Squares in everyday life

14 Square Examples in Real Life – StudiousGuy

A square is a quadrilateral geometric shape that consists of four equal sides and four equal angles. The area of a square can be obtained by evaluating the numerical product of its two sides. The perimeter of the square is four times the magnitude of the side.

Index of Article (Click to Jump)

1. The sum of all the angles of a quadrilateral is equal to 360°, and all the angles of a square are equal in magnitude; therefore, the angles formed between the two adjacent sides of a square is equal to 90°.

2. The opposite sides of a square are parallel to each other.

3. The two diagonals formed by joining the opposite corners of a square are equal in length and have the value √2 times the magnitude of the side of the square.

4. The diagonals bisect each other at an angle of 90°.

1. Floor and Wall Tiles

Most of the tiles used in constructing and decorating home walls and floors are square-shaped. Hence, the tiles are one of the prominent examples of square-shaped objects used in everyday life.

Everyone has a stack of napkins placed on the top of the dining table. A napkin is a square-shaped piece of paper or a cloth that is used to wipe the mouth, hands, or objects. Hence, it is yet another example of square-shaped objects used in daily life.

The chessboard is one of the best examples of the square-shaped objects used in everyday life. Not only the outer boundary of the chessboard is shaped like a square, but it also contains 64 small square boxes on the inside.

A stamp is a small piece of paper that is affixed on the front side of the envelope containing the letter before posting it. Most of the stamps are square in shape.

A cushion is a bag of fabric that is stuffed with cotton, fur, wool, or beans. The cushions used to decorate the living room are generally square in shape.

In real life, the square geometric shape can be observed easily by looking at the front face of a cubical desk clock. Some of the wall clocks are also square-shaped.

A loaf of bread is generally cuboidal in shape; however, if you pick one thin slice of the bread you can easily identify its square shape.

The shape of the cheese slices is square. This is because it is easier for the manufacturing industries to wrap a square slice instead of wrapping a round slice.

Most of the windows installed in homes are square in shape. In some cases, not just the outer frame but the glass inside the grilles is also square-shaped.

If you clearly observe the front face of the chocolate cube, all four sides are equal, and the opposite sides are parallel to each other. Hence, the cube taken out of a bar of chocolate is yet another example of the square-shaped objects seen in everyday life.

Photo frames come in a variety of shapes. One of the most popular shapes of a photo frame is a square.

Some of the biscuits are baked in the shape of a quadrilateral that has all sides equal, i.e., in the shape of a square. So, next time while eating a biscuit don’t forget to get yourself reminded of the square geometric shape and its properties.

A craft paper is a colourful and textured piece of paper that is used to model a number of paper artefacts. It is generally square in shape.

14. Bedsheet

One of the most commonly used objects in daily life that is square in shape is a bedsheet. It thoroughly covers the mattress and protects it from dust and stains.

What are Some Examples of Squares Used in Real Life?

Amina Reshma Last Updated: Sep 16, 2022, 7:07 AM EST

2 Min Read

A square is defined as “a plane figure with four equal sides and four right (90°) angles.“¹ 

The world is filled with geometric shapes, and geometric forms can be found everywhere. Most things are made up of geometric shapes, whether two-dimensional (2D) or three-dimensional (3D).² Among the most commonly seen forms around us are squares. You will be surprised by how fascinating and valuable a square can be when you discover more about it. They work well for construction, decoration, and the creation of 3D shapes. The following are a few examples of squares being used in real life:²,³

• Tiles

Most tiles used in building and decorating interior walls and floors are square in shape and range in size from small to large. The convenience of working with square tiles is an added benefit. ⁴

• Chess

A chessboard is one of the best examples of a square-shaped object in daily life. The chessboard’s interior is made up of 64 tiny square boxes in addition to its square-shaped outer border.

• Toasts, Sandwich, Waffles, Brownies, and Chocolates

These popular snacks can be clearly seen to have equal sides on all four, with the opposite sides running parallel to one another. Therefore, these foods can serve as a wonderful illustration of the square objects encountered in daily life.

• Photos and Picture Frames

A square is a perfectly balanced shape with equally long sides. As a result, neither the horizontal nor vertical direction is highlighted. One of the main reasons why photographs and frames are typically square is that it makes the object appear more esthetically pleasing.⁵

• Windows

The vast majority of windows installed in homes have a square shape. It is possible for the inner glass of the grilles to be square as well, not just the outer frame. This is because joining two pieces of wood or aluminum with straight cuts is simpler and faster when producing the components in large quantities. Additionally, cutting the glass into square shapes is simpler too.

• Construction, Decoration, and Art

Squares are easy to make, cut, or build from everyday materials.  A square is one of the few regular polygons that can tessellate a surface. This makes a square very practical for construction, decoration, and artistic creation.⁶ 

If you enjoyed reading this article on squares, you can learn more about numerous other practical math uses and examples on BYJU’s FutureSchool Blog.

References:

1. square | mathematics | Britannica. (n.d.). Retrieved September 8, 2022, from https://www.britannica.com/science/square-mathematics 
2. What are Examples of Geometric Shapes in Real Life? (n. d.). Retrieved September 8, 2022, from https://examples.yourdictionary.com/what-are-examples-of-geometric-shapes.html 
3. 157 Things That Are Square Shaped. (n.d.). Retrieved September 8, 2022, from https://thingdb.io/things-that-are-square-shaped/ 
4. Tile Sizes and Shapes Buying Guide | Tile Shopping Advice. (n.d.). Retrieved September 8, 2022, from https://www.avalonflooring.com/ideas/blog/tile-sizes-and-shapes-buying-guide 
5. Square Photography: 6 Reasons the Square Format Is Amazing. (n.d.). Retrieved September 8, 2022, from https://digital-photography-school.com/6-lessons-the-square-format-can-teach-you-about-composition/ 
6. Proof That Only 3 Regular Polygons Tessellate | Proofs from The Book. (n.d.). Retrieved September 8, 2022, from http://proofsfromthebook.com/2014/07/16/proof-3-regular-polygons-tessellate/ 

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Most of you are familiar with some of the fundamental geometric shapes that surround us, such as squares, pyramids, rectangles, circles, and others. But are Read More...

Municipal budgetary educational institution

"Secondary school No. 1 of the city of Yurgy

named Hero of the Soviet Union A.P. Maksimenko"

9000

: Babich Sergey,

student 5th grade

Head: G. A. Induchnaya,

teacher mathematics

Contents

1. The square and its properties…………………………………………………….

2. Experimental verification of some properties of a square……………..

3. Fascinating square..………………………………………………….

4. Cultural square……………………………………………………….

5. Fashion square……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… ……………….

7. Mythical square……………………………………………………..

8. Square and advertising………………………………………… ………………..

9. I want to know everything ..................................................................................................................................................................................

900

B around the world there are many objects of various shapes, the largest number of rectangular and square.

Came from school older brother,

Laid out of matches square.
Mom gave me chocolate,

I broke off a slice - square.
Both the table is a square and the chair is a square,

And a poster on the wall - square,
The board where the chess stands,

And each cell - square,
Horses and elephants stand there,

Fighting figures.
SQUARE - four sides,
All its sides are equal,
And all angles are right.

me it became interesting how often a square occurs in the world around a person.

Problem: Is it possible to say that the figure "square" meets a person "at every step"

Purpose: the study of the role of the square in everyday life.

Hypothesis: A person meets a square figure in everyday life (everyday life, art, fashion, environment, advertising, hobbies, etc.)

Tasks:

• Learn information sources on the topic;

• Explore definition and basic properties of a square;

• Make movable square model;

• C using an experiment to check some properties of a square;

• Analyze, where and how the square is used during leisure;

• Carry out observing and photographing a figure in the surrounding world;

• Find out are there artists whose paintings depict a square;

• Explore the role of the square in directions: fascinating square, trendy square, mythical square, safe square, advertising square;

• Search poems, riddles about the square;

• Create an interactive folder with the results of the study.

1. Square figure

The word "

Square, like any geometric figure, it has its own history.

B In the ancient world, a square usually means the four cardinal points. in Assyria and ancient Peru, four cardinal points, four directions, that is, a square is and is the whole world.

Most obviously, the square is associated with the number four, which symbolizes order, equality, justice, wisdom, honor, sincerity, earth. The square represents the four cardinal directions, the four seasons.

1. Definition and properties of a square

A square is a quadrilateral with all four sides and angles are the same.

Properties:

1. All four sides of a square are the same length, that is, they are equal to

2. All four corners of the square are straight

3. The diagonals of a square have the same length

4. Each diagonal of the square divides the square into two identical figures

5. The diagonals of the square are bisected by the intersection point

6. The diagonals of the square intersect at right angles

7. The intersection point of the diagonals is called the center of the square

8. Each diagonal bisects a corner of the square

9. Both diagonals divide the square into four equal triangles

10. The sum of the angles of a square is 360 degrees

2. Experimental verification of some properties of a square

Using the manufactured movable model square, a paper model of a square, a triangle with a right angle, I checked some square properties.

Experiment: Made a blank in the form square sheet

1. Examination properties No. 1: bent the sheet horizontally, vertically, diagonally

2. Examination properties No. 2: attached to the corners of the square a right angle of a right-angled triangle

3. Examination properties No. 3: a) using the animation function "rotation"

b) using bending along the diagonals, then along vertical and horizontal

diagonal 1, diagonal 2

6. Property check #5, #9: folded the sheet diagonally, and the resulting triangle in half

6. Checking property No. 6: to the bend along diagonals attached the right angle of a right triangle;

3. Fascinating Square

For identifying the level of familiarity with the figure of the square of my classmates (students of the 5th grade) we compiled and conducted a questionnaire (Appendix 1)

the results of the survey of 24 children surveyed, 8 did not name a single games.

B In the course of my research, I found out that many games use a figure "square".

Most popular board games: tangram, tag, checkers, tic-tac-toe, marine fight, chess, magic square, alkerk.

Game "Tangram"

Tangram - an old oriental puzzle from figures obtained by cutting the square into 7 parts in a special way: 2 large triangles, one medium, 2 small triangles, a square and parallelogram. As a result of folding these parts with each other, we get flat figures, the contours of which resemble all kinds of objects, ranging from human, animals and ending with tools and household items. Such kind of puzzles are often called "geometric constructors", "cardboard puzzles" or "cut puzzles".

Game "Fifteen"

Game in 15 , tag , taken — popular puzzle invented in 1878 by Noah Chapman. It is a set of identical square tiles with printed numbers, enclosed in a square box. The length of the side of the box is four times the length of the side bones for a set of 15 elements, respectively, remains in the box unfilled one square box. The goal of the game is to move the tiles around box, arrange them by numbers, preferably by doing as much as possible less movement.

Checkers - board game for two players, which consists in moving checkers in a certain way along checkerboard cells (8x8, 10x10). During the game, each player owns checkers of the same color: black or white (sometimes other colors, one of which is considered dark, and the other - light). The goal of the game is to take all the opponent's checkers or deprive them of the opportunity move (lock). There are several variants of checkers that differ in rules and the size of the playing field.

Basic rules of the game that apply to all drafts variants:

All checkers participating in the game are exposed before the start of the game. on the desk. Then they move along the fields of the board and can be removed from it in in the case of a battle with an opponent's checker.

It is obligatory to take a piece that is under attack.

There are only two types of checkers: common and queens. At the beginning of the party all checkers are simple. A simple checker can turn into a king if it reaches the last opposite horizontal row of the board (lady's field).

Simple checkers move only forward to the next field. Kings can walk forward and backward.

Tic-tac-toe

Logic game between two opponents on a square field of 3 by 3 cells or larger. One of the players is playing "crosses", the second - "zeros". The traditional Chinese game (Gomoku) uses black and white stones.

"Battleship" is a game for two players in which players take turns name the coordinates on the opponent's map unknown to them. If the opponent at these coordinates has ship (the coordinates are occupied), then the ship or part of it is “burned”, and the gets the right to make one more move. Target player - be the first to hit all enemy ships. field - usually a 10x10 square of each player on which the fleet is placed ships. Horizontals are usually numbered from top to bottom, and verticals are labeled letters from left to right. In this case, the letters of the Russian alphabet are used from "a" to "k" (the letters "e" and "y" are usually omitted) or from "a" to "i" (using letters "yo"). Since there are various options for specifying the coordinate system, it is better to agree on this in advance.

Placed:

1 ship - a row of 4 cells ("four-deck")

2 ships - a row of 3 cells ("three-deck")

3 ships - a row of 2 cells ("double-deck")

4 ships - 1 cell (“single -deck”)

Shakhmati (Persian chess , literal translation “ Shah died ”) - Table Logical Figure A 64-cell board for two opponents, combining elements of art (in terms of chess composition), science and sports.

The game is played on a board divided into equal parts. square cells, or fields . The size of the board is 8×8 cells. Vertical rows of fields (verticals) are indicated by Latin letters from a to h on the left to the right, horizontal rows (horizontals) - in numbers from 1 to 8 from the bottom up; each field is identified by a combination of the corresponding letter and number. fields painted in dark and light colors (and are called, respectively, black and white) so that the fields adjacent vertically and horizontally are colored in different colors. The board is positioned so that the near corner field to the right of the player was white (for white this is the h2 square, for black it is the a8 square). 9{2}} various numbers in such a way that the sum of the numbers in each row, each column and on both diagonals are the same. If the sums of numbers in the square are equal only in the rows and columns, then it is called semimagic.

Alquerque Arab. "fortress"), aka kirkat , eng. quirkat (Persian or Turkish. "windmill")

Checkers-type board game, common in the Middle Ages. Came from the Arabs to Spain. Gave impetus to European varieties of checkers, and also the Madagascar game of fanarona (fanorona).

Rules

Board 5 x 5 (similar board used in the Nepalese logic game Bag-Chal).

Also, like in checkers, there are simple moves - to any free field along the line boards, and moves with a capture - jumping one's checker over someone else's to free field. Therefore, there are also combinations, as a result of which you can take several checkers at once. But about the strengthened checker - the king - here nothing is known yet.

On odd rows (a, c, e, g, i; 1, 3, 5, 7, 9) checkers game has 25 fields, where the lines of the diagonal and orthogonal grids converge, along which they only walked chips (12 white and 12 black) to adjacent fields. At the beginning of the game, the field d5 is free, and the fields on rows 1 and 3, as well as a5 and b5, are occupied by white chips, the rest fields are black. The goal of the game is to beat the opponent's pieces. Beat chips jumping over a broken chip. The same kind of game is possible on the cell board 5 x 5.

On The 5 x 5 checkers game mentioned above was another game. White chips stood on the same fields as above. On the square d5 there was a black chip that kept all completeness of movement (walk and beat) as above, and White could move (but not beat) forward and sideways (but not back). The goal of the game is to lock the black checker by analogy with locking the "wolf" in the game-task "wolf and dogs". Games of this kind (with the locking of a stronger counter, but simpler) were later known called "fox and geese" in England and "wolf and sheep" in Germany.

Renju (Japanese) - board game for two players, sports version of tic-tac-toe up to five in a row, combining, in addition to sports elements, also elements of art and philosophy. Originated in China more than four thousand years ago, variations were known to both the Inca civilization and Ancient Rome. At the beginning of our era, a game from China came to Japan, where it received greatest distribution. The adopted sporting variant, as well as the name, also born in Japan. Old variations of the game are also known as "gomoku" and "gomokunarabe", which means "five stones" and "five stones in a row".

Basic rules

Two opponents play: one with black pieces (stones), the other - white. The game is played on a squared board. size 15 by 15 lines.

Players take turns making moves. First blacks go. Each move the player puts on the board in any free crossing the lines of the board one stone of its color. The one who can wins be the first to build a continuous row of five stones of your color - according to horizontally, vertically or diagonally.

A number of fouls are determined for the player playing black — prohibited moves. He cannot build 3x3 and 4x4 forks and a row of 6 or more stones (the so-called "long row"), as well as any forks with a multiplicity more than two. For white fouls does not exist, when building a continuous row of more than 5 stones white wins.

In addition, in order to equalize the chances and compensation for the advantage of the first move for the first five moves (three black stones and two white ones) additional conditions are imposed, which are usually called the opening regulations. Beginners can play without it, while in title competitions it is not uncommon quite complex rules are used.

Player may pass - refuse make another move if he considers it unprofitable to move. If both players pass in a row, a draw is recorded, the game ends. You can pass only after how the sixth (third white) stone appeared on the board.

The game continues either until one of the players, or to a draw (by agreement of the parties or due to two successive passes), or until neither side has theoretical possibility to place a five. In the latter case, the result game is also recorded as a draw ^[9] . In practice, the latter case is extremely unlikely, usually the game ends in a few dozen moves ^[8] .

Movable games

among moving ones can be noted: CLASSICS, SQUARE, MOVING FIFTS.

Classics. You can draw on a different number of numbers. Jump like this:
• On the number 1 - with one foot.
• On the numbers 2 and 3 - left and right, respectively.
• On the number 4 - with one foot.
• On the numbers 5 and 6 - left and right, respectively.
• On the number 7 - with one foot.
• On the numbers 8 and 9 - left and right, respectively. Then jump and turn.
• On the numbers 9 and 8 - left and right, respectively.
• On the number 7 - with one foot.

• And so on until the end.

Game "Square" is a popular yard ball game.

Playing field

Playing field is drawn on the ground or asphalt a square of arbitrary size (one side of 22 steps), divided into four smaller squares, each for a different player. A circle is drawn in the center of the field, intended for submission.

Rules of the game

opponent. You can only serve diagonally.

2. Unlimited touches.

3. The player may hit the ball "before" and "after" (maximum 1) contact the ball of his square.

4. If a player returns the ball to his square, he is credited with 1 Goal.

5. If the ball falls on a line (between 2 players) or on a circle, retakes the player who touched the ball last.

6. If the player served the ball to the opponent's line (from the side of out), then the ball is replayed by the player who touched the ball last.

7. If the ball went into touch (outside the common square), the player whoever threw the ball gets 1 point.

8. If the ball fell on the player's square and hit the field 2 times, The player has 1 goal.

9. As a rule, the game lasts up to 11 goals. You can score goals any part of the body other than the hands.

10. If one of the players conceded 11 goals, he is out of the game. When 2 players remain on the playing field, they each occupy two square, and play until one of them concedes 7 goals.

In a two-on-two game, players diagonally opposite each other friend - are considered allies and have a common account.

"Mute" - stuffing the ball on the leg (knee, head), foot fix it on the opponent's square. The opponent, knowing this maneuver, has the ability to knock down stuffing. At the same time, each player cannot leave his square (touch simultaneously with two feet of someone else's zone).

By the way, before the start of the game, you can agree that the ball hits only once, that is, there is no “stuffing” in the game! So even more interesting play (highest level) It is also sometimes played with the “Through” rule that if the ball touched your zone and the next touch on the ball was made by another player, not you, then you get a goal.

Mobile tags

on the street. Equally interesting for boys and girls aged 4-8 years. The optimal composition of participants is from four to twelve children. Play the game can be on any small area or in the hall.

The rules of "Fifteen" are very reminiscent of a game of salochki. In the same way as in Salki, we choose or appoint a driver. On the on the site with chalk or flags we mark the playing field with a size of 5-7 meters width and the same length.

The driver or "Fifteen" stands in the center sites. The rest of the players are located throughout the playing field, who is where wants. Participants are not allowed to run out of the field during the game.

The game starts at the command of the teacher. The driver tries to catch up and “tarnish” any player by touching him with his hand. The rest of the participants try to run away or dodge the Fifteen. The "stained" player immediately leaves the area, and the driver tries crush the next opponent.

Game ends as soon as caught last member. Another way to end the game: "Fifteen" must knock predetermined number of players. For example, five.

After the end of the game, you can repeat party with another driver.

General I counted over 18 games that use the square shape.

Fun Hobbies

Checkerboard Drawing

Checkerboard Drawing is a fun activity for kids of all ages. Regular drawing in a notebook of drawings with a pencil develops children's attention, spatial imagination, coordination of movements, perseverance.

Older children or beginners who cannot draw at all, without labor will be able to draw their first images, ranging from simple diagrams and gradually moving to more complex drawings, developing their artistic skills and imagination.

Do you keep a personal diary or diary in a box and do not know how to decorate boring pages or just want to have fun? Then, pencil drawings in a notebook will help you, it's very simple and fast.

You will need:

1. Pencils, markers or pens.

2. Notebook or a checkered notepad, and if you want to draw a large drawing, you can use graph paper.

3. Good mood and this site.

On our site you will see a lot of schemes, ranging from the simplest, ending up very difficult. All schemes are divided into topics, for example: cats, dogs, ponies and more.

This type of drawing makes everyone feel like a real artist and learn to draw such masterpieces:

Origami arts; ancient art folding paper figures. Classic origami is made up of square sheet of paper.

The art of origami has its roots in ancient China, where paper was invented. Origami was originally used in religious rituals. For a long time this art form was available only to representatives upper classes, where a sign of good taste was the possession of folding technique from paper.

4. Cultural square

Squares have had a very strong influence on culture humanity. Many of the paintings created are square in shape. Some depicted squares in square paintings, which symbolizes, in fact, a square.

One of the most famous paintings in Russian art is the painting by Kazimir Malevich “BLACK SQUARE".

Look, gentlemen, at this hall:

Everything from the paintings of others goes back.
Magnet pulls viewers eyes

To the mystery of the eternal "Black Square".

"Black Square" - the work of Casimir Malevich, created in 1915, one of the most discussed and most famous paintings in Russian art.

Black Square painting, 1915, stored in the Tretyakov Gallery. The painting is a canvas 79.5 by 79.5 centimeters, which depicts a black square on a white background.

"Red Square" - painting by Kazimir Malevich, painted in 1915 years. Title on back "Woman in two dimensions". Represents a red rectangle on a white background, slightly different in shape from a square.

Magic Albrecht Dürer square

Magical the 4x4 square depicted in Albrecht Dürer's engraving "Melancholia I" is considered the earliest in European art. The two middle numbers in the bottom row indicate date of creation of the picture (1514).

Sculpture

Square - stallion, Orlovsky trotter of bay color. Winner of the "Bars" and All-Union "Derby" prizes (won two main prizes for four-year-old trotters). It is the only horse in Russia, which has two monuments. Lived more than 30 years, left more than 600 descendants.

Poetry about square

Riddles about square

5. Fashion square

U us at home and on the INTERNET, I found products with a square ornament.

It turns out that the square is a very necessary figure in the fashion world.

Grandma's square. Nobody remembers who came up with the so-called grandmother's square, but this motif enjoys great popular because it knits easily and allows you to experiment with color.

Russian ornament

Belarusian ornament

Ukrainian ornament

Patchwork

Patchwork is patchwork. More often, the flaps are taken in square shape

6. Safety square

Road signs

"Pedestrian transition" is an informational sign. He indicates the place of the ground crossing of the carriageway of the street. Installed such a sign near the special markings for pedestrians - "zebras".

"Main road" - A road on which the right of way has been granted passing unregulated intersections.

PEDESTRIAN ZONE

One of the most important road signs for children is and sign "Pedestrian zone". Cars are not allowed to drive here move only to pedestrians. Note that on such a section of the road there should be two sign - the first signalizes the beginning of the pedestrian zone, and the second - about its ending.

Recommended speed

Speed, from which traffic on this section of the road is recommended. The zone of action of the sign extends to the nearest crossroads.

Bicycle lane

7. Mythical square

Square in mythology

mythological, symbolic and other non-traditional interpretations. Most obviously the square is associated with the number four, symbolizing such concepts as order, equality, truth, justice, wisdom, honor, sincerity, earth. Square symbolizes the four cardinal points, the four seasons, the four human age, the four basic elements of the world (fire, water, earth, air).

8. Square and advertising

Square means honesty, straightforwardness, sincerity, morality. The square shape evokes a feeling of solidity and stability. Logo square shape is well suited for large and solid organizations.

9. Interesting about the square

The flag of Lima, being raised on a ship in the harbor, means that the ship is in quarantine

War square

Kare (French carré) - infantry battle order, constructed in the form of a square. Used in various European armies XVII-XIX centuries to repel cavalry attacks, as well as lightly armed infantry. In Russian Karet armies were especially often used in wars with Turkey. In a square, usually 800 people, but not always.

Square - the name of the officer's insignia on buttonholes in the Red Army until 1943.

Conclusion

If if we didn’t know about the square, then in our life there would be no interesting games and entertainment, beautiful clothes and ornaments, famous paintings, important road signs and many other important, interesting, useful!!!

I the square itself said:

sides mine are

AND corners are straight as speech

I pinnacle of straightness!

I without any discounts - forever!

Unfortunately, there are questions that I cannot answer answer and information that I don't understand yet, so in my work I opened section "I want to know everything!". Here I put questions and information that I still incomprehensible, but I will study, learn and learn in the future.

I want to know everything!

Squaring a circle?

·Table of squares?

The square of the hypotenuse is equal to the sum squares of legs?

Quadratic equations?

·Square root?

???????????????

Own I designed the research work in the form of a folder to which I will add everything that I will learn new about the square!!!

Geometry in everyday life | Article in the journal "Young scientist"

Geometry is a branch of mathematics that studies the properties of geometric shapes, which in Latin means “appearance”, “image” [3]. The subject of geometry research can be seen in life. After all, this science originated in Ancient Egypt and developed in connection with the needs of human practical activity: with various measuring works that had to be performed when marking land, during the construction of buildings and structures, and laying roads. Ancient architecture boldly used a variety of geometric shapes. Egyptian pyramids have the shape of regular quadrangular pyramids.

Wherever we are and whatever we do, we are surrounded by objects that have the shape of geometric shapes. Moreover, something that has angles, segments and planes is an object of artificial origin and is made by man. And objects of natural origin have rounded shapes, such as a ball, circle, arc [1].

The circle is used in art, construction, and technology. On roads and sidewalks, one cannot do without such a detail of housing and communal services as a sewer manhole cover. They cover the openings that provide access to underground utilities. Manhole covers have a whole story. So, for example, the coat of arms of the state, propaganda slogans were depicted on the first. Now the lids display the serial number, date and initials of the manufacturer. But sometimes there are different embossing, patterns. The sewer system in each state developed in its own way, but the time of the appearance of the first sewer manholes almost everywhere comes down to the middle of the 19th century. At first they were made in different shapes: triangular, square, and oval. In recent years, only round models have been made. [7]. And there are a number of reasons for this.

First, it is related to the economy. For example, in order for a person to freely enter the well through a square hatch, the hole will have to be made a little larger in area. This means that in the manufacture of a hatch for such an opening, more metal had to be spent. Unlike a round hole, which is easiest for a person to crawl into. It is believed that the production of round hatches is 40% more profitable compared to the production of square ones.

Secondly, safety. The round shape prevents the hatch from falling down. No matter how hard you try, you won't be able to push the lid into the well. What can not be said about the square shape of the hatch: if you put a square cover with an edge along the diagonal of the hatch opening, it will easily fall through. As a result, the well will remain open, and people and animals can fall into it, as well as cars can get stuck.

Thirdly, again, savings. The round shape evenly distributes the load when hitting the car hatch. Therefore, this allows a slight reduction in the section size (thickness), which ultimately contributes to additional cost savings.

Fourth, convenience. To quickly move the cover, the round hatch from the well can simply be rolled edgewise. Even one person can handle it. But rolling a square hatch will not work - it will either have to be transported, or carried by two or even three. After all, hatches are made mostly of cast iron.

And finally, it is believed that opening a round manhole cover is easier due to the fact that any point on its circumference is also a point of stress concentration. Square covers have only two similar points - the corners of one of the sides [4].

Note that even now hatches are not round everywhere. In India, triangular shapes are common. Square shapes are used in the United States and other countries in the Americas. In some countries, hatches may represent a generally indefinite geometric figure. They come with eight corners and very rarely there are models in the form of a rhombus, semicircles.

But in the construction of all kinds of buildings, a person mainly uses rectangular shapes. Round rooms are rare and are built because of some functional features of such buildings. Circuses, churches are built in the form of a circle, and stadiums can also be rounded.

Archaeologists have found that in fact the first dwellings had oval shapes. In some regions, they have survived to this day. And there were many such examples. Wigwams are among the Indians. Yurts - among the Turkic and Mongolian nomads. Tents are among the eastern nomadic peoples. Some nationalities are still building round housing. The Eskimos build their igloos from snow and ice in the shape of a hemisphere. The Chukchi put up plagues and yarangas. All these dwellings have two common features. Firstly, almost all of them can be easily disassembled, transported and assembled in a new place. Secondly, such dwellings are built in a desert area. It is important that the aerodynamics of spherical houses allow the winds to bend around them [5].

It is difficult to say when people started building rectangular houses. But archaeologists and historians agree on one thing - this happened when a person switched to a sedentary lifestyle. After all, houses began to be built for a long time. And, as it turned out, it is the rectangular shape that allows you to use space more economically. Such houses are easier to build on and divide into rooms. This means that they provide the maximum area and economic benefits. But today, builders and architects consider the construction of rectangular houses to be unsafe. Parallelepipeds (rectangles in volume) are bluff objects. When wind circles a building, areas can be created in which the airflow swirls. High-rise buildings that stand close to each other form depressions in which the wind speed doubles. Andrey Chorny, head of the turbulence laboratory at the A.V. Lykov Institute of Heat and Mass Transfer in Minsk, explains: “The wind speed increases very quickly with height. When the air mass hits the building, it seems to spread in different directions, including going up and down the wall. The flow descending from the building enters the street, and its speed can even exceed the speed of the oncoming flow, that is, the "original" wind" [6].

But when flowing around such a parallelepiped house, the wind breaks off from the corners, and weakens on the side walls and behind the dwelling. And on round houses, on the contrary, the flow on the walls accelerates. It turns out that it is warm inside, and the wind is fierce outside. The architects found a way out in the construction of buildings of various shapes [2].

But not only in construction and housing and communal services, geometric shapes are used. As a result of the synthesis of psychology and geometry, a new science emerged. Psychogeometry allows you to predict and evaluate character traits, a model of behavior and a person's lifestyle using the simplest geometric shapes. Young science is based on the fact that different geometric shapes evoke certain emotions in a person. So, an oval and a square are most quickly registered by the eye and perceived by the brain, which means they are better remembered than complex and irregular shapes. The developer of psychogeometry is Susan Dellinger, Doctor of Psychology, from the USA. She worked with the staff for many years and summarized her experience. The test she created was named after her. This test is now often used when hiring a specialist. The applicant for a certain place is invited to choose one of five shapes - a square, a triangle, a rectangle, a circle or a zigzag. Then the meaning of these geometric figures is correlated with the character of a person. And the employer immediately determines whether the candidate is suitable for this vacancy or not.

The same technique began to be used when creating logos for various companies. When designating car brands, designers use circles, ovals, triangles and zigzags. It has been proven that line shapes affect the speed and quality of information perception: horizontal and vertical lines reproduce calmness and clarity, while curved lines reproduce grace and ease.

Geometry plays an important role in our life. It is needed not only to name parts of buildings or forms of the world around us. With the help of geometry, we can solve many problems and answer various questions. Geometry gives not only an idea of ​​the figures, their properties, mutual arrangement, but also teaches to reason, ask questions, analyze, draw conclusions, think logically.

Mathematics has always accompanied a person in life. It helps the development of other sciences. It also develops a person’s ability for creativity and scientific imagination, resourcefulness and ingenuity, and most importantly, forms logical thinking: it teaches you to compare, contrast and classify.

Literature:

1. Depman I. et al. Behind the pages of a mathematics textbook grades 5–6. / M.: Enlightenment, 2004, - 287 p., ill.
2. Magazine "Around the World" No. 8. /M: Publishing house "Vokrug sveta" LLC, August 2017, -132 p.

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