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How does geometry relate to basketball
How does geometry relate to basketball
Math in Basketball – How Math Is Used in Sports – Cool Math
At first glance, basketball and math seemingly have little in common. While basketball is hugely popular in American schools, math has a considerably smaller fan following. However, a closer look at the sport reveals that there is a considerable amount of math in basketball. Pointing out how math is used in basketball is a great way to get your kids more excited about angles and percentages, while helping them realize how important math is in everyday life.
The angle at which the ball is thrown is determined as the angle made by the extension of the player's arms and a perpendicular line starting from the player's hips.The math in basketball involves a wide range of math topics. Kids can practice geometry, percentages and even basic mathematical operations while playing or watching a game of basketball.
Whether they realize it or not, basketball players make use of many geometric concepts while playing a game.![]()
The most basic of these ideas is in the dimensions of the basketball court. The diameter of the hoop (18 in), the diameter of the ball (9.4 in), the width of the court (50 ft) and the length from the three point line to the hoop (19 ft) are all standard measures that must be adhered to in any basketball court. Knowing these measurements is useful for kids who would like to practice basketball at home without access to a full-fledged basketball court.
The path the basketball will take once it’s shot comes down to the angle at which it is shot, the force applied and the height of the player’s arms. When shooting from behind the free throw line, a smaller angle is necessary to get the ball through the hoop. However, when making a field throw, a larger angle is called for. When a defender is trying to block the shot, a higher shot is necessary. In this case, the elbows should be as close to the face as possible.
Understanding arcs will help determine how best to shoot the ball.
Basketball players understand that throwing the ball right at the basket will not help it go into the hoop. On the other hand, shooting the ball in an arc will increase its chances of falling through the hoop. Getting the arc right is important to ensure that the ball does not fall in the wrong place.
The best height to dribble can also be determined mathematically. When standing in one place, dribble from a lower height to maintain better control of the ball. When running, dribbling from the height of your hips will allow you to move faster. To pass the ball while dribbling, use straighter angles to pass the ball along a greater distance.
Understanding geometry is also important for good defense. This will help predict the player’s moves, and also determine how to face the player. Facing the player directly will give the player greater space to move on either side. However, facing the player at an angle will curb his freedom. Mathematics can also be used to decide how to stand while going on defense.
The more you bend your knees, the quicker you can move. Utilizing geometry, math in basketball plays a crucial role in the actual playing of the sport.
Statistics is essential for analyzing a game of basketball. For players, statistics can be used to determine individual strengths and weaknesses. For spectators, statistics is used to determine the value of players and analyze the performance of an individual or the entire team. Percentages are a common way of comparing players’ performances. It is used to get values like the rebound rate, which is the percentage of missed shots a player rebounds while on the court. Statistics is also used to rank a player based on the number of shots, steals and assists made during a game. Averages are used to get values like the points per game average, and ratios are used to get values like the turnover to assist ratio.
- Addition and Subtraction in Basketball
For young basketball fans, math in basketball is a great opportunity to practice simple skills like counting, addition and subtraction.
Young kids can add up the points made in every shot to get the team’s total score. Kids can also be asked to use subtraction to determine how many points a team will need to catch up with the leading team, or to win the game.
How Geometry Changed The Way You Play Basketball
The Olympic Games are a perfect occasion to stop and observe the intense relationship between geometry and sport. In their broadcasts we hear about angles, lines, trajectories … All the playing fields of any sport are full of geometry, although, of all of them, perhaps the basketball court is the one that brings together the most different elements. In it you can see parallel lines, others perpendicular, rectangles, circles, semicircles, arcs of circumference, and all this crowned by a ring that in mathematics we would describe as a torus.
Understanding this geometry is essential to understand the game and, therefore, to master this sport. Thus, for example, a definition of the center of the field is the central point of the rectangle which, in turn, is the court, or, if a more precise definition is preferred, the cut-off point of the angle bisectors that form the corners.
from the field. We can also understand the midfield line as the bisector of the side lines. However, on the basketball field, one line stands out above all, since it has redefined modern basketball: the triple line.
This three-point line, also called the 6.75 line, is mathematically defined as the set of points equidistant from the center of the basket – 6.75 meters, according to regulations of the International Basketball Federation (FIBA) , and 7.24 meters in the NBA.
Perhaps the basketball court is the field of play that brings together the most geometric elements. In it you can see parallel and perpendicular lines, rectangles, circles, semicircles, arcs of circumference, and a ring that in mathematics we would describe as a torus.
However, this definition does not correspond to the area of the game that today we know as the triple line, since the arc that should be drawn is flattened on the sides. This modification is due to the fact that, on the one hand, we did not want to make the field wider than it already is and, on the other hand, a player should be able to stand without stepping on the triple line or the side with some ease of movements.
In the measurements of an NBA court, the differences are more notable (6.71 meters in the corners versus 7.24 official meters, more than half a meter of difference!):
In the NBA, the triple line differs up to 53 centimeters depending on the position@Sportymates
This three-point line proposal came precisely from the hand of the NBA, which officially introduced it in the 1979/1980 season. Initially, its use was purely residual, not to mention throwing a triple from the corners: Why shoot a triple from the corner if there is no option to score by bouncing off the board? Who would want to shoot from a place where it is much more difficult to take distance references when aiming?
However, in 1984 its establishment spread to the rest of the world. As time went by, the teams realized the potential of this launch due to its proximity to the basket, in addition to allowing it to “open the field” making defense difficult. So much so that it has become one of the favorites for basketball players, as shown by Kirk Goldsberry – an eminence in the use of advanced statistics applied to basketball – in a graph where the difference between the line is perfectly observed.
triple and that geometric place that we described:
NBA Shot Charts
There are players who have made the corner their specialty, as their shooting maps show:
Shooting map of PJ Tucker this season, player who shoots more than half of his shots from the cornersNBA Shot Charts
If we go back to world basketball, which is the one played in the Olympics with the line at 6.75 meters, the differences in distances are reduced with respect to what happens in the NBA, since the radius of that arc of circumference that is draw is less. Even so, these weeks we will see how the teams exploit the launch from the corners and, on our screens, we will be able to appreciate this unique case in which geometry has completely changed the way of understanding the sport.
Diego Alonso Santamaria (@deporteymates) is a professor of Mathematics at IES Virgen de la Calle, Palencia.
Carmen Esparcia Arnedo She is a professor of Physical Education at IES Virgen de la Calle, Palencia.
Timon G-Longoria Agate is coordinator of the Mathematical Culture Unit of the ICMAT and editor and coordinator of this section
Coffee and theorems is a section dedicated to mathematics and the environment in which it is created, coordinated by the Institute of Mathematical Sciences (ICMAT), in which researchers and members of the center describe the latest advances in this discipline, share meeting points between the mathematics and other social and cultural expressions and remember those who marked its development and knew how to transform coffee into theorems. The name evokes the definition of the Hungarian mathematician Alfred Rényi: “A mathematician is a machine that transforms coffee into theorems.”
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Sports psychology: team geometry. - Sports Psychology
Hello everyone!
Let me start by sharing something fun! My vacation is finally starting and on Saturday evening I'm going to rest on the route Moscow-Kyiv-Odessa - Moscow.
So that you don’t get bored during this time, firstly, I’m publishing a fairly large post, and secondly, at the end I’ll write a proposal, which you, of course, can refuse, but I wouldn’t want to
Let's talk about the team today. About several psychological types of players that you may encounter. The information for the players is rather just funny - informative, but for the coaches it can bring real benefits. I chose a fairly simple typology called "psychogeometry".
Psychogeometry was developed by the American psychologist Sally Dillinger.
Psychogeometry is based on 5 personality types and their corresponding geometric shapes: Square, Triangle, Rectangle, Circle and Zigzag.
It is easy to determine one or another type - you present these figures to a person (or audience) and ask them to choose 1 or 2 of them that you like best.
That's the whole test. The representative of each type prefers "his own" figure with a probability of over 80%. The most interesting thing is that if you practice properly, you don’t even need a test. True, as in other typologies, “pure” types are quite rare, most are mixed.
It should also be noted that we are talking not so much about personality types, but about habitual attitudes and ways of behavior for a person. The same character may use a "square" behavior in one situation and, say, a "triangular" behavior in another.
Square
Characteristic
See how stable, even, solid... correct it is. People of this type follow the order, rules and traditions, moral norms in everything. A square is a workaholic, he is very hardy, attentive to details, lives according to a plan, is punctual, organizes himself and others. You can rely on him, he always fulfills the promise, or does not make promises.
However, in the merits of the square lies its weakness.
He is too correct, so in sports he rarely gets to the very top. Having stumbled upon uncertainty, the Square slows down until it finds the right solution, from its point of view, and therefore is often late with the decision, and this is unacceptable in the game.
In communication, the Squares are rather dry, have a narrow circle of friends (if they have at all). They are accommodating team players as long as the other team members "do the right thing". However, they know how to get their way.
Making decisions, the Square relies primarily on what, in its opinion, is right, regardless of anyone's personal opinions, grievances and discontents. On the other hand, for him the word of the coach is the law: the Square will exactly follow the instructions from above, even if he does not agree with them too much.
In the team of the Square, they obey, they can appreciate and respect, but they very rarely love. He is dry and aloof for this. Therefore, Squares are good workhorses, but not leaders at all.
External signs
Clothes: modest, conservative, neat. Square - a man is always clean-shaven and short-haired. Squares don't tend to stand out.
Mobile phone: old and purely functional.
Speech: logical, consistent, thorough, slow paced. Likes to operate with facts and figures. Often uses speech stamps, bureaucratic jargon. A normal Square, assessing a critical situation, would rather say: "we have some difficulties" than "nightmare!". Likewise, they are stingy with praise. Their highest rating for even outstanding work would be: "OK".
Non-verbal signs: tense posture, either straight, like a stick, or hunched over. Gesticulation and facial expressions are poor. Laughs rarely, and laughter does not sound natural, "done". The handshake is firm (although without a show of strength), including for women. Greeting, as if evaluating look partner in the eye.
Triangle
Characteristic
At its base, it is as fundamental as the Square, but pointed and pointed upwards.
Like a space rocket. His main vector is career, achievements, enterprise, competition.
The triangle is ambitious, determined, self-confident. He has no less energy than the Square, but it is spent not on restoring order, not on work as such in the sweat of his brow. All this may make sense for the Triangle, or be indifferent, the main thing is the Set Goal. Most Triangles love sports and are physically well developed. A square can reach sporting heights because it is as indispensable as a workhorse. For the Triangle, achievement constitutes a motive in itself. If necessary, he can do dirty work for this.
Unlike Squares, Triangles are not stopped by a new situation, they do not wait until the correct solution is born or descends "from above". They are adventurous, guided by themselves and their own ideas, rather creating their own rules of the game than obeying someone else's.
Unlike the Square, a sports career is fundamentally important for the Triangle. Therefore, he can change teams on his own initiative if he does not see prospects in that team.
where he plays. When choosing a new team, the Triangle may prefer to "decrease" in status and give up leadership positions if it sees new horizons.
External signs.
Clothes: is fashionable, with a pretension. Men have facial hair. If the Square is always clean-shaven, the Triangle can afford, for example, a "French beard" that mimics a three-day stubble. Jewelry in the form of rings is possible. A chain around the neck is very likely, maybe with a crucifix.
The cell phone of the Triangle is a poem in itself. Actually, lately they prefer something more "fancy" to ordinary mobile phones, like a PDA, smartphone or tablet. Gadgets, according to the Triangle, add status to it. And be sure, this miracle of technology will lie on the table or stick out of your pocket for everyone to see!
Speech: speaks briefly and clearly, always to the point. The pace of speech is quite high. Often uses jargon, buzzwords. They are able to operate with facts and figures, but if there are not enough arguments, they may well use emotions to defend their position, up to abuse, as well as tricks to discredit the opponent.
Triangles are easily converted to "you", using this appeal as a tool. Thus, they demonstrate their position to their subordinates, equals - disposition, superiors (if they allow) - the level of claims.
Non-verbal signs: the posture is not tense, rather relaxed; sitting down, takes the most comfortable position for himself. Often sits cross-legged. Gestures when talking. The gait is fast and energetic. Remember "Terminator - 2": it is with such a "triangular" gait that the heroes at the end of the film go to smash the laboratory. The handshake is imperious, hard, with a clear demonstration of strength.
Rectangle
Characteristic
The rectangle is shown standing on the shorter side. You see: Like the Square with the Triangle, it is angular, but unlike them, it is not stable. According to S. Dillinger, the Rectangle is a temporary shape, symbolizing the state of transition and change. We often assume, so to speak, a rectangular shape during critical periods of biography and personal development.
However, there is nothing more permanent than temporary ... Some Rectangles are born, and so they live to a ripe old age.
The rectangle is not satisfied with itself and its position. His life is clearly not going the way he would like, but he either does not know what he wants, or does not see the opportunity to achieve what he wants. It is characterized by inconsistency and unpredictability, impulsiveness, inner agitation. Sometimes he is capable of steps that are bold to the point of recklessness, because he has nothing to lose; in other situations, even not too dangerous ones, he folds because of self-doubt.
The self-esteem of the Rectangle is low, so he needs to get external support. The best way to befriend a Rectangle is to compliment him and show him respect. He is trusting and often finds himself a stronger "leader", because of which he can easily become an object of manipulation.
The Rectangle is also characterized by attempts to imitate the behavior of acquaintances: it seems to try on different roles.
In everyday behavior, Rectangles are poorly organized, forgetful, absent-minded. They are often heavy smokers.
External signs
Clothes: unkempt, not according to the situation.
Speech: uncertain, confused, very emotional. Often there are "pauses of indecision", tongue twisters, interjections and parasites. The rectangle, when he is worried (and this is a common state for him in a stressful environment), tries to blurt out everything at once, which is why he gets confused both in words and in thoughts.
Non-verbal signs: awkward jerky movements, exaggerated gestures. When he sits down, he is either squeezed (on the edge of the chair) or falls apart, exaggeratingly demonstrating supposedly calm and relaxed. Gait unsteady, changing. The handshake is either exaggeratedly sharp, or, on the contrary, sluggish. Palms often sweat. The look is running, with difficulty endures a long "measuring with the eyes."
Circle
Characteristic
Note that this is the first figure without corners.
The circle is not rigid, but it cannot be called unstable: it can roll, but it cannot fall.
Each of the figures of psychogeometry has a main vector. For the Square, this is the desire for order, for the Triangle - for achievements, for the Rectangle - dissatisfaction with oneself. For the Circle, this vector is relationships with others. For him, the main thing is the harmony of relations, lack of conflict, democracy. Circles are gullible, in conflict situations they strive to reach consensus.
Circles are characterized by a high need for communication. They are good communicators, friendly, generous, compliant. In relations with others, they are flexible, they can communicate equally well with a wide variety of representatives of society and psychological types. Easily fall under the influence of others.
The circle is usually cheerful, witty, loves company, has a wide circle of acquaintances.
In general, Circles are quite lazy and are not at all inclined to give all the best in training as Squares do out of principle, and Triangles do it for the sake of achievements.
Another property of Circles is that they are very fond of comfort. Delicious food, cozy seating, dress in soft and comfortable.
Circles are not very ambitious and rarely become leaders due to their malleability and lack of desire to defend their interests. They are not envious and not prone to intrigues.
Circles are usually loved in a team, but they rarely become real leaders: they lack energy, pressure, and ambition.
External signs
Clothing: informal, slightly casual. Prefers youth style. Krug's normal uniform is a sweater and jeans.
Speech: inconsistent, easily off topic. Circles are good storytellers, they speak emotionally, expressively, figuratively. They are prone to rave reviews and compliments. An interesting detail: Circles often tend to use "we" instead of "I". Showing off the results, the Square will say "the team has achieved", the Triangle - "I have achieved", and the Circle - "we have achieved", even if his role was the main one.
Non-verbal signs: The circle usually gives the impression of being relaxed and free. When sitting, takes the most comfortable position for himself. Moves smoothly. Often smiles. Circles tend to communicate "mirror" behavior: the repetition of the posture and gestures of the interlocutor. Greetings are emphatically friendly: the Circle greets you as if you had not seen you for a hundred years, although you only parted yesterday. At a meeting, it is always not averse to exchange a couple of phrases.
Zigzag
Characteristic
A zigzag is fundamentally different from all other figures: the line is not closed. In relation to him, the concept of stability is not applicable: he, as it were, hangs in the air, like lightning. Not surprisingly, in sports, zigzags are much less common than other figures.
The main Zigzag vector is creativity, rebellion, enthusiasm, thirst for change. The square is "wrapped" on the order, the Circle - on the consensus, the Triangle - on the career, the Rectangle - on yourself, the poor.
Zigzag - so that the swamp does not stagnate, something happens all the time, "so that ideas sparkle, and a fight would be nice, but this is already ideal ..."·. Zigzags are often found in creative environments, there are many of them among scientists, and they often succeed in this field.
There are no authorities for Zigzag. He is creative, not interested in consensus. He likes to sharpen the conflict of ideas, witty, caustic, strives for independence, for diversity in all spheres of life. Unrestrained and excitable, eccentric in actions and words.
Zigzag can work to the point of exhaustion on the implementation of his ideas, but he rarely manages to complete anything: he quits because he gets bored. In life, he is scattered, fickle, undisciplined. Morality, laws, public opinion are indifferent to him. Here is an absolute example of Zigzag: a hacker who walks around dirty, eats beer, works day and night to hack another program or launch a particularly sophisticated virus into the network.
In the game, Zigzag often also demonstrates his adventurism: some fanciful passes, throws from incredible positions - you must have met such people. Since they almost do not recognize authorities, their discipline is also very weak and it is almost impossible to influence Zigzag.
External signs
Clothing: is usually demonstrative. Zigzag - a hacker - disheveled, deliberately sloppy. Zigzag is a creative in an advertising company, a director, a producer - on the contrary, he is super fashionable. Zigzag - a woman who is active in her personal life - is always on the crest of fashion, and sometimes runs ahead of her.
Speech: bright, fast, with rich vocabulary, jargon is often used, a lot of humor. Zigzags are often artistic, expressive, while speech is inconsistent (jumps from topic to topic), associative. We talked about one thing, got hooked on another ... By the end of the conversation, it is no longer clear where we started.
Body language: Relaxed, rapidly changing postures, lively gestures, rapid gait, lively facial expressions, mannerisms.
That's all in a nutshell. Of course, the diversity of human personalities cannot be reduced to five types.
Firstly, each of the listed figures can be stupid or smart (except, perhaps, Zigzag), educated or uncouth. Smart Triangle is a successful player, one of the leaders of the team, who strives for victories and leads the team. Stupid Triangle is an ambitious player who pulls the game on himself and does not allow his comrades to play. Smart Square is an excellent tactician who knows how and loves to play in positional attack. Stupid Square is just a “brake” for the team. Smart Circle is the “soul of the team”, a person who may not be a leader on the court, but who many sympathize with. The Stupid Circle is an empty balabolka; from communication with him you want to run in five minutes.
Secondly, of course, there are mixed types.
Basketball, like other sports, is dominated, of course, by Triangles. But most often - with elements of other figures.
Knowing what “pieces” your team consists of, if you are a player, it will become easier to understand partners, and for a coach, the ability to assemble a team from the right “pieces” is one of the keys to success.
Since I will not be able to communicate with you for the next couple of weeks, I propose the following option. Write in the comments or in a personal message what figures your team consists of, and then we will analyze the strengths and weaknesses of such a set of players, possible problems and optimal combinations on the court.
Thank you for your attention!
See you at Slamdunk party on Saturday! We conjure good weather together!
Research project of 7th grade students on the topic "Mathematics in Basketball"
Ministry general and vocational education
Sverdlovsk regions
Municipal autonomous educational institution -
secondary secondary school No.
91
in-depth study of individual subjects
MO City of Yekaterinburg
Chkalovsky district
Name sections (subsections): natural science (mathematics)
Research job: Mathematics in basketball
Author(s) of the job: Korshunov Maxim Alexandrovich , 7th grade
Khamidulin Andrey Sergeevich , 7th grade
Head (heads) jobs: Grishina Anna Alexandrovna ,
teacher mathematics and informatics
____________________
____________________
2020
Contents
Introduction. 3
Chapter 1 Mathematics and basketball.
5
1.1. Basketball game. 5
1.2. Game features. 6
Chapter 2.9
2.1. Location of players on the field. 9
2.2. Calculation of dependencies. 10
Conclusion. 15
List References: 16
Appendix 1. The first rules of the game. 17
Application 2. Game basketball field. 19
Application 3. Questionnaire for 7th grade students. 20
Application 4. Survey results. 21
Application 5. Screenshot of the report of the results of checking the project file by the " Anti-plagiarism " system. 22
Mathematics is a science that studies numbers, quantitative relations and spatial forms. Mathematics is a subject that studies this science. We often hear and see such definitions. For us, mathematics is a way of describing various phenomena of nature and especially society. Since in Mathematics acts as an assistant in all spheres of human activity. For example, performing calculations when creating machines, exploring space, even creating literary works and that requires mathematics.
We were interested in the question “Sport. Can mathematics to help this area of human activity with precise and strict language? Of course, the very first answer is chess.
But, we decided to check out other sports as well. Since we are already we have been playing basketball for several years, then our choice fell on this particular type sports.
The topic of our research is “Mathematics in Basketball”.
Purpose of research : to study the influence of mathematics on basketball, to calculate the mathematical model of the best game with the maximum number of hits.
Tasks :
1. To study the literature on the research topic;
2. Compare and contrast common terms and concepts in mathematics and basketball;
3. Analyze the results obtained;
4. Show the application of the acquired knowledge in basketball;
Hypothesis: is it possible to build a mathematical model of an ideal basketball game.
Object research: mathematics and basketball.
Item research: mathematical component in basketball.
the following methods were selected : study of literary sources, processing of the received information, analysis, synthesis, research, practical.
Product project : creation of a mathematical model of the best game with the maximum the number of hits.
Practical significance : results can be use in additional education and self-education.
Basketball (basket - basket, boll - ball) is team game in which players throw the ball into the "basket", consisting of a ring with a mesh at the bottom. It is located at a height of just over 3 meters. from the floor (10 feet), to be more precise 3.05m. Picture 1
Dr. James is considered to be the founder of the game Naismith, who decided to diversify gymnastics lessons at the training center Christian Youth Association in Springfield, Massachusetts (USA) 1891.
His idea was to throw a soccer ball in two fruit baskets without a bottom, which he attached to the balcony railing. Fans on the balconies they caught flying balls and tried to throw them into the opponent's basket, therefore, shields appeared that became the protection of the basket, and in 1893 appeared already iron rings with mesh. Given the shortcomings of the first matches, D. Naismith in during the year develops the first 13 points of the basketball rules (Appendix one).
The new game is so addictive that in 1894 The first official rules were issued in the USA. Within 10 years basketball begins to "capture the world", first the East - Japan, China, the Philippines, and then the game comes to Europe, South America, the end of this journey becomes the Olympic Games in St. Louis (USA), where the Americans organized demonstration tournament between teams from several cities. Basketball was indicative also at the 1924, 1928 Olympics.
In 1923 France hosts the first international women's tournament, in which countries participated: England, Italy, USA.
The game is gaining more and more popularity and recognition in the world, and at 1932g. was The International Basketball Federation (FIBA) was founded. The first composition of the federation included 8 countries - Argentina, Greece, Italy, Latvia, Portugal, Romania, Sweden, Czechoslovakia. In 1935, the International Olympic Committee decided to recognition of basketball as an Olympic sport. In 1936 at the Olympic Games in Berlin in the program appeared basketball. D. Naismith was the guest of honor of the games - creator of this game. Teams from 21 countries participated in the basketball tournament.
Basketball comes to Russia at 1906g, to the city - Petersburg, in the sports society "Mayak" and before the October Revolution 1917 remains the game only of this city. Actively play basketball throughout country begins after 1923, and the WTO began to participate in world championships from 1959
The game does not have one main technique, it includes various game techniques and performance variations.
chief the rule for the player is: accessibility, rationality of actions together with purposefulness, jumps are accurate and fast, giving the player maneuverability on field.
There are two teams of 12 people. There are 5 players from each team on the playing field. Goal: to score bigger opponent's ring the number of balls to prevent the second team from grabbing the ball and scoring into their own ring. Depending on the where the player throwing into the ring is located, a different number of points are counted for hitting. For a free throw 1 point is counted, for a throw from an average or close distance (in the jargon - paint) - 2, and 3 points given for a throw from behind the 3-point line. (Annex 2)
The ball is played with the hands only. Prohibited: running with the ball in your hands without hitting it on the floor, deliberately hitting it fist or leg, block with any part legs. Accidental touches with the foot or leg are not violations of the rules of the game. The beginning of the game is considered controversial throw in the central circle of the field, two players from rival teams.
The match is divided into four periods 10 minutes each (12 minutes in the NBA). Between the 2nd and 3rd quarters of the game is regulated break 15 minutes, other pauses are two minutes each, and in addition, coaches (in the NBA - and players) can take timeouts. After half the game, the teams must swap halves of the field.
The winner is the team that during the game was able to score more points. In case of a tie after the end of the regular time of the game, overtime is assigned, usually this is additional five minutes of play if given there is not enough time, the second, the third is assigned ... until one of the teams scores more points, and there is no the winning team is declared.
In order for the game to be effective and not like a chaotic movement around the field, players are assigned roles:
- point guard point guard or playmaker (eng. Play maker) - number one team responsible for choosing the combination of the game, which way to go and how build an attack.
This player not only needs to see teammates, but also calculate the situation on the site.
- attacks - perfect possession of the ball and movements;
- protection - possesses the skills of tackling the ball. The main goal of such a player is to insure team from a fast break of the opposing team.
Such division was in the past. In the modern professional basketball, priority is given to versatile players who combine the qualities which allow the player to play adjacent positions. This is how the position stands out comboguard (eng. Combo Guard). Based on the name, it can be determined that the player combines a combination of qualities necessary for defense and attack.
Players can be classified not only by type of activity on court, but also by height and weight:
- Average height 183-195 centimeters, weight 75-90 kilograms - this is point guard defender (eng. Point guard) or playmaker (eng. Play maker).
- The average height of a player is 190-200 centimeters, weight 85-100 kilograms - attacking defender (eng.
Shooting guard).
- Average height 195-210 centimeters, weight 95-110 kilograms - light forward (English Small Forward).
- The average height of a professional player is 200-215 centimeters, weight 105-115 kilograms - heavy forward (English Power Forward)
-Average height 210-220 centimeters, weight 110-125 kilograms - center (English Center).
Analyzing the game after training or a match often, you ask yourself: “Is it possible to improve your results or how to come up with the ideal model for the game and always score the maximum number of points?
To find answers to these questions, we decided to turn to our peers, but before that find out “How many of them know about this game generally?". For this purpose, a survey was conducted among 7th graders. (Annex 3)
As a result, we find that only 80% of the respondents know such a game, and about the rules and features in general, only 50%. Analyzing all this, we there was an idea to create a mathematical model of an ideal game, which means to solve the following tasks:
1.
Reviewed various positions of the player on the field.
2. Formulas studied depending on the distance between the player and the basket.
3.According to with these formulas, the positions of the players of the school team were calculated.
4.Checked practical way these results.
Drawing 2
Depending on the position of the players located on the field in certain areas where they can best be implemented in accordance with their classification. Looking at the positions we investigated and got such a picture (Figure 2).
When a player "fouls" during a shot, then he gets on the penalty (in the figure - the yellow line) line and throws as many times he could score points on the throw - 1 point. Zone in which any goal will be counted as two points, shown in red in the figure. Purple zone - this is the zone in which any goal will be counted for 3 points. This is the location of the zones for the left ring.
Basketball - dynamics, movement speed and quickness. In addition, this competent execution of throws. At the same time, you need to know how to properly fulfill. Let's try to figure out how to throw the ball, under what angle and at what speed to hit the basket when throwing from different distances.
On average, a player makes about 20 shots from different distances and that the game is of high quality, and the player showed good results, he needs to distribute his forces throughout the game, without putting in too much effort. But the player not only throws the ball, but also overcomes the barrier in the form of a defender, for this the ball must be thrown through it and get into the basket. It is clear that the closer the defender is to me, then the higher the trajectory of the ball will be required, and then this is subject to constant hit. But people with 100% accuracy very rarely meet m, then additional calculations are needed.
Let's introduce some designations and consider their data:
1.
D M is the diameter basketball ball. A standard basketball has a diameter of 24 cm.
2. m is the mass of the ball. In the standard is 600 g.
3.H - height hoops of a basketball hoop above floor level. In standard gyms - 3.05m.
4. D K - ring diameter, it is equal to 45 cm.
5. L - distance from the center of the ring to the place of the throw.
Figure 3
during the calculations, we will consider a basketball ball, while neglecting the influence of air on the flight of the ball. Let's choose a system coordinates yOx to describe the movement: axis Ox - directed horizontally, the Oy axis is directed vertically, the origin of the coordinate system O coincides with the center of the ball at the start of the throw. Since the ball is moving with free acceleration fall g=9,8m/s 2 , directed vertically down, then using kinematic equations of motion we obtain:
, where v 0 x is the horizontal projection of initial ball velocity, v 0 y – vertical projection of initial velocity ball.
After mathematical transformations, we obtain the trajectory equation ball: , where α is the angle between the direction of the initial speed v 0 and the positive direction of the 0x axis, and the tangent of the angle α is:
, where β is the angle at which the ball flies into the basket.
After transformations of the equations, we obtain a formula for determining the initial velocity ball:
Performing calculations to find the initial speed at different throwing angles for different areas of the field (different types of points), we were several best angles are marked (Table 1). At the same time, in calculations, the growth the player was taken into account as the average height for our school basketball team 1.71 m. The flight path L changed depending on the location of the player along zones on the site, the angle α varied from 20 0 to 90 0 .
Table 1
| No. p/p | υ 0 m/s | h, m | L, m | α |
| Single point zone |
| 1 | 5.61 | 1.71 | 4.3 | 30 0 |
| 2 | 4.8 | 1.71 | 4.3 | 45 0 |
| 3 | 4.1 | 1. 71 | 4.3 | 60 0 |
| Two-Point Direct Zone |
| 4 | 6.5 | 1.71 | 5.8 | 30 0 |
| 5 | 5.4 | 1.71 | 5.8 | 45 0 |
| 6 | 4.5 | 1.71 | 5.8 | 60 0 |
| Two-point side zone |
| 7 | 5. 6 | 1.71 | 4.35 | 30 0 |
| 8 | 4.8 | 1.71 | 4.35 | 45 0 |
| 9 | 4.1 | 1.71 | 4.35 | 60 0 |
| Three-Point Direct Zone |
| 10 | 6.9 | 1.71 | 6.48 | 30 0 |
| 11 | 5. 7 | 1.71 | 6.48 | 45 0 |
| 12 | 4.7 | 1.71 | 6.48 | 60 0 |
| Three-point side zone |
| 13 | 7.5 | 1.71 | 7.55 | 30 0 |
| 14 | 6.1 | 1.71 | 7.55 | 45 0 |
| 15 | 5 | 1. 71 | 7.55 | 60 0 |
The selection of these corners is also related to the coverage area of the ring:
at an angle of 60° to the plane of the basket, then only 0.8661 parts of the ring are used.
2.If the throw taken at a 45° angle, the target is 0.7071 rings.
3. When thrown under an angle of 30 °, the affected area is reduced to 0.5 rings.
Received the data helped us determine the ideal muzzle velocity for a given angle and flight path length.
Another factor affecting the flight of the ball becomes - rotation ball. According to the rules, the ball must be thrown with reverse rotation. This is necessary in order to to keep the ball in its flight path, increasing the chances of hitting basket, by slowing down the speed of the ball. But it's all physical phenomena that we will not count.
As a result of calculations conclusions can be drawn:
- the smaller the angle throw, the smaller the chances of getting the ball into the basket, which means there should be increased accuracy.
This can be achieved by increasing the height of the flight path.
- the higher flight path, the longer the flight path of the ball.
- first case ideal and almost never found in sports, but the most acceptable throw angle ball 60 0 .
- attached at throw force determines the initial speed of the ball, which in turn determines the height of the ball's flight path. If you apply maximum force, then the accuracy will drop.
After analyzing all the results, we decided to check them on practice. Throwing the ball was carried out in accordance with the length of the trajectory flight and angle of inclination, which we first measured with a protractor. (Picture 4) In each of the cases, the hit was accurate, which means our calculations are confirmed.
Figure 4
30 0 ) (angle 60 0 )
9002 affecting the quality of the throw, for example, physical and psychological.
As well as in our calculations, we did not take into account physical phenomena and their calculations, which will be studied by us in the future in the course "Physics" and then our formulas and calculations will be finalized.
Working on this topic, we confirmed our hypothesis: it is possible whether to build a mathematical model of an ideal basketball game. But would like add that this is possible when taking into account a large number of factors - rotation ball, flight path, player height, etc.
In conclusion, let's add that basketball is not only a beautiful sight sports, but the connection of physics and mathematics, where mathematics is an assistant.
For us, this project was the starting point in the study of only mathematics, physics, but in the awareness of the vast field of application of mathematics to human activity, and as Alfred said North Whitehead: "The most interesting property arithmetic is that it applies to everything: to taste sensations and sounds, to apples and angels, to thoughts and bones.
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2. Pichurin L. F. Za pages of the textbook of algebra: book. for students in grades 7–9 avg. school - M .: Enlightenment, 1990.– 224 p.: ill.
3.http://sdushortambov.ru/index.php?option=com_content&task=view&id=73&Itemid=1
4.https://vm.ru/sport/163491-13-pravil-basketbola-dzhejmsa-nejsmita
5. https://sportyfi.ru/basketbol/priemi/peremeshchenie/
-o-pravilah.html
7.http://life.mosmetod.ru/index.php/item/kak-zabrosit-myach-v-basketbolnuyu-korzinu
8.http://images.yandex.ru
9.https://www.nkj.ru/archive/articles/33854/
1. The ball can be thrown in any direction with one hand (now you can throw with two hands).
2. You can hit the ball hit with one or two hands in any direction, but never with a fist (this hasn't changed, but accidental touches don't count).
3. The player cannot run with the ball. The player must throw the ball from the point at which he caught it, an exception is made for a player running at high speed (now with the ball you can run).
4. Ball needed keep brushes. You can not use the forearms and body to hold the ball.
5. In any case hitting, grabbing, holding and pushing the opponent are not allowed. First violation of this rule by any player shall be called a foul; second foul disqualifies him until the next ball has been potted, and if any the obvious intention to injure the player is a disqualification for the entire game. At it is not allowed to replace a disqualified player. (now allowed 5 fouls with removal to the bench and replacement of the player).
6. Hitting the ball fist - violation of paragraphs of rules 2 and 4, the punishment is described in paragraph 5.
7. If any of side commits three fouls in a row, then a goal is recorded for its opponent (this means that during this time the opponent must not commit a single foul).
8. Goal counts if a ball thrown or bouncing off the floor enters the basket and stays there. Defending players are not allowed to touch the ball or basket in throw moment. If the ball touches the edge and the opponents move the basket, then a goal is counted (now the ball bouncing off the floor does not bring points to the team, but the ball can be helped in flight).
9. If the ball goes out of bounds, he must be thrown into the field by the first to touch his player. In the event of a dispute, the referee must throw the ball into the field. thrower the player is allowed to hold the ball for five seconds. If he keeps it longer, then the ball is given to the opponent (nowadays, if the team is delaying time, they are given foul).
10. The referee must monitor the actions of players and fouls, as well as notify the referee of three fouls committed in a row. He is vested with the power to disqualify players according to rule 5.
11. The referee must watch the ball and determine when the ball is in play (inbounds) and when going into touch (out of bounds), which side shall be in possession the ball, as well as perform any other action that is normally performed by the referee (Now the referee can help the side judge).
