, division, multiplication, exponentiation and extraction of roots. Instead of specific numbers in algebraic formulas, variables are indicated: x, y, z ... They can be replaced by numbers of a very different nature and purpose: starting with time and distance, and ending with mass and density. This makes algebra a universal science, suitable for all branches of physics, astronomy, computer science and many other disciplines.

#### Geometry

Unlike limiting generalized algebra, geometry describes only relationships between objects on the plane and in space. Determining angles, faces, bisectors, medians, diameters, perimeters, areas, volumes are the main tasks that geometry can solve. For example, the area of a parallelogram is calculated as S = a ∙ h (where a is the side and h is the height), and the volume of a cone is calculated as V = (1 / 3) ∙ π ∙ R² ∙ H, where R is the radius of its base, and H is its height. The very name "geometry" comes from the Greek words "earth" and "measure", and appeared in the time of Euclid.

#### Trigonometry

A branch of mathematics entirely devoted to triangles, and using special trigonometric formulas for calculations: sin, cos, tg, ctg, and so on. They take into account the relationship between the hypotenuses, adjacent and opposite legs. Today it is impossible to imagine neither geography, nor astronomy, nor architecture, nor geodesy without trigonometry. It is used in all areas of engineering and, among other things, allows you to determine the distance to the nearest stars - due to the technique of triangulation.

Technological progress and exploration of the universe around us is impossible without the exact sciences. Originating back in the days of ancient civilizations, physics, chemistry and mathematics have greatly simplified human life, made it more meaningful and reasonable. It is thanks to them that today we can live in conditions of increased comfort, peace and security.

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## Formulas (mathematics, physics, chemistry)

A formula is the easiest way to express relationships between constants and variables in mathematics, physics, and chemistry. If the textual description of the law of universal gravitation takes several sentences or paragraphs, then in the form of a formula it fits in just one line: F = G ∙ (m1 ∙ m2) / r². The same applies to other equations used in algebra, geometry and trigonometry, as well as in various branches of physics and chemistry.

### Math formulas

Fundamental to all other exact sciences is mathematics, and mainly arithmetic and algebra. Without them, even the simplest calculations with such operations as multiplication, division, exponentiation and root extraction are impossible. Widely known algebraic formulas include:

- The Pythagorean theorem, discovered by the ancient Greek philosopher back in the 5th century BC. It has survived to this day unchanged: a² + b² = c², where c is the length of the hypotenuse, a and b are the legs of a right triangle.
- Euler's formula: V − E + F = 2. It describes the relationship between the number of vertices V, edges E and faces F in arbitrary convex polyhedra.
- The definition of pi: π = c / d, where c is the circumference of a circle and d is its diameter.

Geometry is an equally important branch of mathematics that describes spatial relationships and shapes. Rectangles, circles, rhombuses, cones, cylinders - all parameters of existing shapes are calculated using geometric formulas, for example:

- Rhombus area: S = D ∙ d / 2, where D is the large diagonal and d is the small diagonal.
- Volume of the ball: V = (4 / 3) ∙ π ∙ R³, where R is the radius of the ball.
- Circumference: L = π ∙ D, where D is the diameter of the circle.

Trigonometry, which is dedicated to one of the basic geometric shapes, the triangle, is considered more difficult to understand. All engineering sciences are based on it today, and the most common functions in this section are sine and cosine, for which there is a set of formulas:

- sin (α + β) = sin α ∙ cos β + sin β ∙ cos α.
- sin (α − β) = sin α ∙ cos β − sin β ∙ cos α.
- cos (α + β) = cos α ∙ cos β − sin α ∙ sin β.
- cos (α − β) = cos α ∙ cos β + sin α ∙ sin β.

In total, there are 73 trigonometry formulas that allow you to simplify and transform equations with one and several unknowns. First, the formula is simplified, and then you can substitute numeric values into it.

### Physical formulas

Physics is the main science of natural science, consisting of many sections and subsections. Mechanics, kinetics, dynamics, statics, optics, thermodynamics, electrodynamics, quantum physics - all these are components of one big science - physics. The number of formulas for it is in the hundreds, the most famous include:

- Acceleration due to gravity: g = G ∙ (M / (R + h))², where M is the mass of the planet, R is the distance between bodies, G is the gravitational constant, and h is the height above the surface.
- Moment of force about the axis of rotation: M = F ∙ d, where d is the length of the arm, and F is the force acting on it.
- Pressure: P = F / S, where F is the modulus of force and S is the surface area.

### Chemical formulas

As for chemical formulas, there are no variables and equal signs in them. The constituent parts of the formula are the names of chemical elements and their compounds: indicating the number of atoms. For example, CuO + HCl → CuCl2 + H2O. The number of chemical formulas has no upper limit, new compounds that are still unknown are regularly invented and discovered.

Today, all areas of production are based on chemistry, physics and fundamental mathematics: from oil and gas to microbiological. They help to improve the quality of life of people and contribute to the development of the economy. Without them, it is impossible to imagine the modern world and its technological progress.

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