STANDING LONG JUMP THEOREM: AN ACCIDENTAL DISCOVERY

Introduction: Assessment of the jumping ability and prescription of jump tasks are integrated in the field of fitness training and physiotherapy rehabilitation. Different kinds of researches on jump analysis have been pursued to gain in-depth knowledge about the kinetics and kinematics of jump biomechanics, in particular, the standing long jump. Standing long jumps can be tested or performed in various ways with alterations in direction of jump (forward, sideward and backward) and leg participation (single leg, double leg). The objective of this article is to share the reports of three types of standing long jump tests conducted for fitness evaluation of clientele; Single Leg Forward Jump (SLFJ), Double Leg Side Jump (DLSJ) and Double Leg Forward Jump (DLFJ), and discuss the accidentally observed trigonometric relationships between these jumps. Methodology: The data of three types of standing long jump were collected from 10 subjects (males = 7, females = 3) who have been exercising at least 2 - 3 times per week since last six months and they also belonged to different countries like India, Australia, Spain and Israel. All the subjects were allowed to jump with shoes on and all the jumps were done on wooden flooring with a height scale (measuring 0 to 205 cm) kept horizontal to mark the point of take-off and landing. A minimum of three chances were given for each jump and strong verbal encouragement was given to extract the best jumps from the subjects because the best jumps were taken for statistical analyses. After gathering the jump performance data, efforts were made to establish possible unexplored links between these three types of standing long jumps. Results: A surprising trigonometric relationship between SLFJ, DLSJ and DLFJ was an unexpected finding and accordingly, a formula was devised on the basis of Pythagorean theorem; DLFJ = √ (mean DLSJ2 + mean SLFJ2). Pearson correlation coefficient test was done to understand the degree of relationship between this formula-projected DLFJ and actual DLFJ displayed by the subjects, through which it was found that r = 0.9987. Conclusion: The theorem for standing long jump introduced by this study using an inexpensive technique has been shown highly positively correlating with actual double leg standing long jumps. This theorem can be stated as ‘double leg forward standing long jump is equal to or almost equal to the square root of the sum of the squares of standing side jumps (mean of right and left side jumps) and single leg forward standing long jump (mean of right and left single leg forward jumps)’. This study will continue to explore the deeper interconnections of different types of single leg and double leg jumps to contribute further advanced insights to the field of biomechanics and exercise. KEY WORD: Theorem for standing long jump, Standing long jump, Side jump