INDEX INTRODUCTION 1 – SOME PRELIMINARY DEFINITIONS 2 – THE MATHEMATICAL APPROACH 3 – HOW TO CREATE COMPOSED SYMMETRIC STEPS 4 – HOW TO CREATE COMPOSED ANTYMETRIC STEPS 5 –...

**Mathematics applied to Skating**

**STYLESLALOM**

**Theory and examples**

*Enrico PERANO*

**INDEX**

INTRODUCTION

1 – SOME PRELIMINARY DEFINITIONS

2 – THE MATHEMATICAL APPROACH

3 – HOW TO CREATE COMPOSED SYMMETRIC STEPS

4 – HOW TO CREATE COMPOSED ANTYMETRIC STEPS

5 – THE EXTENSIONS OF AN ELEMENTARY STEP

6 – HOW TO COMPLETE A GIVEN MIX OF STEPS

7 – ADVANCED TOPICS: THE PRINCIPLE OF DUALITY

**PREFACE**

"Cogito ergo sum", that means "I think, so I am*".It was asserted by Cartesio, a great French philosopher and** mathematician, who lived in the 17th century. His expression, that today has become proverbial, could be presented in contemporary terms as "*I think, so I skate*". *

* This book is a proof of it and wants to be a meeting point between the experts on an abstract discipline, like Mathematics, and people who practise competitive sports, or who apply hard himself to a sports discipline. In fact, using an innovative approach that is made intelligible to everybody, this book suggests an "* association

*" that is as much unusual as surprising, and denies the commonplace by which the thematics are considered abstracted because it’s supposed that they are immersed in their numbers world, without a connection with reality and daily problems. The same idea claims that mathematics are "ackward*

*" and hopeless at any practical or sports activity. On the contrary, this book shows that Mathematics application, only using some elementary concepts that are immediately understandable without prerequisites, allows to invent new skills within a sports discipline, like just skating, and to complete it. Mathematics can be essentially used to help athletes in sports disciplines, like styleslalom that consists of performing tricks by skates , called steps, while running around three lines of cups or cones. These ones are placed at the same distance between them: two lines of 20 cones, one at 50 cm, the other at 80cm and one line of 14 cones at 120 cm. In fact you can assign to every step some mathematical properties, such as symmetry, periodicity, antimetry and associate a graph that describes these properties. Then you can compose the graphs obtaining more complex schemes from which you can deduce the choreographies of the corresponding steps. All that to say that Mathematics, as well as teaching to make calculations, gives also a method of discussion and permits to solve problems that aren’t necessarily mathematical. So, those who are seriously devoted to a sports activity and perhaps have always thought of being not very mathematically inclined or not at all, above all because they don’t see the practical use of it, now can change their mind and appreciate Mathematics if they read this book . In fact it’s possible to find in it how much this scientific discipline can help to develop individual creativity in the sports field using an amusing and actual way. After all, this book can associate two categories of people, who were incompatible till now. So I can only wish you a pleasant reading of my handbook, and I hope that you will have fun while reading as much as I had fun while writing it.***INTRODUCTION**

*In 1995, when I started practicing Slalom, only about 10 steps had been created.*

*Styleslalom consisted of repeating these steps one after the other from the first to the last cone.*

*In 1996 I introduced a theory to build many new steps from the basic steps that were known in those years.*

*In the same year FIHP asked me for the technical dictionary which gives the meaning of my technical terms, with the intention to use it as the base for the rules of freestyle slalom. In fact, already then, FIHP was interested in having the Style slalom as an official discipline, like Hockey, Artistic or Race.*

*This method can always be used because it may be applied to any step.*

*The aim of this book is to describe precisely the theory on which I’ve based this method.*

*In addition to the book a DVD with about fifty videos is inserted. These videos are partly demonstratives, partly more didactic and the tricks shown on some of them are performed by athletes of the Italian National Team, which I coach.*

*On didactic videos the most difficult tricks are shown at a reduced speed and some comments have been added. These videos are a very important tool to understand the subjects deeply.*

* *

*A_Mathematic_application_to_Styleslalom_The_principle_of_Duality.pdf*