It is known that man in his practical activities has to solve not only repeatedly repeated tasks, but also new, never met.
The world around us is full of mathematical objects - numbers, functions, geometric shapes.
All modern civilization is a product of the development of technology, inconceivable without precise mathematical calculations.
But mathematics does more than help us cope with the world. It goes to the very core of the world. This amazing fact was first pointed out by Pythagoras, one of the most influential thinkers in human history.
With his motto "Everything is a number" he anticipated for thousands of years both the future role of mathematics and the nature of its objects. In their mode of existence they differ radically from the objects familiar to us through the senses.
This peculiarity, many believe, makes mathematics the primary source of belief in the existence of a world "inhabited" by timeless and supersensible objects.
Geometry, one of the oldest branches of mathematics, deals with exact figures.
But no matter how carefully we try to draw a circle, it will still be imperfect and wrong.
The real circle, about which theorems are proved, does not exist in this world.
The famous English philosopher and mathematician and Nobel Prize winner Bertrand Russell noted in his History of Western Philosophy: "This leads one to assume that all exact reflection deals with an ideal opposed to sensuous objects. It is natural to go one step further and prove that thought is nobler than feeling, and that objects of thought are more real than objects of sense perception. Mystical doctrines about the relation between time and eternity also receive support from pure mathematics, for mathematical objects, such as numbers (if they are real at all), are eternal and timeless. And such eternal objects can in turn be interpreted as thoughts of God."
You will not meet a single person in your life who has not done mathematics.
Each of us knows how to count, knows the multiplication table, knows how to build geometric shapes. With these figures we often meet in the surrounding life.
From early childhood in communication and games with the child's parents, without knowing it, teach him mathematics.
For example, many times a day uttered the phrase: "Well, eat 2 more spoons, sunshine," "Let's put together these 3 cubes," "We have to go with you just 2 houses," "Through 5 trees, I'll take you in hand. Read to a child the rhyme "One-two-three-four-five - the little bunny went for a walk," and the baby wonders what this mysterious spell "One-two-three-four-five.
Math includes not only learning numbers and arithmetic, but also spatial thinking, logic, determining the size and shape of an object.
Some might think that various intricate lines and surfaces can only be found in books by mathematical scientists. But that's not true.
- It is worth a close look, and we immediately find all sorts of geometric shapes around us.
- It turns out that there are a lot of them, we just have not noticed before. Here's a room.
- All of its walls, floor and ceiling are rectangles, and the room itself is a parallelepiped.
- The floor tiles are squares, rectangles, or regular hexagons.
The furniture in the room is also a combination of geometric bodies. Table - a flat parallelepiped lying on two other parallelepipeds - nightstands, which have drawers. On the table is a lamp with a lampshade in the form of a truncated cone. A bucket is either cylindrical or a truncated cone.
There are dishes in the cupboard. Glass cut into facets, shaped as a hexagonal truncated pyramid.
The tea saucer is a truncated cone; the funnel consists of a cone and a cylinder.
Let's pour water into the glass, the edges of the glass surface are circular. Tilt the glass so that the water doesn't pour out. Then the edge of the water surface will become an ellipse.
Let's go outside. There are houses in front of us. The house itself is a prism and its walls are planes. The columns in front of the house are cylinders.
In Moscow we have the Kremlin. Its towers and walls are beautiful! How many geometric shapes are put into their foundation!
Along the street cars move. Their wheels are circles. Get on the train. The station is far behind.
But even here, geometry doesn't leave us. Along the road there are wires strung on poles - they are straight lines, and the poles are perpendiculars to the ground.
Here is a high-voltage transmission line, the wires from their own gravity slightly sag to the ground, but in winter they are, on the contrary, stretched, as the metal from the cold shrinks.
The problem of determining the necessary length of such a wire for transmission over long distances is dealt with by mathematics.
Very often we encounter a spherical surface: ball bearings, gas storage tanks - they are made spherical because less metal is consumed in the process.
We live on a globe, although in reality the shape of the earth is not a ball, but a more complex body - an "ellipsoid of rotation". At the poles it is flattened, the ratio of the minor axis to the major axis is 299/300. This is not much,