1000 as further described below.

The three-dimensional multilayer flexile stack 1000 includes a third slidable layer set 300. The third slidable layer set 300 includes a set of one or more layers that have a plurality of faces. The third slidable layer set 300 is moveably embedded within the second intermediate layer set 200. The third slidable layer set 300 is further securely affixed to the second intermediate layer set 200 only along a distal terminus of the second intermediate layer set 200. The third slidable layer set 300 is securely affixed to the second intermediate layer set 200 via a second securing element 125. The second securing element 125 may include one or more of the securing elements disclosed above with respect to the first securing element 115. The second securing element 125 includes removable attachment securing elements. By removable attachment of the second securing element 125, the third slidable layer set 300 may be replaced by a user with another third slidable layer set 300, such that the another third slidable layer set 300 has different communicable information 315 upon at least one face, as further described below. In this way, a user may change from one activity to another as explained in the various methods of use below.

A third securing elements 135 are depicted in FIG. 1E. The third securing elements 135 may be attachment mechanisms such as fastening elements. Fastening elements may include snap buttons, press buttons, press studs, press fasteners, dome fasteners, poppers, and similar mechanical attachment mechanisms. In operation the third securing elements 135 may be mated to removably connect pairs of opposing lobes of each layer of the first base layer set 100, 110 having arcuate contours. Therefore when opposing lobes of each layer of the first base layer set 100, 110 having arcuate contours of the three-dimensional multilayer flexile stack 1000, 2000, 3000, 4000 and 5000 are extensively flexed, the third securing elements 135 may be mated such that the entire three-dimensional multilayer flexile stack 1000, 2000, 3000, 4000 and 5000 forms a looped configuration as best shown in FIG. 3D and partially shown in FIG. 1E. As such when the entire three-dimensional multilayer flexile stack 1000, 2000, 3000, 4000 and 5000 forms a looped configuration, the three-dimensional multilayer flexile stack 1000, 2000, 3000, 4000 and 5000 may be wrapped around a limb of a user, such as the arm of a teacher or the arm of a student. Likewise, the looped configuration may be used for attachment to a bag or luggage for case of transport. In this position, numerous methods of use of the three-dimensional multilayer flexile stacks 1000, 2000, 3000, 4000 and 5000 are also available as further described below.

Again as shown in FIGS. 1A-1E, a manipulable handle 305 is attached to a proximal terminus of the third slidable layer set 300. The manipulable handle 305 that is attached to the proximal terminus of the third slidable layer set 300 may be manipulated by a user to allow the user to slidably move the third slidable layer set 300. Specifically, the third slidable layer set 300 is reversibly extensible in two directions along the first dimension, for example up and down, forward and backward, or in and out. Manipulation of the manipulable handle 305 by a user in a first direction thus causes the third slidable layer set 300 to move in the first direction to a maximally extended position, for example from FIG. 1A to FIG. 1B to FIG. 1C to FIG. 1D. Manipulation of the manipulable handle 305 by a user in a second direction thus causes the third slidable layer set 300 to move in the second direction to a maximally reverse extended position, for example from FIG. 1D to FIG. 1C to FIG. 1B to FIG. 1A.

As shown for example in FIGS. 1B-1E, the third slidable layer set 300 further contains communicable information 315 upon at least one face of at least one layer within said third slidable layer set 300. In the figures, communicable information 315 is represented by letters of the Greek alphabet such as α, β, γ, δ, etc. The communicable information 315 that is represented by Greek alphabet letters comprises at least one sequence of indicia. This indicia may include alphabetic, numeric, alphanumeric, or pictographic indicia. Moreover, the indicia may also or alternatively include reference indications with respect to a sacred book chapter and verse markers, for example Biblical book demarcations. The indica may also or alternatively include various color spectrum sequences, geometric shape sequences, character representations of fictional or non-fictional characters. The indica may also or alternatively include various character or marker sequences from a non-English language alphabet, an American sign language sequence, an international sign language sequence, or a musical scale sequence.

The communicable information 315 thus contained within the communicable information three-dimensional multilayer flexile stack 1000, 2000, 3000, 4000 and 5000 may be used to facilitate various activities between one or more users of the three-dimensional multilayer flexile stack 1000, 2000, 3000, 4000 and 5000. These activities may include methods such as teaching methods and/or learning methods. For example, the three-dimensional multilayer flexile stack 1000, 2000, 3000, 4000 and 5000 may be used to teach the English alphabet to children or to adults for whom English is a second or third language. Similarly, the three-dimensional multilayer flexile stack 1000, 2000, 3000, 4000 and 5000 may be used in support of a study method for those learning the English alphabet. As will be apparent to those of ordinary skill in the art, the three-dimensional multilayer flexile stack 1000, 2000, 3000, 4000 and 5000 may also be used to facilitate teaching methods and/or learning methods where the subject matter or topics include numeration, pictographic sequences such as in stories, memorization or study of sacred book chapter and/or verse sequences, primary or secondary color spectrum sequences, geometric shape types and sequences, and/or character representations of fictional or non-fictional characters, such as lists of presidents, inventors, or fairy tale actors.

Moreover, the three-dimensional multilayer flexile stack 1000, 2000, 3000, 4000 and 5000 may further be used to facilitate teaching methods and/or learning methods where the subject matter includes teaching or learning of various character or marker sequences from any non-English language alphabet, for example a Chinese or a Hebrew alphabet character sequence, and/or an American sign language character sequence, and/or an international sign language character sequence, or for teaching or learning of musical scale sequences. As will be readily understood by those of ordinary skill in the pedagogical and andragogical arts, many other applications and objectives many be attained using the three-dimensional multilayer flexile stacks 1000, 2000, 3000, 4000 and 5000 for assessments, for brainstorming activities, or for use in remote locations without the need for electricity or access to the varieties of electromagnetic wave connectivity, to name a few.

Yet, the three-dimensional multilayer flexile stacks 1000, 2000, 3000, 4000 and 5000 is by no means limited to the arenas of pedagogy or andragogy. Exemplary methods of applying the three-dimensional multilayer flexile stacks 1000, 2000, 3000, 4000 and 5000 include varieties of therapies or therapeutic methods, whether for counseling, within the healing arts, or for motivational activities. Limited only by the imagination of the users, educators and/or parents may further employ the present three-dimensional multilayer flexile stacks 1000, 2000, 3000, 4000 and 5000 in disciplinary methods, amusement methods, gaming methods, play methods or therapies, entertainment methods or similar activities. Therefore, it will be apparent that the three-dimensional multilayer flexile stacks 1000, 2000, 3000, 4000 and 5000 have broad and diverse applications and adaptability.

Returning now to FIGS. 1A-IE, manipulation of the manipulable handle 305 by a user in a first direction causes the communicable information 315 contained on at least one face of at least one layer within the third slidable layer set 300 to be revealed for communication with at least one user as the manipulable handle 305 is extended along a first dimension, as shown for example in FIG. 1C.

Similarly, manipulation of the manipulable handle 305 by a user in a second direction causes the communicable information 315 contained on at least one face of at least one layer within said third slidable layer set 300 to be concealed from communication with at least one user as the manipulable handle 305 is reversibly extended along the first dimension, as shown for example in FIG. 1B.

Therefore, in operation, manipulation of the manipulable handle 305 by a user to extend or reversibly extend the communicable information 315 contained on at least one face of at least one layer within the third slidable layer set 300 along respective first and second directions further enables the three-dimensional multilayer flexile stacks 1000, 2000, 3000, 4000 and 5000 to facilitate teaching methods and/or learning methods, memorization, therapies, disciplinary methods, amusement, gaming, singular or multi-user play, or imaginative entertainments.

Moreover, the third slidable layer set 300 may be constructed to contain communicable information 315 upon at least two obverse faces of at least one layer within said third slidable layer set 300. In this embodiment, upon extending the manipulable handle 305 along the first dimension, a first face of at least one layer within the third slidable layer set 300 is revealed for communication with a first user and a second face of the at least one layer within the third slidable layer set 300 is simultaneously revealed for communication with a second user. The structure of this embodiment is particularly useful for multi-user play, therapist/client interactions, multi-user gaming, or any other method of use involving more than one user. Additionally, this structure is also advantageous for use cases in which a single user may switch between two roles. As one example during a self-testing session, a single user may begin by acting as an instructor by revealing the communicable information to be memorized but later conceal the communicable information to act as a student during recitation of the memorized communicable information.

Turning now to the FIGS. 2A and 2F, depicted therein are three-dimensional multilayer flexile stacks 1000 in motion. As explained above for FIGS. 1A-1E, a manipulable handle 305 is attached to the third slidable layer set 300 for reversibly extensible manipulation by users to thus allow users to slidably move the third slidable layer set 300.

Beginning then in FIG. 2A, a user manipulates the manipulable handle 305 and thus extends the third slidable layer set 300 along at least a first dimension, for example a Y axis dimension. Since, as described above, the first securing element 115 is attached such that the first base layer set 100, 110 along with the second intermediate layer set 200 are cooperatively displaceable, at least in part, and as was further described the third slidable layer set 300 is also securely affixed to the second intermediate layer set 200 via a second securing element 125, therefore extending of the third slidable layer set 300 causes cooperative flexion of the first base layer set 100, 110 along with the second intermediate layer set 200 as depicted in FIG. 1B at 205 and in FIG. 1C at 215.

Specifically, depicted in FIG. 2A and FIG. 2F are exemplary motion vectors of the three-dimensional multilayer flexile stacks 1000, including representative cooperative flexions. As defined and shown therein, Ū_yrepresents a translational displacement vector along a Y axis direction, and Ū_xrepresents a translational displacement vector along an X axis direction, and Ū_zrepresents a translational displacement vector along a Z axis direction. Therefore, a three-dimensional net translational displacement vector Ū_xyzmay be defined as the vector summation of each of the three dimensions of translational vector displacements. Thus, Ū_xyz=Ū_x+Ū_y+Ū_z=the three-dimensional net displacement vector.

Moreover, in addition to translational displacement, a flexural motion may further include rotational displacement components about each axis. Accordingly, a rotational displacement matrix R(ϕ, θ, ψ) may be defined, wherein Rx(θ) represents rotation matrix about the X axis, Ry(θ) represents rotation matrix about the Y axis, and Rz(ψ) represents rotation matrix about the Z axis. The flexural motion of the three-dimensional multilayer flexile stacks 1000 thereby comprises both translational displacement Ū_xyzand rotational displacement matrix R(ϕ, θ, ψ).

FIGS. 2A, 2F shows exemplary motions, flexions, and cooperative displacements of the first base layer sets 100, 110, the second intermediate layer sets 200, and the third slidable layer sets 300 of the three-dimensional multilayer flexile stacks 1000 at a partial extension in relation to the three-dimensional net translational displacement vector Ū_xyz, and a rotational displacement matrix R(ϕ, θ, ψ).

As will be readily understood by those of ordinary skill in the art, the three-dimensional multilayer flexile stacks 1000 have at least three degrees of translational freedom and three degrees of rotational freedom during flexure. The three-dimensional multilayer flexile stacks