1. Mathematics as an essential component of the sport training. Authors: Dr.C. Islay Pérez Martínez. Sports Science Department (BUSE) MSc. Ariadna Quintana Díaz. University of Matanzas(Cuba)

2. In the sports, the mathematics have different applications; among them, we have the following examples: In the planning of the training. The control of the loads. The evaluation of the competitive results. The selection of talents. To predict results.

3. Equation to determine the heart frequency of training. CRT = CRR + 0,6 (MCR – CRR) CRT = Cardiac rhythm of training B. /MIN. MCR = Maximum cardiac rhythm. B. /MIN. CRR = Cardiac rhythm of rest. B./ MIN. MCR = 220 – AGE EXAMPLE: CRT = CRR + 0,6 (MCR –CRR) CRT = 70 +0,6 ((220 –20) –70) CRT = 70 + 0,6 (200 –70) CRT = 70 + 0,6 * 130 CRT = 70 + 78 CRT = 148 B/MIN.

4. The work threshold (area of energy work) related with the power of the work, it determines the percentage of the heart frequency of training regarding the maximum and the predominant energy system. According to Menshikov and Volkov (1985) to the same one it corresponds the following values: 70% Aerobic work. 80% Mixed work. 90% Anaerobic work SCALE OF WORK: IntensityPercentEnergy Area Maxim96 – 100Anaerobic Sub - maxim90 – 95Anaerobic Big86 – 89Mixed Medium80 – 85Mixed Sub - medium71 – 79Aerobic Small60 – 70Aerobic

5. WINT = HEART FREQUENCY OF WORK - HEART FREQUENCY IN REST MAXIMUM HEART FREQUENCY - HEART FREQUENCY IN REST WINT = 160 - 70__ = 90__ = 90_ (220 – 20) – 70 200 – 70 130 WINT = 0,69 DETERMINATION OF THE COEFFICIENT OF INTENSITY

6. Aerobic Rhythm. The aerobic rhythm is basic for a correct planning of the volume and the intensity in the athletics races. With this calculation we can obtain an information that allows us to dose and to adapt the training to each athlete's individual characteristics. Result of the race test: 13500 meters travelled in 45 minutes (2700 sec) Speed (Aerobic Rhythm): 13500 / 2700 = 5 m/sec. 1000 m / 5 sec = 200 sec/km = 3:20 min/km.

7. Example of Rhythm of Training for an athlete with an aerobic rhythm of 3:20 min/km. Aerobic Rhythm: 3:20 min/km Form of calculating the rhythm of training: 70% of the Aerobic Rhythm: 4:46 min/km (200 sec*100 / 70= 286 sec = 4:46 min/km) Rhythm of slow continuous race (70% of the aerobic rhythm) 4:46 min/km Rhythm of slow race of long distance (80-85% of the aerobic rhythm) 4:10-3:25 min/km. Rhythm of fast continuous race (90-95% of the aerobic rhythm) 3:42-3:25 min/km. Rhythm of training to extensive intervals (105-110% of the aerobic rhythm) 3:10- 3:00 min/km.

8. Purpose Rhythm. The purpose rhythm allows the athletes to train in a specific way for a certain race. Next the example of a runner of 1500 plane meters appears. Example of as using it with an athlete that competes in 1500 meters: Result of a test of 1500 meters: 1500 meters in 4:15 min. Expectation of time: 4:15 min = 255 sec Speed average in m/s: 1500 m / 255 sec = 5, 9 m/s. Purpose rhythm for 100 m: 255 sec / 15 = 17 sec. Purpose rhythm for 400 m: 17 sec * 4 = 68 sec. Purpose rhythm for 1 km: 17 sec * 10 = 170 sec (2:50 min)

11. Control of the recovery using the rhythm of heart beaten. The control of the recovery after the training is extremely important because it offers us the information about if the sportsman is assimilating the received loads correctly. In this way, we can avoid to fall in a state of overtraining that is harmful for the body. When the rhythm of beating returns to 100 bpm (beaten by minute) in: 3:00 minutes or less: Very good recovery. 5:00 minutes: Satisfactory recovery. More than 5:00 minutes: Poor recovery.

12. Rhythm of beating after 5 minutes (beaten per minute): 100-105: Very Good. 106-115: Good. 116-120: Satisfactory. 121-130: Poor. Higger than 130: Very poor.

13. Classification for the regulation of the exercises with weights. (A. Novikov y L. Matveyev. 1986) LoadsRepetitions% Maximum1100 Sub-maxim2 – 390 – 95 Big4 – 880 – 89 Moderate9 – 1260 – 79 Medium13 – 1840 – 59 Small19 – 2525 – 39 Very small+ 25-25

14. When the exercises with weights are planned you can use the following nomenclature: % / Series = 80 / 3 Repetitions 8 In this exercise, would be made 3 series of 8 repetitions with 80% of the maximum force, valid for 24 repetitions in total.

15. Tonnage: The tonnage is the result of multiplying the lifted weight, for the quantity of carried out repetitions. Repetitions: The total of the repetitions is the sum of the repetitions carried out in a series, in a training, week, month, etc. Weight / series = 120/3 Repetitions 2 Example: 60 Kg 70 Kg 80 kg/2 90 kg/3 5 4 3 2 Tonnage: 60 x 5 + 70 x 4 + 80 x 2 x 3 + 90 x 3 x 2 = 300 + 280 + 480 + 540 = 1600 Kg Repetitions: 5 + 4 + 2 x 3 + 3 x 2 = 21 Control of the load in the exercises with weights

16. Dosage example when the % of the maximum force is used. To execute squatting from behind (maximum result 150 Kg). 60% 70% 80% / 3 = 90kg 105kg 120kg/3 3 3 2 = 3 3 2 = 90 x 3 + 105 x 3 + 120 x 3 x 2 Tonnage = 305 Kg Repetitions = 3 + 3 + 3 x 2 = 12 rept.

17. Weeks Sessions of training Dosage Quantity of exercises Total Legs ThoraxArmsPromLegsThoraxArmsPromExercisesRepetitions 113O/32O/3IO/32O/3I/45 4180 15 23O/32O/31O/32O/3I/45 4180 15 2333/423/412/423/42/144I/72 5360 18 436/426/414/426/42/144I/72 5360 18 3538/528/517/528/52/180 I/90 6540 18 641/531/520/531/53/2702/150 I/758630 18 Example of planning of the load in exercises with weights.

18. Total of Hours 90 8020280 Total of minutes 5400 4800120016800 Component Stage of General Preparation Stage of Special Preparation Competitive Period Transit Period Total General Physical Preparation 55%21%12%70%33% 297011345768405520 Special Physical Preparation 14%23%21%10%18% 756124210081203126 Technical Preparation 15%27%19%15%20% 81014589121803360 Tactical Preparation 12%25%44%-25% 64813502112-4110 Theoretical Preparation 4% 5%4% 216 19260684 Total 5400 4800120016800 DISTRIBUTION OF THE BLOCK OF DETAILED INFORMATION

19. HOW TO ACHIEVE A CORRECT DISTRIBUTION OF THE LOADS IN THE TABLE OF GENERAL INFORMATION? WEEKS9 MULTIPLY THE NUMBER OF WEEKS FOR THE PROPOSED % HOURS9.10= 90 MINUTES90.60=5400 G. P. P.55%55.9= 495 2970 S. P. P.14%14.9= 126 756 TEC. P.15%15.9= 135 810 TACT. P.12% 12.9= 108 648 P. TEO. P4%4.9= 36 216 TOTAL5400900/9= 100 STAGE OF GENERAL PREPARATION (EXAMPLE)

21. Selection of sport talents: To identify sport talents several physical test are applied that evaluate the capacities of force, speed, endurance and flexibility, the size and the weight are also measured. To those results are applied statistical techniques and they conform to databases that represent populations. For example, the following tables show the Percentiles of the speed test for males and force test for the females. With these data when comparing the individual results of the students you can determine if they possess the suitable conditions for the practice of the sport.

22. Percentiles of the test of speed masculine sex. Percentiles of the test of force - feminine sex. AGE

23. The following table shows the values used in Cuba for the evaluation of the tests of physical efficiency in the Physical Education.

24. Conclusions: Mathematics has a paramount importance in most of the fields of science; in sports, specifically, it has many applications. In this paper, we have shown some examples of the application of mathematics to the world of sports. It is demonstrated that a successful process of sport formation cannot be lead without making use of mathematics. In sport the loads without control are dangerous for health and this control is exercised with the use of mathematics.

25. “The load without control is unthinkable and dangerous” Peter Tschiene