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This video discusses how mathematics can be used to examine different aspects of sport. It begins by looking at the number 67 and its relevance to shooting a three-point shot. The presenter then goes on to discuss how rotational symmetry can be used to advantage a player in sport.

**00:00:00**In this video, a mathematics professor and author discusses her work in the field of sport and math. She talks about her book, Jump Problems, and its impact on the field of sport mathematics. She also discusses her work in integrative numeric calculus and its applications in various sports. She concludes the video with a talk about math and sport in 2020, which was cancelled because of the Parkland shooting.**00:05:00**This YouTube video provides a brief overview of the mathematics behind sports, including explaining the concept of longitude of compensation. It then goes on to discuss how this plays out in the 200-meter race, with particular emphasis on the differences between the times of the two runners who start on opposite sides of the track. Finally, the video provides a summary of the relevant regulations governing track events.**00:10:00**In this video, mathematics and sport are discussed. Mathematics is used to determine how distances between points on a playing field will be compensated for. This is used to create a schedule for a sports tournament. The first example is of how to compensate for a runner's distance when running a race. The runner's distance is measured from the inside edge of the street curb to the inside edge of the next street curb. Differences in the distances between streets are accounted for by the runner's height and the length of the semi-circle the runner runs. The second example is of how to schedule a football game. A numerical system is used to designate teams, and the game is played one day per week for three weeks. The first number assigned to a team is 1, the second number is 2, and so on. The fourth number is assigned randomly to a team. The team with that number plays the next team.**00:15:00**In this video, mathematics and sports enthusiast explain how to solve a problem in which a player has to face each opponent once, starting from the first day of competition. This problem gets more complicated as the number of teams participating in the competition increases. However, they suggest using a 6x6 grid in which each team will face each other three times. If the player wants to face the fifth opponent, for example, he would first have to face the other teams in the fourth row, fourth column, and third row, and then the second row. This problem can be simplified if the player only considers the first four rows and columns.**00:20:00**In this video, mathematician and sport enthusiast Unidos Por Aristas Borrados (UPAB) demonstrates how different types of graphs can be helpful in real life situations. One example is a graph labeled "Aristas Dirigidas" which is a type of graph with directed edges. Another example is a graph labeled "Flechas" which is a type of graph with arrows pointing in one direction. Finally, Unidos Por Aristas Borrados demonstrates how to solve a problem using seven different graphs. One of these graphs is labeled "Grafo Etiquetado" because its nodes (circles) have numbers and labels inside them. The other six graphs are all labeled with arrows pointing in different directions, and each graph has eight nodes. Unidos Por Aristas Borrados explains that each of these graphs is used to represent a different kind of competition. The first graph, "Grafo Blanco," represents a team competition where each team competes against each other. The next graph, "Grafo Amarillo," represents a single-elimination tournament where each team plays one match. The next two graphs, "Grafo Rojo" and "Grafo Verde," represent a double-elimination tournament**00:25:00**In this video, mathematics and sports are discussed. The second day of the competition is examined, and another graph is constructed with the same nodes and then the 1 is compared with the 3. Then, the 13 is generated and three perpendicular aristas are drawn that connect two nodes. The enfrentamientos of the second day are depicted in three graphs, with the 3 facing the 2, 4 facing the 4, and 5 facing the 8. The 6 faces the 7, and the 1 faces the 8. The third day's enfrentamientos are depicted in a fourth graph, with the 1 facing the 5. The three perpendicular aristas that connect the two nodes are then drawn, and this gives the enfrentamientos for the third day. The same process is followed for the fourth day, with the 1 facing the 4. The three perpendicular aristas that connect the two nodes are then drawn, and this gives the enfrentamientos for the fourth day. The enfrentamientos for the fifth day are depicted in a fifth graph, with the 3 facing the 2. The three perpendicular aristas that connect the two nodes are then drawn, and this gives the enfrentamientos for the**00:30:00**In this video, mathematician and sport commentator Pasi Sahlberg explains how impossible it is for a team to play alternating home and away games in a soccer competition. This impossibility is due to the fact that there are three or more teams in the competition, and one team must play both home and away games. To try and solve this problem, Sahlberg shows how to use a mathematical tool known as reduction to absurdity. This tool allows two teams to play one game each at home and away, as long as at least one team starts the game at home. However, this is not always possible, as two teams may have to play each other in the same game. Sahlberg then goes on to explain how a ball-player's height, shooting and jumping techniques can be modeled using a curve known as a parabola. This curve, though only sketched in the video, displays the ball's movement in close proximity to the basket throughout the entire shot.**00:35:00**The video discusses how to analyze a basketball game using mathematics, and how the position and movement of the ball in the air can be described with a mathematical curve. The summary then goes on to mention how real-world data can be used to improve the accuracy of the model.**00:40:00**In this video, mathematics and sport are discussed. Line drives in free-throw shooting, but also players who take a step back to avoid stepping on the line are observed. There are 50 such cases, but we believe that these are known facts once we focus on a specific player. The variables with which I wish to work are the launch angle, the speed of launch, and the angle at which the ball is released. These expressions are also found in x and y equations when the ball's velocity and launch angle are taken into account. However, I will not go into mathematical detail here. For this particular position, xd, tm, and tt have additional formulas depending on the shape of the parabola that represents the ball's trajectory from when it is released by the player to when it arrives at the basket. For x, these expressions appear in terms of the velocity and launch angle in y, and for y they appear in terms of the velocity and launch angle in x. When one takes these expressions to the final moment of time, when the ball is entering the basket, it turns out that the ball must enter the basket exactly at the center if we have fixed the angle of launch, z, to be the speed with which the ball must**00:45:00**Shaquille O'Neal's shooting accuracy was analyzed in terms of angles and velocity. It was found that combinations of angle and velocity, rather than just one or the other, were the best way to shoot free throws for Shaq. Furthermore, if you could hit an angle at which Shaq always makes his free throws, but at the same time guarantee a basket, then there is only one such angle, z1000, at which the ball would enter the basket. However, there are many angles between z1000 and zm marks at which the ball would enter the basket, with the latter being the most likely. It is suggested that, for those who study mathematics, the best angle to shoot free throws for Shaq is z1000, at which the ball enters the basket just in front of the free throw line, but still touches the backboard.**00:50:00**The presenter discusses how to allow for both speed deviations and angle deviations while guaranteeing the ball enters the house. There are some considerations that coaches of any player of any basketball team can make by analyzing different values of the idea of 5 visits. For example, high-level players should throw more often closer to the center of the basket, while lower-level players should throw balls near the back of the basket. However, an analysis of 11 different data sets would be needed to draw any conclusions about which players should throw differently. Finally, the presenter provides references for further study.**00:55:00**In this video, mathematics and sport are discussed. The presenter points out that while the number 67 is interesting mathematically, it is not really relevant to sport. For example, if you are considering whether or not to shoot a three-point shot, you would not consider the number 67. However, the presenter goes on to say that if you consider all the possible configurations of shots Jackson could have taken, then 67 does play a role. For example, if Jackson took a mid-range shot, then 67 would be involved in the calculation of the probability of making the shot. The presenter then goes on to discuss the concept of rotational symmetry in sport, and how it can be used to advantage a player. He gives the example of a tennis player who can hit a ball in any direction because the ball is symmetrical. A football player, on the other hand, can only hit the ball in one direction because the ball is not symmetrical. The presenter finishes the video by giving a simple mathematical example of rotational symmetry in sport.

The video discusses the pros and cons of shooting free throws compared to other sports. It points out that, in shooting free throws, a player is always in control of the shot and can choose their angle and speed. The video explains that it is a matter of skill and practice, and there is no one skill that is better than any other.

**01:00:00**This video discusses the pros and cons of shooting free throws compared to other sports. It points out that, in shooting free throws, a player is always in control of the shot and can choose their angle and speed. As the game progresses, a player's fatigue will likely become more noticeable, but it is ultimately up to the player to determine how well they perform. All in all, the video explains that it is a matter of skill and practice, and there is no one skill that is better than any other.

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