University of Silesia in Katowice

|tekst: Dominika Ściepura, studentka kierunku matematyka|
|dr Anna Glenszczyk, opiekun|
|Praca została napisana na potrzeby Warsztatów z logiki|

Maths in sports

Upon hearing the word “mathematics”, many of us would recall the terrifying classes in the secondary school, during which the teacher tried to explain what pyramids look like, what quadratic functions and derivatives are, scaring us with short tests or Matura exam fail. We could often hear back then that we need mathematics, the queen of sciences, to live, and we could not do without it. However, the youth, particularly those who did not want to connect their future with this field, were unable to comprehend that they would also need mathematical knowledge in their lives. It was athletes rather than humanists that found it most difficult to understand. They thought training and inborn talent was all they needed to achieve success. And they couldn’t be more wrong.

Mathematics and swimming

We can actually find mathematics in sport almost everywhere. In fact, there is no sport that wouldn’t apply at least a few mathematical issues in order to train proper or achieve success in the field.

Let’s take swimmers, for example. At every training session they have to cover a certain distance, during which the coach often change their swimming style, which is why it is so important to count the number of pool lengths properly and convert them into metres. Sometimes the coach tells us to swim 200 metres, and other times to swim 8 lengths.

The queen of sciences is also used for proper calculation of heart rate after sprint races. This can be done not by using special waterproof measuring devices, but by putting two fingers in the proper place on the neck and using a stopwatch located on the wall of every swimming pool. The heart rate is usually stated on a per minute basis, whereas the measurement is performed within 10 second only. Therefore, it is essential to multiply the obtained value appropriately, so as to achieve the result in a proper unit.

Speaking of watches, it is also important to know how to use the stopwatch. During trainings, the coach usually signals start for the first series, while the subsequent competitors should be able to calculate it for themselves, to which stopwatch “arrow” they should start, depending on the intensity and length of the distance, as well as the number of people on the track. The following competitors usually start running every 10-15 seconds.

What is more, in certain training tasks, mathematics is used when the next move is to be added every three kicks or the swimming style is to be changed entirely after 5 seconds, or calculated using the number of arm moves how many more strokes are left to the wall from the “third corals” to make the relapse correctly when swimming the backstroke.

However, swimming is not only about calculating the beaten distance, but also about the proper technique. It is thanks to it that we can achieve our goals without using too much energy. In order to develop it, we also need to be familiar with the basic mathematical terms, such as the angle between two arms. We also need to have some spatial imagination. When swimming the crawl, the important thing is to keep our head all the time parallel to arms in circular motion, whereas during their movement right near the head, the angle between the elbow and the ear should amount to 90 degrees.

Mathematics and dance

Technique is not only important for swimmers. Every athlete should take care of it. Let us consider, for example, dancers in ballroom dancing. The proper body arrangement is also very important for them. Mathematics appears already at the moment of placing the partners’ hands. The man should keep his hand perpendicular to the partner’s spine, in the middle of her back. The woman should keep her left elbow parallel to the man’s shoulders, trying to maintain it at the 180-degree angle together with her arms.

When the partners are ready to dance to the music, they should be able to catch the rhythm, and at the same time properly calculate the moment of start so that they can begin the dance together. In the case of waltz it is relatively easy, because it’s enough to count 1-2-3. However, it’s not as simple with Latin American dances. For example, when choosing jive, the partners must jointly count 7-8 , 1-2 3 and 4, 3 and 4 7-8, which makes joint movement coordination significantly more difficult.

However, dancing is not just about hand arrangement or musical rhythm. When beginning you adventure with any dance, you have to learn the steps. With the help of mathematics, the beginning dancers have the possibility to learn new steps, because it’s just enough to calculate each move properly.

When starting to dance e.g. rhumba, everyone knows that each step to the side is taken on “4”, holding on “1”. The same with the quickstep: if you want to dance the “promenade”, it is important to calculate the already taken steps, so as to add the “quick” step at the right moment and perform another movement arrangement. Thanks to such appropriate arrangement, the dance will look elegant, and the partners’ bodies will form a coherent whole.

Mathematics and horse riding

We can also find elements of mathematics in sports involving animals, for example in horse riding.

Starting from the riding hall, which should have proper dimensions. Depending on whether it is a professional or training hall, they will be different, because one is 22*42 m, and the other one is 22*60 m. It should also be remembered that the obstacles used for training need to be located at the right places. This can be calculated based on the size of horse steps and riding style, i.e. trot or gallop. This is because horses, just like people, extend their steps along with the increase of the riding speed. For example, the poles for a large horse trotting should be set every 135 cm, but if the horse is in gallop, the distance should be 300 cm. However, such dimensions are only stated during training. When we are at a parkour, during a competition, we should be able to convert the arrangement of obstacles to steps ourselves. If we want to do it, we should know the length of a horse step in gallop, how close to an obstacle a horse bounces from and how many metres behind it lands on the ground. It usually amounts to 3-4 metres.

The horse’s size is also very important, especially for the owner. Thanks to the basic dimensions, such as weight in withers or size of a hoof, it is possible to buy a proper saddle or horse-shoe. If they were wrongly selected, they could hurt and graze our animal. The correct attitude is also significant. It is important for our spine to run perpendicular to the horse’s back, and the angle between the thigh and the knee was 45 degrees. Such arrangement allows us to keep control of the horse, without giving them false signals about the change of a riding style.

Mathematics and building athletic form

Speaking about sport, it is also worth noticing what the preparation of athletes for trainings and competitions looks like. They try to take care of their health, including the diet. They often begin to count calories, paying attention to the proper amount of nutrients. However, for the diet to be proper, everyone should know their caloric demand which can be easily calculated, using mathematical formulas.

For example, this formula for women looks as follows:
PPM = 665.09 + (9.56 * body weight in kg) + (1.85 * height in cm) – (4.67 * age),
where PPM refers to basic metabolism.

Next, the relevant physical activity coefficient should be selected to be ultimately multiplied by the above result and obtain the caloric demand.

Example: woman 18 years old, height 170 cm, weight: 65 kg, activity: sedentary job, 2-3 training sessions per week, so her activity coefficient is 1.6.
PPM = 665.09 + (9.56 *65) + (1.85*170) – (4.67*18) = 665.09 + 621.4 + 314.5 – 84.06 = 1516.93 kcal
PPM * activity coefficient = 1516.93 * 1.6 = 2427,088 kcal (caloric demand)

In this way athletes can calculate caloric demand, but not the proper amount of nutrients.

Therefore, in order to calculate the proper amount of ingredient such as protein, the body weight must be multiplied by 1-2.5 (depending on the type of physical activity).

Example: woman 18 years old, weight 65 kg, training 2 times per week, aiming to achieve certain appearance.
In this case, the amount of protein she should eat amounts to 1.5 g/kg of body weight, which means that she should eat 65 * 1.5 = 97.5 g protein per day.

With this knowledge, athletes can take care of proper diet, which will provide them with the right amount of energy and good well-being.

Mathematics is everywhere

As can be noticed, there are endless examples of the use of mathematics in sports. Starting from appropriate sport techniques, through proper body position, correct calculation of distance and caloric demand, to counting required dimensions of training spaces, mathematics is always needed. Thanks to it, you can take care of your health and body shape, try to develop your skills, like in the case of learning new dancing steps, or achieve success using not only your muscle strength, but also proper pull techniques, which can be easily seen in swimming.

Thus, let us remember that mathematics may prove to be necessary in life, regardless of the interests of profession.