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." People used quantities for more than two thousand years until they underwent a series of generalizations.
Value in math is a very important topic to study in school. In fact, further education from simple to increasingly complex is built from children's understanding of magnitude. By measuring the various segments and the area with a ruler, weighing the mass on the scales, determining the speed based on distance and time, the child gradually learns to comprehend the material world and builds his perception picture, 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 measure related to a quantity of this kind. Allocate length, mass, volume, speed, area and time. In simple terms, this is something that can be measured and expressed in numbers.
Students take this section of mathematics in elementary school, and all measurements at this stage are made by natural numbers. In primary school mathematics, such a number series is a sequence of numbers from 1 to infinity. In high school, numbers are also used with a negative value to calculate the value.
Historical essay
In ancient civilizations, mainly in connection with the vast development of trade, a need arose for measuring goods, determining distance, time, calculating cropland, and more. At first, people measured objects by comparing them with a person or an animal. But all these measures were rather relative, because everyone has their own body proportions, and the value in mathematics is primarily accuracy. Therefore, over time, the need arose 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 part of the earth’s meridian crossing Paris. In addition to the meter, such a value as a kilogram was established. It was equal to one cubic decimeter of water at a temperature of 4 ° C. And also ar as a measure of area, liter and gram.
Since the meter was the basis of the new quantities, the measurement system began to be called metric. In the French National Archives there are still platinum meter standards in the form of a ruler with strokes at the ends and a kilogram in the form of a cylindrical weight.
Russian measurement system
From Ancient Rus to the adoption of the metric system of measures in the Russian Empire, it was customary to measure using the length of the elbow, the width of the palm, and the length of the foot - feet. The distance from the tip of the arm extended up to the heel of the opposite leg was called a sagene, the distance between outstretched arms was called a fist feather, etc. For example, we took the audibility of a cock cry or the horse’s ability to get from point A to point B without rest. So people measured the distance of the paved route.
Even now in proverbs and sayings we can find reminders of the existence of ancient quantities. This is evidenced by such expressions as “hear a mile away”, “oblique fathom in the shoulders”, “measure on your arshin” and other winged phrases.
In 1899, on June 4, a unified metric system was adopted, which was optional. It became mandatory on September 14, 1918 already under the Soviet regime, almost immediately after the Great October Revolution.
Basic mathematical values
Children in school, studying values in mathematics, by grade 4 already have a broad understanding of such values as length, mass, volume, area, speed and time.
- Under the length of the subject is understood to be a characteristic of linear size. It is measured in millimeters, centimeters, decimeters, meters and kilometers. Children go through this topic at school, starting from the first grade.
- The mass of an object is another physical quantity, measured mainly in grams and kilograms. And also the volume of bodies, which is calculated in liters and milliliters. However, you should not mislead the child and consider weight and weight as equal concepts. Mass is a constant in mathematics, while weight depends on the strength and speed of attraction of an object to the ground.
- The area of a geometric figure is understood to mean the space occupied by it on the plane, which is calculated in mm 2, cm 2 , dm 2 , m 2 and km 2 .
- Time is a rather relative concept and for a person it is connected with his sensations, you cannot see it, but you can feel it in the change of day, night and season. Therefore, to familiarize children with the concept of time, they use accurate instruments, such as an hourglass and a clock with an arrow. Time is calculated in seconds, minutes, hours, days, years, and so on.
- Based on the topic of time and length, children learn the concept of speed. In fact, speed is a distance traveled in a while.
Infinite Measurement in Mathematics
In high school, students study the theme of infinitely small and large numbers. These are numerical values that either tend to zero or to infinity. The mass of the drifting ice floe in the ocean, which is in the process of melting, will relate to an infinite small value. Indeed, under the influence of continuous heat, the ice will melt, and the mass of the block will be zero. The opposite process in terms of physics is the expansion of the universe. It strives for an infinitely large value, expanding its limits.
Constant and variable
In the process of developing mathematics, values 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, the constant value “Pi” = 3.14 is used. The Pythagorean constant √2 = 1.41, used in mathematics, is also unchanged. A constant value is a special case and is considered as a variable with the same value.
A variable in mathematics is an inverse process that, for various reasons, changes its numerical value.