The value is considered as one of the foundations of mathematics, in particular one of its sections - geometry. This concept goes deep into the past. It was described in the III century BC. e. the ancient Greek mathematician Euclid in his work "Beginnings". Humans have been using quantities for over two thousand years, until they were subjected to a series of generalizations.
Value in math is a very important topic to study in school. In fact, from the children's understanding of the value, further learning is built from simple to more and more complex. By measuring various segments and areas with a ruler, weighing mass on a scale, determining speed based on distance and time, the child gradually learns to comprehend the material world and builds his own picture of perception, and also determines for himself the role of mathematics in the world around him.
The concept of magnitude in mathematics
A quantity in mathematics is a property of objects that can be measured by comparison with a unit of measurement related to a quantity of this kind. Allocate length, mass, volume, speed, area and time. In simple terms, this is what you canmeasure and quantify.
This section of mathematics students go through in elementary school, and all measurements at this stage are made in natural numbers. In elementary mathematics, such a number series is a sequence of numbers from 1 to infinity. In high school, numbers with a negative value are also used to calculate the value.
Historical background
In ancient civilizations, mainly due to the extensive development of trade, there was a need for measuring goods, determining distance, time, calculating crop areas and other things. At first, people measured objects by comparing them with a person or animal. But all these measures were rather relative, because everyone has their own body proportions, and the value in mathematics is, first of all, accuracy. Therefore, over time, it became necessary to create a single standard of the system of quantities.
So, in France in 1791, during the Great Revolution, the unit of length was considered to be a meter, which was one forty-millionth of the earth meridian crossing Paris. In addition to the meter, such a value as the kilogram was established. It was equal to one cubic decimeter of water at 4°C. As well as ar as a measure of area, liter and gram.
Since the new quantities were based on the meter, the measurement system became known as the metric one. In the National Archives of France, there are still platinum standards of the meter in the form of a ruler with strokes at the ends and the kilogram in the form of a cylindrical weight.
Russian measurement system
From Ancient Russia to the adoption of the metric system of measures in the Russian Empire, it was customary to take measurements using the length of the elbow, the width of the palm, the length of the foot - a foot. The distance from the tip of the outstretched arm to the heel of the opposite leg was called a fathom, the distance between the outstretched arms was a fly fathom, etc. To measure the distance, they took, for example, the audibility of a cock's cry or the ability of a horse to get from point A to point B without rest. So people measured the distance of the laid route.
Even now, in proverbs and sayings, we can find reminders of the existence of ancient values. This is evidenced by such expressions as “hear a mile away”, “oblique fathom in the shoulders”, “measure on your own arshin” and other catch phrases.
In 1899, on June 4, a single metric system was adopted, which was optional. It became mandatory on September 14, 1918, already under Soviet rule, almost immediately after the Great October Revolution.
Basic maths
Children at school, studying quantities in mathematics, by the 4th grade already have a broad understanding of such values as length, mass, volume, area, speed and time.
Under the length of an object, it is customary to understand the characteristic of a linear size. It is measured in millimeters, centimeters, decimeters, meters and kilometers. Children go through this topic at school starting from the first grade
- Mass of the item - moreone physical quantity, measured mainly in grams and kilograms. As well as the volume of bodies, which is calculated in liters and milliliters. However, do not mislead the child and consider mass and weight as equal concepts. Mass is a constant in mathematics, while weight depends on the strength and speed of an object's attraction to the earth.
- Under the area of a geometric figure, it is customary to understand the space it occupies on a plane, which is calculated in mm2, cm2, dm 2, m2 and km2.
- Time is a rather relative concept and for a person it is associated with his feelings, he cannot be seen, but can be felt in the change of day, night and seasons. Therefore, to introduce children to the concept of time, they use precise instruments, such as hourglasses and clocks with an arrow. Time is measured in seconds, minutes, hours, days, years, and so on.
Based on the topic about time and length, children learn the concept of speed. In fact, speed is a segment of the path traveled in some time
Infinite dimension in mathematics
In high school students study the topic of infinitely small and large numbers. These are those numerical values that either tend to zero or to infinity. The mass of a drifting ice floe in the ocean that is in the process of melting will refer to an infinitesimal quantity. Indeed, under the influence of continuous heat, the ice will melt, and the mass of the block will be equal to zero. The opposite process from the point of view of physics isexpansion of the universe. It tends to an infinite amount, expanding its limits.
Constant and variable
During the development of mathematics, quantities were divided into two classes: constants and variables.
A constant value, or the so-called scientific language constant, remains unchanged, that is, under any conditions, it retains its value. For example, to calculate the circumference of a circle, the constant value "Pi" \u003d 3.14 is used. The Pythagorean constant √2 \u003d 1.41, used in mathematics, is also unchanged. A constant value is a special case and is treated as a variable value with the same value.
A variable in mathematics is an inverse process that, for various reasons, changes its numerical value.
