THEORY AND EXAMPLES OF APPLICATION

THE ORIGIN OF THE STYLESLALOM

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. The most spectacular steps were Ala Step e and its generalization I called the Mabrouk Step. Nobody knows the origin of the the Ala and Mabrouk steps. Somebody told me that they were seen performed for the first time without the cones in Switzerland, in a VHS coming from US, in the ’80ies and ’90ies. This tape inspired the swiss freestylers who then tried these tricks between the cones.
In America the Mabrouk step is called “grapevine” and the ala step was then called “crazy” step by the french skaters.
I saw the Mabrouk step for the first time in Zurigo in 1995, performed by the winner of the competition who took place in that city. I gave it this name in memory of Hedi Mabrouk, a great skater from Lausanne, dead a few months before.
In 1996 I introduced a system to build many new steps from the basic steps that were known in those years. I developed this method basing on some simple mathematical rules.
In that same year FIHP asked me for a specialist dictionary which gave the meaning of my technical terms, with the intention to use it as the base for the rules of freestyle slalom. In fact, since then, FIHP (Federazione Italiana Hockey Pattinaggio) was interested in having the Style slalom as an official discipline, like Hockey, Artistic or Race skating. This technical dictionary can be seen at this link: a scientific approach to styleslalom.

I created the first compositions with Crazy and Mabrouk steps and I called them Ala flowers and Mabrouk flowers. They became well known in the 90ies and I will show them later in this document as examples.

My method is however generally valid because it can be applied to any step , so it can always be used.
Below I’ll resume the theory with very few rules that allow a freestyler to create new compositions starting from steps he already knows.

1 – SOME PRELIMINARY DEFINITIONS

STEP:

Set of tricks performed with the skates during the running of a line of cups following a predefined direction, according to this fundamental rule: every couple of subsequent cups must be crossed at least once by one or both skates.

FIGURE:

Trick performed with the skates during the running of only one or two cups, that isn’t repeated while crossing the subsequent cups.

ELEMENTAL STEP:

Step that can’t be broken up into simpler steps

Example 1:

The following steps are defined as elemental steps: the simple forward and backward crosses, simple or crossed eagle and antieagle, only one leg (forward or backward direction), sideways tip-tap also performed on one leg, the sideways walk, the footgun, and so on.

–>> These steps are shown in next VIDEO1

STYLESLALOM - Alcuni passi elementari

COMPOSED STEP:

Step that contains two or more connected elemental steps

Example 2:

Some examples of composed steps are: the double forward and backward crosses, and, in general, any imaginable mix of elemental steps.

–>> These steps are shown in next VIDEO2

SIDEWAYS STEP:

A step where the frontal plane of the body is always parallel to the cups line during all its performance. It is also defined right or left handed sideways step depending if the running of the cups is on one’s right or left. Sideways step examples are Ala step, eagle, anti-eagle and the sideways walk shown, respectively, in the previous videosv.

PERIODIC STEP:

Composed step whose performance is repeated every n cups (n≥2). The lowest n that satisfies this condition is called the period of the step and it is indicated with the symbol T

NOTE 1: the Mabrouk step is periodic and its period is 4

NOTE 2: any non-periodic composed step performed among n cups may become periodic if is repeated equally every n cups

NOTE 3: the period of an elemental step is always equal to 2

SWITCH: CHANGE BETWEEN TWO DIFFERENT STEPS

NOTE 4: a switch can be performed in different ways and so it is possible to perform different switches between two identical steps. In particular the switch used to change from a step A to another step B may be different from the one used to switch from step B to step A.

OPPOSITE STEP (or SWITCHSTANCE):

Given two steps A and B, B is defined “the A opposite” and we write, B = Ā , if it’s obtained performing A in the opposite direction.

Example 3:

VIDEO 3 shows the performance of some elemental steps and their opposite ones. The Ala and Mabrouk steps, sideways walk, tip-tap, and the forward running across the cups only on one leg, eagle, heel-toe, footgun are described.

–>> These steps are shown in next VIDEO3

SYMMETRIC STEP:

A step is defined symmetric when it is still equal to its opposite, so when performing the opposite you always obtain the same step.

Example 4:

Like the double forward and backward crosses, also the following steps are symmetric:

1) The forward walk

2) The backward walk

STYLESLALOM - La camminata indietro

The running backward walk (crazy leg) , already shown in VIDEO 2.1.4b on “Dancing tricks”.

2.1.4b (Crazy legs).wmv

4) The modified version of forwarding walk, which is shown in VIDEO 2.2.4a and VIDEO 2.2.4b on “Dancing tricks”.

2 – HOW TO CREATE COMPOSED SYMMETRIC STEPS

The fact that the opposites of some steps are different from the original steps, suggests a method to create new steps that will no longer be elemental but will be composed, by adding to every step its opposite.

For example, consider performing a non-symmetric step only in the space corresponding to the first period of two cones and then, switching on the third cone (or also on the fourth one), executing the opposite step in the next space of width T=2.

So you obtain a that is no longer elemental and is composed by the original step with its opposite, a symmetric step, with period step equal to TS =6.

This method allows you to build a symmetric step from a non-symmetric step by adding its opposite, this means creating new compositions from elemental non-symmetric steps and can be resumed by the following rule.

RULE 1

Once chosen a non-symmetric step, try alternating it with its opposite, by using a different basic step to change from one to the other one.

The role of the switching figure by which a step is alternated with its opposite is fundamental in building the resulting composed step. In fact, also if you alternate the same step with its opposite, you can obtain different choreographies by changing the switching figure.

According to RULE 1, any elemental step can be used as a switching figure but the resulting composition can be better if you switch from one step to its opposite with a figure which corresponds to an elemental step that is already symmetric, such as the forward or backward walks.

Some examples are shown in the following.

Example 5: The 2 forward Ala flowers

The Ala step and its opposite alternated every cone using the forward walk as a switch figure.

  • Component Steps: forward walk, Ala step performed from both sides
  • Sequence: forward walk + Ala step + forward walk + Ala step from the other side (switch stance)
  • The switch between one step and the next one must be performed on every cup

 

–>> These steps are shown in next VIDEO 6

Example 6: The 2 backward Ala flowers

The Ala step and its opposite alternated every cone using the backward walk as a switch figure.

    • Component steps: backward walk, Ala step from both sides
    • Sequence: backward walk + Ala step from one side + backward walk + Ala step from the other side (switch stance)
    • Elemental steps must be changed at every cup
    • Properties: symmetric, composed, and periodic step, with period T=6

These steps are shown in next VIDEO 7

NOTE 5: By the term “Ala flower” I mean sideways Ala cross. I like to call these compositions “flowers” because if you practice them with wet wheels, the lines covered on the floor leave impressions of flower petals if they are overlapped on a single cone

Example 7: The 2 forward Mabrouk flowers

The Mabrouk step and its opposite alternated using the forward walk as switch figure

  • Component Steps: forward walk, Mabrouk step from both sides
  • Sequence: forward walk+Mabrouk step from one side+forward walk+ Mabrouk step from the other side (switch stance)
  • The switch between one step and the next must be performed on one cup.
  • Properties: symmetric, composed, and periodic step, with period T=10

–>> These steps are shown in next VIDEO 8

Example 8: The 2 backward Mabrouk flowers

The Mabrouk step and its opposite alternated using the backward walk as switch figure

  • Component steps: backward walk, Mabrouk step from both sides
  • Sequence: backward walk + Mabrouk step from one side + backward walk + Mabrouk step from the other side
  • Elemental steps must be changed at one cup
  • Properties: symmetric, composed, and periodic step, with period T=10

–>> These steps are shown in next VIDEO 9

NOTE 6: I like to call “flowers of Mabrouk” the compositions described in examples 7 and 8, even if they have nothing to do with flowers.

Example 9: Forward eagle walk

The next VIDEO 10a shows the skating across n cones both in eagle and in its opposite alternating the eagle steps with a cross performed in forward walk. If n is reduced to 1, the running, both in eagle and its opposite, is only across one couple of cones, and a new composed step, called forward eagle walk, is obtained. It is shown in VIDEO 10b.

Example 10

The sideways walk and its opposite changing every two cones with the forward eagle cross.

–>> These steps are shown in next VIDEO 11

Example 11

The sideways walk and its opposite changing every cone using 180 turns.

–>> These steps are shown in the next VIDEO 12

Example 12

The Ala step can be alternated with its opposite every n cones using 180 turns too.
Choosing n=1, the transition from one Ala step to its opposite is performed every couple of cones and in ’96 I called the composed step obtained half-moons step.

–>> These steps are shown in the next VIDEO 13

Example 13

The step shown now is called backward eagle walk and consists of backward running across the cones in eagle alternated with its opposite using a cross in backward walk.

–>> These steps are shown in next VIDEO 14

Example 14

The 2 Ala flowers alternated by the crossed eagle

–>> These steps are shown in next VIDEO 15

Example 15

The 2 Ala flowers alternated using the forward eagle walk

–>> These steps are shown in the next VIDEO 16

Example 16

The 2 Ala flowers alternated using the backward eagle walk

–>>These steps are shown in the next VIDEO 17

Example 17

Backward eagle walk alternated by tip-tap on one leg

–>> hese steps are shown in next VIDEO 18

Example 18

Forward half -compasses

–>> These steps are shown in the next VIDEO 19

Example 19

Backward half-compasses

–>> These steps are shown in the next VIDEO 20

Example 20

Voltè alternated by the forward walk

–>> These steps are shown in the next VIDEO 21

Example 21

Two compasses alternated with their opposites

–>> These steps are shown in the next VIDEO 22a

–>> These steps are shown in the next VIDEO 22b

3 – HOW TO CREATE COMPOSED ANTIMETRIC STEPS

The idea of extending a simple step using suitable symmetries to built more complex choreographies, that is steps mixtures, can be extended if we refer to another mathematical term, the one of inverse function.

INVERSE STEP:

given two steps A and B, B is defined as “ the inverse of A and it is indicated with if it is obtained inverting the movements of the skates when performing step A.

Example 22:

VIDEO 23 contains the performance of some elemental steps and of their inverse ones: the forward and backward walks, internal and external sideways tip-tap on the same leg, the simple or double forward and backward crosses, only on one leg forward direction and on the same leg backward direction, forward and backward footgun on right leg.

NOTE 7: If you film a step performance, and push the rewind button when you play the film, you will see the performance of the inverse step.

NOTE 8: Performing the inverse or the opposite of a step you sometimes obtain the same step, this means that the inverse and the opposite of a step can be the same step.

Example 23:

The opposite and the inverse of most sideways steps, like sideways walk and Ala step, are the same steps. In fact, if you rewind the right-handed sideways step, the inverse step obtained is the left-handed version of the same sideways step, which is its opposite.

ANTIMETRIC STEP:

When a step is identical to its inverse, so, when inverting the movements of your skates, you obtain the same step.

NOTE 9: According to this definition, if you film the performance of an antimetric step and play the film, you should see the performance of the same step pushing the rewind button, but actually steps equal to their inverse are non physically possible. However, there are steps whose inverse coincides with their opposite, so in practice, the term antimetric will mean precisely these steps. It can therefore be said, for example, that the sideways steps are antimetric.

Example 24:

Next VIDEO 25 shows the Mabrouk step and its inverse obtained inverting the sequence of images.

You can note that the step is equal to its opposite, so we conclude that Mabrouk step is antimetric.

NOTE 10: The inverse of the opposite of an elemental step is equal to the opposite of the inverse of the same step. So we can write:

where A represents a generic elemental step.

Choose the running forward across the cups only on the right leg as an example of an elemental step and apply the relationship stated in NOTE 10.

To invert A means to run across the cones on the right leg but backwards, while the opposite of the inverse of A, that is, is running backward across the cups on the left leg.

On the contrary the opposite of A,, is performed running forward across the cups line but on the left leg, while its inverse, ,is obtained running backward still on the left leg.
You can note that the result we have obtained is the same.

NOTE 11 :It may happen that the inverse of a non-antimetric step is almost impossible to learn, also if you follow the hint proposed in NOTE 7, and you watch its performance by playing the film of the original step backward.
On the contrary, this problem doesn’t exist when you try to learn the opposite of a step because you must only learn to perform the same step on the opposite side, which means performing it in the unusual direction.

The addition of inverse steps allows the introduction of a second rule to make new more complex compositions, from simpler steps.

RULE 2

Choose two steps, A and B, where one is the inverse of the other, (supposing that A isn’t antimetric, so A is different from B). Try to alternate them every one or two cups, using one of the elemental steps you know as a switching figure.

This rule allows you to create an antimetric step starting from a simpler step that is not antimetric.

Example 25:

The forward walk is the inverse of the backward walk and they can be alternated using the eagle or the antieagle as a switching trick.

NOTE 12: Rule 2 can also be applied to symmetric compositions that have been composed by alternating an elemental step with its opposite.
This means that you can add a symmetrical composition and its inverse to obtain a more complex choreography that remains symmetric and, at the same time, has become antimetric.

Example 26:

The forward eagle walk and the backward eagle walk are both symmetrically composed steps, one the inverse of the other, and can be alternated with a simple eagle, as the next video shows.

Example 27:

Switches of forward and backward half compasses

Example 28: The 4 Ala flowers

Switches of forward and backward Ala flowers

  • Component steps: forward walk, backward walk, Ala step from both sides
  • Sequence: forward walk + Ala step + forward walk + Ala step from the other side + backward walk + Ala step + backward walk + Ala step from the other side: the forward Ala flowers + the backward Ala flowers.
  • Properties: symmetric, antimetric, and periodic step, with period T=10

Example 29:

I want to propose you create a trick using these rules. So, watch the following movies and you will see a step called ” anti-eagle back cross”

You must first understand and perform the inverse step, then to alternate them using, like switch step, what your imagination suggests to you!

Hint: you can see the inverse step performance if you play the film pushing the bottom backward!

4 – THE EXTENSIONS OF AN ELEMENTAL STEP

There are steps that, in origin, are neither symmetric nor antimetric so their opposites and inverses exist and they can also be unequal between themselves. We have seen that from these steps it’s possible to make symmetric compositions that may also become antimetric to obtain choreographies that are both symmetric and antimetric.

The choreography obtained by transforming an elemental step that in origin is neither symmetric nor antimetric into a symmetric and antimetric step is defined extension of the original step.

For example the 4 Ala flowers are the extension of the Ala step.
The extension of an elemental step is the best composition that can be obtained from it.

NOTE 13: From an elemental step that is neither symmetric nor antimetric it’s possible to obtain two extensions: the first is the extension previously described, while the second is called dual extension and it’s performed by inverting the process by which the first is obtained, this means firstly making the elemental step antimetric and then making the resulting step symmetric.
The dual extension also contains the opposite and the inverse of the starting elemental step, but the order in which such steps are performed changes and so the switching figures used to pass from one step to the other change too.
As an example of an elemental step, consider running forward across the cups only on the right leg and try to create its two extensions.
The result is shown in the following video.

You can note that the two extensions are different only in their switching figures.
Also, the dual extension coincides with the basic extension obtained from another step that consists of running forward across the cups on the left leg.

From an elemental step, it’s usually better to produce the symmetric composition by adding it to its opposite and then later make it antimetric.

In fact, it is written in NOTE 11 that the inverse of an elemental step may exist in theory but not be accomplished in practice, while, on the contrary, it’s always possible to learn the opposite and then to add that to the original step.

Consequently, we usually create the extension of an elemental step and not its dual extension, so that, if the inverse can’t be performed, the symmetrical composition can still be used.

5 – HOW TO COMPLETE A GIVEN MIX OF STEPS

From a mix of steps, that isn’t symmetric or antimetric, we can single out the simpler steps that compose it and add their corresponding opposites and inverses to create symmetrical or antimetrical choreographies or even both.
The component steps don’t need to necessarily be elemental, they may be composed but obviously simpler than the rest of the steps in the choreography.

Example 30:

In the following movie, I perform a composition of two elemental steps, called A and B.

This step can be extended by applying RULE1 to the whole composition or only to every single step.

RULE1 applied to the whole composition (A+B), by adding (A+B) to its opposite

• RULE1 applied to step A, by adding A to its opposite

• RULE1 applied to step B, by adding B to its opposite

6 – PATHOLOGICAL STEPS

An elemental step isn’t compounded by simpler steps and its period is usually equal to 2. It consists of performing the same movement in the spaces between two cones in succession and repeating this movement in the subsequent spaces two by two. On the contrary, a compounded step consists of a mix of elemental steps and its period is certainly more than 2.

These two definitions of elemental and compounded step are part of the technical vocabulary on Styleslalom, related on link: a scientific approach to styleslalom, which I wrote in 1996 and now they are known to most skaters who practice our sport.

But in those last years, the development of Styleslalom has been exponential and now a lot of new steps or figures are known, much more than in the ‘90ies. So it’s necessary to revise these definitions and to generalize them including the special cases that couldn’t be considered otherwise. In fact, by introducing for example one or more figures, it’s possible to obtain some steps that are always elemental according to this definition but with a period reduced to 1, or some compounded steps with a period only equal to 2 as a traditional elemental step.

It’s also possible to make choreographies of only figures that are repeated through the cones within a given period. These mixtures of figures can always be considered steps also if they aren’t elemental or compounded steps according to their classic meaning. All these examples of steps are defined as “pathological steps(1)  so to differentiate them from the standard steps without figures. There can be various cases of pathology and the following is a list of the most significant ones.

(1) The term pathological is currently used in mathematics to define those functions that have atypical properties and therefore are difficult to classify.

1. When you perform only half movement of an elemental step in its period, crossing only one of the two spaces around two subsequent cones according to the chosen step and, using a figure, usually a rotation one, you repeat this half movement running across the other cones. So an elemental pathological step with a period equal to 1 is obtained.

Example 31a:

if you turn around a cone in antieagle on the toes and then you make a 360 before going on, you can repeat the same rotation in antieagle around the next cone and so on. So you make the same movement around every cone performing a step with a period equal to 1. This step consists of an elemental step ( running through the cones in antieagle on the toes) + one figure, so it is always elemental because it hasn’t been created by two different elemental steps. It’s an example of an elemental pathological step.

VIDEO 1.11a.wmv Passi di periodo 1: primo esempio

Example 31b:

Another elemental pathological step, with a period equal to 1, like the previous one, is shown in the next video. It’s obtained using now the crossed eagle on the toes

Passi di periodo 1: secondo esempio

2. When you perform both halves of an elemental step but interrupting them with a figure

Example 32:

If you run on one leg through space between two cones and then you make a 360 before running through the next space, the result is to cross around each cone alternately on the right and left using always the same step (only one leg) but interrupting the continuity of the movement before each cone by a rotation figure. This is another example of an elemental pathological step.

3. The figures can be also used to change an elemental step at each cone. So a compounded pathological step with a period only equal to 2 can be obtained. The method is the following: you go over a cone with an elemental step A and you change your position using a figure so to go over the next cone with another elemental step B instead of proceeding with the second half of the same step A. But you practice only one half of B too, then you change again your position using another figure so you repeat step A and so on.

Example 33:

Let’s consider running across the cones in antieagle on the toes keeping the legs lined up or in eagle still on the toes with the legs crossed. If you go over a cone rotating around it in antieagle on your toes at your right clockwise and, before going on, you cross your legs using a rotation figure, you shall go over the next cone in crossed eagle. Then, using the opposite rotation figure of the previous one, you can go over the third cone in antieagle again. So a compounded step with a period equal to 2 is obtained.

Esempio di passo composto patologico con periodo 2

It’s possible to make different pathological steps from the same elemental one according to which of its two halves you decide to perform. Referring for example to the case shown in Video A, if you were always rotating around a cone in antieagle on your toes at your right but anticlockwise, another much more difficult pathological step would be obtained. Similarly, the compounded pathological steps obtained from two elemental steps A and B can be more than one, depending on which half of A and B you connect to the other by a figure.

4. In the previous cases the figures have been used to change steps and to interrupt or to connect the two halves of one or more elemental steps. But it’s possible to go over each cone, for example rotating around them, using only some figures, without any elemental step. The pathological steps which are obtained in this way are only choreographies of figures.

Example 34:

The step shown in the next video consists of two rotation figures alternated around the cones, one clockwise, the other anticlockwise. Both figures are performed crossing the legs and maintaining the skates on the toes. The result is a pathological step with a period equal to 2.

Esempio di passo patologico costituito esclusivamente da figure

The crossing around a cone in crossed eagle on the toes can be thought of as a part of the multi-turning rotation around the cone maintaining that position, and so it’s a figure, but the same trick can also be half of the elemental step consisting of running across the cones in crossed eagle on the toes.

7 – A MATHEMATIC APPLICATION TO STYLESLALOM:

THE PRINCIPLE OF DUALITY

In technical-scientific field, from a relationship between some variables it’s often possible to deduce a second truth as well if the variables contained in the first relationship are substituted with others, called dual variables, obtained according to appropriate correspondences. So, building a table that lists a set of terms S and the corresponding set of dual terms S*, from every problem P you can make and solve the dual problem P* if you substitute in the equations describing P every term of S by the corresponding dual term of S*. Now let’s see how to apply this principle to Styleslalom for creating new choreographies

1Only the heels of one or both skates touching the groundOnly the toes of one or both skates touching the ground
2Skates gliding in eagle positionSkates gliding in anti-eagle position
3Legs lined up in same or opposite direction during all the skates travel, while a step is performed.Legs kept crossed in same or opposite direction during all the skates travel , while a step is performed

While performing step A, if both the legs or skates are positioned according to at least one of the three rules specified in the columns of the table, the step obtained by replacing the legs or skates position with the one on the same line but in the opposite column is defined dual of A. The dual step will be of the first, second, or third type depending on whether the replacement corresponds to the first, second, or third line in the table.
The dual step will be of the first order if it’s obtained from the original step by using only one replacement, of the second or third order if two or three replacements shown in the table are simultaneously applied.

NOTE 14: The dual version of a step only exists if the legs or skates positions correspond to at least one of the three shapes listed in the table and this position is maintained for the entire step. For example, the dual version of the Ala step doesn’t exist because its performance consists of alternating continuously between eagle and anti-eagle positions, therefore the skates don’t maintain the same positions for the entire step.

NOTE 15: One or more dual versions of a step that meets at least one of the three conditions of the table, can exist in theory but not be physically feasible. For example, let’s consider skating across the cups line with the skates in eagle on the heels, as a step. Its dual version of the second type, obtained by applying the rule in the second line of the table, in theory, becomes running across the cones constantly on the heels, but in anti-eagle, and this trick proves very difficult, perhaps impossible!

SOME EXAMPLES

Now let’s see some examples with increasing difficulty, that include at first dual steps of the first order obtained by applying the principle of duality to some simple elemental steps, and then some superior order dual versions of composed steps.

Example 35:

Consider the following as elemental steps through cones:

  1. skates in eagle on all four wheels.
  2. legs lined up in the same direction with the first skate on the heel, the second on the toe.
  3. legs lined up in the same direction with both skates on the heels
  4. legs lined up in the same direction with both skates on the toes
    and find their possible dual versions of the first order.

Solution:

If the second and third rules of the table are applied to step (1), two dual versions of the second and third type are obtained: one version consists of running across the cones with the skates in anti-eagle while the other version consists of running across the cones in eagle but with crossed legs. These steps are shown in the next videos.

Un'applicazione della Matematica allo Style - VIDEO 1.avi
Un'applicazione della Matematica allo Style, VIDEO 2.wmv

The first step has been shown by Sara Barlocco and Chiara Lualdi in VIDEO 1, while the second one is performed in VIDEO 2 by Daniele Lenzi, a great style slalom rider of the ‘90ies, that created this step and called it “killer eagle”, a name still used in Italy. VIDEO 2 shows his performance of this trick during the competition where He showed it for the first time (Asti Contest, 1999). The same trick is also performed by Tiziano Ferrari, an athlete of the Italian National Team, 12 years later. The more interesting of the two dual versions of step (2) is certainly the third type one, obtained by maintaining the legs crossed for the entire step, with the first skate on the heel and the second on the toe. The result is a very stylish movement across the cones, one of the steps that have been shown multiple times during the Styleslalom World cup 2009. Its Italian name is “cobra” and you can see its performance in the next video from Ilaria Massa Pinto (Roxa Team).

Un'applicazione della Matematica allo Styleslalom. VIDEO 3a
Un'applicazione della Matematica allo Styleslalom. VIDEO 3b

You can see that step (3) is the dual version of step (4) according to the first rule of the table. However, if the third rule is applied, other dual versions of the first order and third type are also possible, this means maintaining the legs crossed with both skates on the heels or on the toes. Effectively two new versions of “cobra” are obtained, but these steps are of very high difficulty and actually, nobody has performed any of them.

NOTE 16: The “killer eagle”, which is the third type dual version of the eagle, must not be confused with the crossed eagle. In fact during the performance of the first step the legs are maintained crossed for all the running across the cones, while in the second case both legs move to cross the trajectories of the skates around each cone.

Example 36:

Let’s try to obtain some dual steps of the first, second, and third order that are physically feasible while running across the cones with the skates in eagle on the heels. The only dual step of the first order, physically feasible, is that of the first type, obtained by maintaining the skates in eagle but on the toes. In fact, applying the second and third rules of the table, the dual steps would consist of running across the cones in anti-eagle with the skates on the heels and the legs lined up or crossed, but these positions are practically impossible. On the contrary, the dual steps of higher order which are obtained from the dual step of the first type described previously applying the second and third rules of the table, are physically feasible and very stylish. They consist of running across the cones in anti-eagle on the toes of the skates and maintaining the legs lined up or in eagle with the legs crossed. These steps are shown in the next video and their performance is, respectively, once more by Chiara Lualdi who executes the version with lined up legs, and by Sarah Veronese, the 2008-2009 Speed Slalom Champion, who shows the eagle on the toes with crossed legs (Butterfly).

Un'applicazione della Matematica allo Style, VIDEO 4.wmv

Example 37:

Suppose gliding with the skates in eagle position on the heels as in the previous example. In this position go into the first couple of cups lightly turning, and, when you have got out of the space between the two cones, do a rotation of 360° remaining in eagle on the heels , then go again into the next couple of cones and so on. This movement is repeated whilst running across all the cups in the line, as the next video shows.

Un'applicazione della Matematica allo Style, VIDEO 5.wmv

Let’s now see a particularly significant dual version of this step. If the first two rules of the table are applied, the resultant dual step that is obtained consists of running across the cones with the skates on the toes, lightly turning in anti-eagle among every couple of cups and doing a rotation of 360°, remaining on the toes, before passing through the next couple of cones. This dual step of the second order is shown in the next video.

VIDEO 1.11a.wmv Passi di periodo 1: primo esempio

8 – CROSS AND SIMPLE FOOTGUNS:

Enrico Perano- Caffettiere semplici e incrociate.wmv
PROVE DI STYLESLALOM CON L ' X-TREME 2011 - 3 di 3.wmv

As you can see in my previous videos, footgun consists of skating only on one skate, totally sitting on it, while the other leg is stretched in a horizontal position and its skate is almost always grabbed by the hand of the same side.
The trick is called crossed footgun or Christie if the raised leg is stretched by passing behind the skate leaned on the ground with which the movement takes place.
Some skaters perform footgun first sitting on both skates maintaining their arms forward, then lifting one skate and stretch the leg so they lean on the ground only on the other skate. On the contrary, other skaters try to remain only on one skate when they are still erecting before squatting.
I prefer this second way for two reasons: first, the trick can be performed with better style, secondly, it’s possible to study gradually the trick because you must take some middle positions with growing difficult. So in the following part, I will explain this second way to perform footgun. First of all, you must hold yourself upright and begin to lift one leg without bending your back forward. Then you stretch out your arm and take with your hand the first wheel of the skate lifted. Practically the leg that is lifted approaches the arm but not vice versa. The best solution may be to stretch both arms forward in horizontal or even in a lightly inclined position and then to lift one leg until the first wheel of the skate touches the palm of the hand which grabs it. The arms stretched forward are a good counterbalance so you do not fall backward when you lift your leg. Of course, when you keep hold of the skate by your hand, your back is a little forward, but you must try to maintain it straight, rather than curve, even if it is slightly bent. Then you begin to squat on the skate leaned on the ground. While squatting, the weight of your body must concentrate on the rear of the skate, so your back always keeps straight also if it gradually inclines. When you learn to take footgun position, you can try to run across the cones in that position, for example, a dozen of cones, at the beginning placed at 150cm distance, then you can reduce the distance to 120, 100cm until 80 cm. Footgun learning can be quicker if you perform the trick without skates before. So I suggest the stretching exercises shown in the next videos.

To control better the position it is good to learn to pass through the cones without grabbing the skate with the hand, but keeping the two arms parallel to the floor, like you can see in the next video:

CAFFETTIERA NON GRABBATA.wmv