Abstract:
A polygonal device for teaching students who prefer kinesthetic learning methods is presented in which the polygonal device can represent two-dimensional polygons of varying shapes and sizes. One or more of the sides, or legs, of the polygonal device are extendable, and the angles of the polygonal device may be manipulated to a desired angle. The devices presented include, but are not limited to, triangles, quadrilaterals, parallelograms, rectangles, squares, trapezoids, and kites. In each of these devices, the legs of the device are non-detachable, i.e. the device does not come apart during normal manipulation and operation.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a continuation of U.S. patent application Ser. No. 12/862,306, filed Aug. 24, 2010, entitled “POLYGONAL DEVICE FOR KINESTHETIC LEARNERS”, now allowed, which claims priority to U.S. Provisional Patent Application Ser. No. 61/236,768, which was filed on Aug. 25, 2009, by Shannon Driskell, entitled “SHAPE SHIFTERS”, the disclosures of which are incorporated herein by reference. 
     
    
     BACKGROUND OF THE DISCLOSURE 
       [0002]    Students who learn kinesthetically may have a hard time learning the abstract ideas behind two-dimensional geometry. Traditionally, sets of detachable sides and angles have been used to teach these kinesthetic learners. The traditional approach may allow a student to manipulate the sides and angles of a polygon, however, it does not allow the student to pick up the finished polygon and have the polygon remain intact. Also, the traditional approach does not allow a teacher to manipulate the polygonal device real-time in front of an entire class and then pass around the created polygon so the students may see the polygon up close, because the detachable sides may fall apart. Thus there is a continuing need for a device to aid in the education of geometry to kinesthetic learners. 
       DEFINITIONS 
       [0003]    For clarity, several of the terms, which are used throughout the written description and the claims, are defined below: 
         [0004]    “Détente structure” is defined as a pairing of a stopper or stub and a hole to secure an extendable leg, constraint, or hinged angle. In reference to the détente structure, a hole may be merely a depression or groove that does not extend the entire way through an object. 
         [0005]    “Device” is defined as apparatus. 
         [0006]    “Diagonal” is defined as an imaginary line connecting opposite corners of a quadrilateral. 
         [0007]    “Extendable” and variants thereof are defined as extendable and contractible, and thus able to be manipulated by a user. 
         [0008]    “Fixed angle” is defined as an angle that cannot be manipulated. 
         [0009]    “Leg” is defined as a side of a polygonal device. A leg may be extendable (able to be manipulated) or non-extendable (fixed). 
         [0010]    “Lockable angle” and variants thereof are defined as angles that are hinged and able to be manipulated by a user, unless a locking mechanism is engaged, in which case, the angles cannot be manipulated by the user until the locking mechanism is released. 
         [0011]    “Non-detachable” and variants thereof are defined as not intended to be taken apart. 
         [0012]    “Polygon” and variants thereof are defined as a two-dimensional shape alternating sides and angles which form a closed shape. A polygon has an equal number of sides and angles. A “polygonal device” is an apparatus that represents a polygon. 
       SUMMARY OF THE DISCLOSURE 
       [0013]    The present disclosure provides a polygonal device that may be employed to teach kinesthetic learners geometry, specifically two-dimensional geometric polygonal shapes. The polygonal device has extendable legs, which are non-detachable from each other, and angles. Certain embodiments have hinged angles to allow a user to manipulate the degree of the angles. In some embodiments, the extendable legs extend telescopically, while in other embodiments, the extendable legs extend via a détente structure, and in further embodiments, the extendable legs extend via a sliding structure. Several embodiments include an angle indicator to provide the angle measurement between two adjacent legs. 
         [0014]    In certain embodiments, a constraint is utilized to force the polygonal device to remain in a certain shape while being manipulated by an associated user. These constraints include, but are not limited to, a square constraint, a kite constraint, and a parallel constraint. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    One or more exemplary embodiments are set forth in the following detailed description and the drawings, in which: 
           [0016]      FIG. 1  is a schematic diagram illustrating an exemplary polygonal device for kinesthetic learners where the polygonal shape is a triangle with a détente leg structure, including a detailed view of an angle; 
           [0017]      FIG. 2  is a schematic diagram illustrating an exemplary polygonal device for kinesthetic learners where the polygonal shape is a square with a détente leg structure; 
           [0018]      FIG. 3A  is a schematic diagram illustrating an exemplary polygonal device for kinesthetic learners where the polygonal shape is a rectangle with a détente leg structure, including a detailed view of an angle; 
           [0019]      FIG. 3B  is a schematic diagram illustrating the locking structure of an angle; 
           [0020]      FIG. 4  is a schematic diagram illustrating an exemplary polygonal device for kinesthetic learners where the polygonal shape is a parallelogram having a détente leg structure; 
           [0021]      FIG. 5  is a schematic diagram illustrating an exemplary polygonal device for kinesthetic learners where the polygonal shape is an octagon, including a telescopic leg structure; 
           [0022]      FIG. 6A  is a schematic diagram illustrating a two-piece détente leg structure; 
           [0023]      FIG. 6B  is a schematic diagram illustrating a three-piece détente leg structure; 
           [0024]      FIG. 7  is an isometric view illustrating an exemplary polygonal device for kinesthetic learners with a sliding leg structure, including a constraint with a sliding structure; 
           [0025]      FIG. 8A  is an isometric schematic diagram illustrating a sliding leg structure; 
           [0026]      FIG. 8B  is a side-view schematic diagram illustrating a sliding leg structure; 
           [0027]      FIG. 9A  is an isometric schematic diagram illustrating a stacked-sliding leg structure; 
           [0028]      FIG. 9B  is a side-view schematic diagram illustrating a stacked sliding leg structure; 
           [0029]      FIG. 10A  is an isometric view of an angle-to-angle angle constraint with variable length; 
           [0030]      FIG. 10B  is a detailed view of an angle with an angle-to-angle angle constraint; 
           [0031]      FIG. 10C  is a side view of the angle-to-angle angle constraint with variable length; 
           [0032]      FIG. 10D  is an isometric view of a pair of single angle constraints; 
           [0033]      FIG. 11A  is an isometric view of a kite constraint; 
           [0034]      FIG. 11B  is a detailed view of an angle and the kite constraint; 
           [0035]      FIG. 12A  is a side view of a pegged section of the kite constraint; 
           [0036]      FIG. 12B  is a side view of a holed section of the kite constraint; 
           [0037]      FIG. 13A  is a schematic diagram illustrating an exemplary polygonal device for kinesthetic learners where the polygonal shape is a square having a sliding leg structure; 
           [0038]      FIG. 13B  is a schematic diagram illustrating an exemplary polygonal device for kinesthetic learners where the polygonal shape is a rectangle having a sliding leg structure; 
           [0039]      FIG. 14A  is a schematic diagram illustrating an exemplary polygonal device for kinesthetic learners where the polygonal shape is a trapezoid with at least one pair of parallel sides having a sliding leg structure; 
           [0040]      FIG. 14B  is a schematic diagram illustrating an exemplary polygonal device for kinesthetic learners where the polygonal shape is a trapezoid with only one pair of parallel sides having a sliding leg structure; 
           [0041]      FIG. 15A  is a schematic diagram illustrating an exemplary polygonal device for kinesthetic learners where the polygonal shape is a kite having a sliding leg structure; and 
           [0042]      FIG. 15B  is a schematic diagram illustrating an exemplary polygonal device for kinesthetic learners where the polygonal shape is a triangle having a sliding leg structure. 
       
    
    
     DETAILED DESCRIPTION 
       [0043]    Referring now to the drawings, wherein various features are not necessarily drawn to scale, the present disclosure relates to educating kinesthetic learners and more particularly to a device that aids kinesthetic learners in the understanding of two-dimensional polygons in geometry. The exemplary devices described herein can also be used in other areas and are not limited to the aforementioned application of education. 
         [0044]    With continued reference to the drawings, each of the polygonal devices has several legs and an equal amount of angles. Each polygonal device illustrated in the drawings has identical leg structures for each of the legs. However, the legs are not required to have identical leg structures. Further, every leg of the polygonal devices is shown to be extendable. However, only one of the legs needs to be extendable, one or more of the legs may be of fixed length. In some embodiments, the legs are marked with a length indicator to show the length of the leg. 
         [0045]    Each device represents a polygonal shape, and thus must be closed and alternate angles and legs. Some embodiments include a constraint which limits the user&#39;s ability to manipulate the device. For example, a device with a square constraint limits the user from manipulating the device into anything but a square. Similarly, a kite constraint limits the user from manipulating the device into anything but a kite. Other constraints besides square and kite are discussed in greater detail in reference to the figures below. 
         [0046]      FIG. 1  illustrates an embodiment of the polygonal device  100  for kinesthetic learners. In this embodiment, the polygonal device  100  is a triangle and comprises three extendable legs  120   a,    120   b,    120   c  (collectively  120 ), and three hinged angles  116   a,    116   b,    116   c.  The extendable legs  120  each include two sections, a first section  102  and a second section  104 . The first section  102  fits into the second section  104  and creates a détente leg structure. The first section  102  includes a stopper  106  and the second section  104  includes a plurality of holes  118 . The structure and operation of the détente leg structure is described in greater detail below in reference to  FIGS. 6A and 6B . In certain embodiments, the extendable legs  120  may be extended through a telescopic structure, which is described in greater detail in reference to  FIG. 5 . In other embodiments, the extendable legs may be extended through a sliding structure, which is discussed in greater detail in reference to  FIGS. 8A ,  8 B,  9 A, and  9 B below. The triangular device  100  with sliding leg structures is described in greater detail in reference to  FIG. 15B . Further, the extendable legs  120  may have any number of sections. Each leg  120  does not need to have the same number of sections as the other legs  120  in the device  100 . 
         [0047]    In this embodiment, the angles  116  of the triangular device  100  include a hinge which allows the degree of the angle  116  to be manipulated by the user. Some embodiments include an angle indicator  114 . The angle indicator  114  is a pointer and a face-plate  108  that indicates angles around a circle. The face-plate  108  may mark angles  116  for an entire circle or just half of the circle and back again. The markings may be marked directly on the device  100  itself, instead of using a face-plate. Further, the markings may be in degrees, radians, or another measurement for angles. The illustrated example shows a face-plate  108  marked for half a circle and back again in degrees. To determine the degree of the angle  116 , the user identifies the number on the face-plate  108  associated with the second leg  112  and subtracts the number on the face-plate  108  associated with the first leg  110 . The first leg  110  can be fixed to zero degrees to make this subtraction process much easier for the user. 
         [0048]    Additional embodiments include a locking mechanism for the hinged angles  116 , which is described in greater detail in reference to  FIG. 3B . In other embodiments, one or more of the angles  116  are fixed, i.e. not hinged. In all embodiments, the angles  116  are non-detachable from the legs  120 . 
         [0049]      FIG. 2  illustrates an exemplary polygonal device  200  for kinesthetic learners where the polygonal shape is a square. The polygonal device  200  comprises four extendable legs  120 , four fixed angles  116 , and a square constraint  202 . 
         [0050]    In this embodiment, the extendable legs  120  each include two sections, a first section  102  and a second section  104 . The first section  102  fits into the section  104 . A détente structure is formed from a stopper  106  attached to the end of the first section  102  and a plurality of holes  118  of the second section  104 . The détente structure is described in greater detail in reference to  FIGS. 6A and 6B . As with the triangular device  100  ( FIG. 1 ), the legs may also have any number of sections, a sliding structure, telescopic structure, détente structure, or a combination thereof. 
         [0051]    In this embodiment, the angles  116  are fixed at ninety degrees. The square constraint  202  has a first section  204  and a second section  206 . The first section  204  of the square constraint  202  fits into the second section  206  of the square constraint  202 . In the illustrated embodiment, the square constraint  202  is telescopically extendable; however, the square constraint  202  may extend through a détente structure or sliding structure. If the legs  120  and the square constraint  202  are both extendable through a détente structure, the spacing of the holes (not shown) on the square constraint  202  must be equal to the spacing of the holes  118  on the legs  120  multiplied by the square root of two. 
         [0052]    With further reference to  FIG. 2 , the square constraint  202  couples a first angle  116   a  and its diagonally-opposite angle  116   c.  With the angle of the square constraint  202  fixed at forty-five degrees in reference to the leg  120   a,  all the angles  116  of the square device  200  are fixed at ninety degrees. Therefore, when the user manipulates the length of a leg  120   a,  then all of the other legs  120   b,    120   c,    120   d  must change their length equal to the manipulated length of  120   a,  keeping all of the sides the same length. 
         [0053]      FIG. 3A  illustrates a quadrilateral device  300  with four legs  120  and four angles  116 . In this embodiment, the extendable legs  120  each include two sections, a first section  102  and a second section  104 . The first section  102  fits into the section  104 . A détente structure is formed from a stopper  106  attached to the end of the first section  102  and a plurality of holes  118  of the second section  104 . The détente structure is described in greater detail in reference to  FIGS. 6A and 6B . As with the triangular device  100  ( FIG. 1 ), the legs may also have any number of sections, a sliding structure, telescopic structure, détente structure, or a combination thereof. 
         [0054]    In some embodiments one or more of the angles  116  of the quadrilateral device  300  are hinged. In other embodiments, one or more of the hinged angles  116  are lockable. Some embodiments include an angle indicator  114 . The angle indicator  114  is a pointer and a face-plate  108  that indicates angles around a circle. The face-plate  108  may mark angles for an entire circle or just half of the circle and back again. The markings may be in degrees, radians, or another measurement for angles. The illustrated example shows a faceplate  108  marked for half a circle and back again in degrees. To determine the degree of the angle, the user subtracts the number on the face-plate  108  associated with the second leg  112  and subtracts the number on the face-plate  108  associated with the first leg  110 . The first leg  110  can be fixed to zero degrees to make this subtraction process much easier for the user. 
         [0055]    In the illustrated example, the user has locked the four angles  116  at ninety degrees, making the quadrilateral device  300  into a rectangle. With the angles  116  locked at ninety degrees, opposite sides  120   a,    120   c  and  120   b,    120   d  of the device  300  must have equal lengths forming the rectangle. 
         [0056]      FIG. 3B  illustrates how to lock the angles  116 . The angle indicator  114  has a movable portion, which may be pressed by the user. When the indicator is up (in the released position) the angle  116  is able to be manipulated by the user. When the indicator is pressed down (in the locked position) then the angle  116  is not able to be manipulated by the user. The angle may be prevented by moving through a ball bearing in a depression, pure friction, a spring mechanism, or any other locking method. When the user wishes to manipulate a locked angle, the user presses up on the angle indicator  114  and releases the angle  116 . 
         [0057]      FIG. 4  illustrates a parallelogram device  400  with four legs  120 , four angles  116 , and two parallel constraints  420 ,  440 . In this embodiment, the extendable legs  120  each include two sections, a first section  102  and a second section  104 . As with the triangular device  100  ( FIG. 1 ), the legs may also have any number of sections, a sliding structure, telescopic structure, détente structure, or a combination thereof 
         [0058]    The angles  116  may be fixed, be hinged, have an angle indicator, be lockable, or any rational combination thereof. 
         [0059]    The parallel constraints  420 ,  440  each include a first section  404   a,    404   b  and a second section  402   a,    402   b  and can extend in the same ways as a leg  120 : via a sliding structure, a telescope structure, a détente structure, or any combination thereof. The parallel constraints  420 ,  440  may have any number of sections. Further, the parallel constraints  420 ,  440  include a cuff  406  at each end. The cuffs  406  wrap around a leg  120  at each end of the parallel constraint  420 ,  440 . The parallel constraints  420 ,  440  may move parallel with the legs  120  to which they are attached because the cuffs  406  only wrap around the legs  120 , they are not fixed at a specific location on the leg  120 . The cuff  406  ensures that the angle between the parallel constraint  420 ,  440  and the leg  120  with which it is connected remain at a right angle. In this manner, opposite legs  120   a  and  120   c,    120   b  and  120   d  remain at right angles with their respective parallel constraints  420 ,  440  respectively. Therefore, opposite legs  120   a  and  120   c,    120   b  and  120   d  remain parallel to each other. 
         [0060]      FIG. 5  illustrates a polygonal device  500  with eight legs  120  and eight angles  116 . The legs  120  include a first section  502 , a second section,  504 , and a third section  506 . The first section  502  fits inside of the second section  504  and the second section fits inside of the third section  506 . The leg  120  may then be manipulated by the user (expanded and contracted). This leg structure is a telescopic leg structure. When not being manipulated by the user, the legs  120  keep their length through friction. Although illustrated with three sections, any number of sections may be used. In some embodiments, the legs  120  have a sliding structure, détente structure, telescopic structure, or any combination thereof. 
         [0061]    The angles  116  may be fixed, be hinged, have an angle indicator, be lockable, or any rational combination thereof. In other embodiments, the polygonal device  500  may be a pentagon, heptagon, octagon (as shown), nonagon, decagon, etc. In several embodiments, the angles  116  are fixed at an angle equal to each other to create a regular polygon  500 . 
         [0062]      FIG. 6A  illustrates the détente leg structure with two sections and is not drawn to scale. The leg  120  includes two sections, a first section  616  and a second section  614 . The first section  616  includes a leg portion  102 , a stopper  106 , an angle portion  116 , and an end  602 . The second section  614  includes a leg portion  104 , a plurality of holes  118 , an angle portion  116 , and an opening  600 . 
         [0063]    The end  602  of the first section  616  fits into the opening  600  of the second section  614 . The opening  600  should be large enough to accommodate the edge  602  and the stopper  106  inserted at an angle to allow the user to disengage the stopper  106  from one of the holes  118   a  and move the stopper  106  to another hole  118   a.  Further, the leg portion  102  of the first section  616  should be long enough so the stopper  106  can reach the last hole  118   a  of the second section  614 . 
         [0064]    When the stopper  106  is engaged in a hole  118   a,  then the leg  120  is prevented from moving without user manipulation. The holes  118   a  may extend entirely through the leg portion  104  of the second section  614  as shown, or may extend only partially through, wherein the hole  118  starts from inside the second section  614 , but does not extend to the surface of the second section  614 . When engaged, the first section  616  is non-detachably coupled to the second section  614 . 
         [0065]      FIG. 6B  illustrates the détente leg structure with three sections. The leg  120  includes three sections, a first section  622 , a second section  620 , and a third section  622 . The first section  622  includes a leg portion  102 , a stopper  106 , an angle portion  116 , and an end  602 . The second section  620  includes holes  118   c,  an edge  604 , an opening  606 , a stopper  608 , and a leg portion  610 . The third section  618  includes a leg portion, an angle portion  116 , holes  118   b,  and an opening  600 . 
         [0066]    The end  602  of the first section  622  fits into the opening  606  of the second section  620 . The opening  606  should be large enough to accommodate the edge  602  and the stopper  106  inserted at an angle to allow the user to disengage the stopper  106  from one of the holes  118   c  and move the stopper  106  to another hole  118   c.  Further, the leg portion  102  of the first section  622  should be long enough so the stopper  106  can reach the last hole  118   c  of the second section  618 . 
         [0067]    Similarly, the end  604  of the second section  620  fits into the opening  600  of the third section  618 . The opening  600  should be large enough to accommodate the edge  604  and the stopper  608  inserted at an angle to allow the user to disengage the stopper  608  from one of the holes  118   b  and move the stopper  608  to another hole  118   b.  One skilled in the art should know how to extend this structure to larger numbers of sections. 
         [0068]    The functions of the stoppers  106 ,  608  and the holes  118   b,    118   c  are identical to the functions of the stopper  106  and holes  118   a  of  FIG. 6A . The holes  118   b,    118   c  also may extend entirely or partially through their respective sections  620 ,  618 . Again, the sections  618 ,  620 ,  622  are non-detachably coupled when properly engaged. 
         [0069]      FIG. 7  illustrates the polygonal device  700  with sliding legs  800  and a sliding constraint  1000 . The legs  800  are described in greater detail with reference to  FIGS. 8A ,  8 B,  9 A, and  9 B. The sliding leg structure of three or more sections has several subtypes including, but not limited to, staggered, ascending, and a combination thereof. A sliding leg structure with only two sections has several subtypes: the first section on top, the first section on bottom, or the second section inside the first section and functioning like a razor knife. 
         [0070]      FIGS. 8A and 8B  describe a staggered sliding leg structure, and  FIGS. 9A and 9B  describe an ascending sliding leg structure. The constraint  1000  is described in greater detail with reference to  FIGS. 10A ,  10 B,  10 C,  10 D,  11 A,  11 B,  12 A, and  12 B. The sliding leg structures shown in the figures all illustrate a leg with three sections; however, the sliding leg structure may have two or more sections. 
         [0071]      FIGS. 8A and 8B  illustrate a leg  800   a  with a staggered sliding structure. The illustrated staggered sliding leg structure includes a first section  802 , a second section  826 , and a third section  834 . The first section includes an angle hole  804 , a leg portion  806 , an angle constraint hole  808 , and a constraint notch  812  flanked by two guards  810  and  814 . The second section  826  includes a first section angle constraint notch  818 , a first section sliding hole  820 , a leg portion  822 , a constraint hole  824 , a third section sliding hole  828 , and a third section angle constraint notch  832 . The third section  834  includes a leg portion  836 ,  846  which is thicker than the leg portion  806  of the first section  802 , an angle constraint anchor  838 , an angle insert  840 , an angle platform  842 , an angle constraint hole  844 , and a constraint notch  850  flanked by two guards  848 ,  852 . 
         [0072]    The leg sections  802 ,  826 ,  834  are assembled into a leg  800  with the use of a first section coupler  816  and a third section coupler  830 . The first section coupler  816  has a body  854  and a head  856 . The body  854  of the first section coupler  816  is inserted through the first section sliding hole  820  of the second section  826  and fixed to the leg portion  806  of the first section  802  such that the first section  802  is non-detachably coupled to the second section  826 . The head  856  prevents the second section  826  from being detached from the first section  802 . 
         [0073]    Even though the first section  802  and the second section  826  are coupled, the first section  802  is still allowed to slide in a direction parallel to the second section  826  using the first section coupler  816  as a guide. The non-circular shape of the body  854  of the first section coupler  816  prevents the first section  802  from rotating in a plane parallel to the second section  826 . Thus, the leg  800  is extendable by sliding the first section  802  relative to the section  826  along the path created by the first section sliding hole  820 . 
         [0074]    The third section coupler  830  has a longer body  858  than the first section coupler  816  and a head  860 . The third section coupling  830  couples the third section  834  to the second section  826  in a way similar to the first section coupler  816 . 
         [0075]    When the leg  800  is fully contracted, i.e. the shortest length possible, the constraint notch  812  of the first section  802  and the constraint notch  850  of the third section  834  create a hole under the constraint hole  824  of the second section  826 . The constraint hole  824  is present to accommodate a sliding parallel constraint and will be discussed in greater detail in reference to  FIG. 14A . The angle constraint holes  808 ,  844  are discussed in greater detail with reference to  FIG. 10B . 
         [0076]    With continued reference to  FIGS. 8A and 8B , once a leg  800  is created, several legs  800  may be coupled together to create a polygonal device for kinesthetic learners. Angles are created by non-detachably coupling the first section  802  to the third section  834 . The non-detachable coupling methods used include, but are not limited to, snapping into place and the use of magnetic strips. The angle insert  840  of the third section  834  of a first leg  800  is fitted into the angle hole  804  of the first section  802  of a second leg  800 . The created angle is able to be manipulated by the user. The first section  802  rests on top of the angle platform  842  of the third section  834  creating an angle with a thickness of the sum of the thickness of the first section  802  and the thickness of the angle platform  842 . 
         [0077]    This thickness is the reason that the leg portion  836 ,  846  of the third section  834  is thicker than the thickness of the angle platform  824  alone. The extra thickness allows the angle platform  842  to be lower in space than the plane created by the second section  826  by a thickness substantially similar to the thickness of the first section  802 . The leg portions  806 ,  836 ,  846  of the first and third sections  802 ,  834  are both just below the plane created by the second section  826 . Therefore, the first section  802  is higher in space than the angle platform  842 . When several legs  800  are coupled in the manner above to create a polygonal device, all of the second sections  826  of the legs  800  with a staggered sliding structure are in the same plane. 
         [0078]    Referring now to  FIGS. 9A and 9B  which illustrate an ascending sliding leg structure, a leg  800  is shown with three sections. This ascending sliding leg structure is similar to the staggered leg structure, except the third section  834  is above the second section  826  instead of below it. Descending in one direction is ascending in the other direction, so the ascending leg structure also means a structure where the first section  802  is above the second section  826 , and the section  826  is above the third section  834 . When using a sliding leg structure, the sliding type may be staggered, ascending, or a combination thereof 
         [0079]      FIGS. 10A and 10C  illustrate an angle constraint  1000  with a sliding structure. The angle constraint includes a first section  1002 , a second section  1018 , and a third section  1030 . The first section  1002  includes an angle constraint coupling  1004 , an angle constraint stopper  1006  and a constraint portion  1008 . The second section  1018  includes a first section sliding hole  1016 , a constraint body  1020 , and a third section sliding hole  1026 . The third section  1030  includes a constraint portion  1032 , an angle constraint stopper  1034 , and an angle constraint coupling  1036 . 
         [0080]    The constraint  1000  also includes a first section coupler  1010  with a head  1012  and body  1014 , and a third section coupler  1022  with a head  1024  and a body  1026 . The first section coupler  1010  body  1014  fits through the first section sliding hole  1016  and non-detachably attaches to the constraint portion  1008  of the first section  1002 . The first section  1002  is free to slide in a direction parallel to the second section  1018 , but the first section  1002  will not rotate in a plane parallel to the second section  1018  because the first section coupler  1010  is not circular. 
         [0081]    The third section coupler  1022  body  1026  fits through the third section sliding hole  1028  and non-detachably attaches to the constraint portion  1032  of the third section  1030 . The third section  1030  is free to slide in a direction parallel to the second section  1018 , but the third section  1030  will not rotate in a plane parallel to the second section  1018  because the third section coupler  1022  is not circular. 
         [0082]    Not shown is a parallel constraint which is identical to the angle constraint  1000 , except the parallel constraint does not include the angle constraint stoppers  1006 ,  1034 . 
         [0083]    With continued reference to  FIGS. 10A and 10C  and with reference to  FIG. 10B  which illustrates an angle, the angle constraint  1000  attaches to the angle of the device. The angle constraint coupling  1004  includes a body  1042  and a head  1044 . The body  1042  fits through the angle constraint anchor  838  and attaches to the first section  1002  of the constraint  1000 . The angle constraint stopper  1006  fits into a hole created by the alignment of the angle constraint holes  808  ( FIG. 8A ),  844 . When the angle constraint holes  838  ( FIG. 8A ),  844  are aligned, the angle created is ninety degrees, i.e. a right angle. The angle constraint  1000  maintains a right angle. The angle constraint  1000  is also called a square constraint. 
         [0084]    The third section  1030  of the angle constraint  1000  attaches to an angle diagonal from the angle attached to the first section  1002 . The use of this angle constraint  1000  in a quadrilateral device creates a square device. The angles are constrained to right angles and the diagonal created maintains the legs to equal lengths. 
         [0085]      FIG. 10D  illustrates a single angle constraint  1052 . The single angle constraint  1052  includes a constraint body  1054 , a constraint coupling  1058  with a body  1056  and a head  1060 , and a constraint stopper  1062 . The single angle constraint  1052  attaches to an angle in the same way the angle constraint  1000  ( FIG. 10B ) above attaches to an angle. If one single angle constraint  1052  is used in a triangular device, the resulting device is a right triangle device. If three single angle constraints  1052  are used three of the angles of a quadrilateral device, the resulting device is a rectangular device. 
         [0086]      FIGS. 11A ,  11 B,  12 A, and  12 B illustrate a kite constraint  1100 . The kite constraint  1100  includes a pegged section  1102  including a peg  1110 , and a holed section  1104  including a hole  1134 . The peg  1110  fits into the hole  1134  to create the kite constraint  1100 . The peg  1110  is non-circular, so the pegged section  1102  is always orthogonal to the holed section  1104 . 
         [0087]    The pegged section  1102  further includes a first section  1108 , a second section  1112 , and a third section  1114 . The first section  1108  includes an angle coupling  1106  with a body  1160  and a head  1162 . The second section  1112  includes a first section sliding hole  1104  and a third section sliding hole  1122 . The third section  1114  includes an angle coupling  1118  with a body  1120  and a head  1116 . The pegged section  1102  further includes a first section coupling  1148  with a head  1150  and a body  1152 , and a third section coupling  1154  with a head  1156  and a body  1158 . The three sections  1102 ,  1112 ,  1114  of the pegged section  1102  are assembled as the angle constraint  1000  of  FIGS. 10A and 10C . 
         [0088]    The holed section  1104  has a structure and is assembled similar to the pegged section  1102 . As mentioned above, the pegged section  1102  is attached to the holed section  1104  via the peg  1110  and the hole  1134 . The non-circular peg  1110  and hole  1134  ensure the pegged section  1102  is kept orthogonal to the holed section  1104 . The resulting constraint is a kite constraint  1100 . 
         [0089]    Referring now to  FIG. 11B , the angle coupling  1106  attaches to an angle. The body  1160  fits through the angle constraint anchor  838  and attaches to the first section  1108  of the pegged section  1102 . The kite constraint  1100  does not include angle constraint stoppers  1066  ( FIG. 10B ), so the angle is free to be manipulated by the user. The circular nature of the angle coupling also allows the angle to be manipulated by the user. 
         [0090]      FIG. 13A  illustrates a square device  1300  with four legs  800  and an angle constraint  1000 , all with staggered sliding structures. The angle constraint  1000 , as mentioned above, ensures that the angles remain as right angles and ensures that all legs  800  are the same length, thus a square device  1300  is created. 
         [0091]      FIG. 13B  illustrates a rectangular device  1302  with four legs  800  and three single angle constraints  1052 ,  1064 ,  1304 . The three single angle constraints  1952 ,  1064 ,  1304  placed on any three angles ensure that all the angles are right angles. Thus, opposite legs  800   a  and  800   c,    800   b  and  800   d  remain the same length and parallel to each other. However, adjacent legs  800  are not required to be the same length. Therefore, a rectangular device  1302  is created. 
         [0092]      FIGS. 14A and 14B  illustrate two trapezoidal devices  1400 ,  1402  with four legs  800  and a parallel constraint  1000 . Trapezoids have two accepted definitions. The first is a quadrilateral with at least one pair of parallel sides. The second is a quadrilateral with only one pair of parallel sides. 
         [0093]    The parallel constraint  1000  attaches to opposite legs  800  via the coupling  1004  ( FIG. 10A ) going through the constraint hole  824  ( FIG. 8A ) and attaching to the constraint  1000 . The non-circular nature of the coupling  1004  ( FIG. 10 ) ensures that the legs  800  do not rotate and thus remain parallel to each other. The angles are free to be manipulated by the user. 
         [0094]      FIG. 14A  illustrates a trapezoidal device  1400  fitting the first definition. It is possible for the legs  800   b,    800   d  not attached to the constraint  1000  to become parallel through user manipulation. 
         [0095]      FIG. 14B  illustrates a trapezoidal device  1402  fitting the second definition. The top leg  800   a  includes two stoppers  1404   a,    1404   b  and the bottom leg  800   c  also includes two stoppers  1404   c,    1404   d.  In conjunction, the stoppers  1404   a,    1404   b,    1404   c,    1404   d  ensure that the maximum length of the top leg  800   a  is shorter than the minimum length of the bottom leg  800   c.  If the top leg  800   a  and bottom leg  800   c  cannot be the same length, then the right and left legs  800   b,    800   d  cannot be parallel to each other. 
         [0096]      FIG. 15A  illustrates a kite device  1500 . The kite device is described in greater detail above with respect to  FIGS. 11A ,  11 B,  12 A, and  12 B. 
         [0097]      FIG. 15B  illustrates a triangular device  1502  with a staggered sliding leg structure. 
         [0098]    As mentioned above, the shape of the polygonal device described herein is not limited to the shapes explicitly described in the figures. The polygonal device may assume other shapes such as, but not limited to, an unconstrained quadrilateral, a pentagon, a hexagon, a heptagon, an octagon, regular polygons, irregular polygons, convex polygons, and concave polygons. The methods of fixed and extendable legs and fixed and extendable angles may all be present in one polygonal device, i.e. the angles and legs do not need to be uniform. 
         [0099]    The polygonal device may be manufactured in any way including, but not limited to, stereo lithography and plastic mold injection. The polygonal device may be made out of any suitable material including, but not limited to, high density polyethylene, nylon 6/6, and other plastics and materials. 
         [0100]    The above examples are merely illustrative of several possible embodiments of various aspects of the present disclosure, wherein equivalent alterations and/or modifications will occur to others skilled in the art upon reading and understanding this specification and the annexed drawings. Furthermore, references to singular components or items are intended, unless otherwise specified, to encompass two or more such components or items. In addition, to the extent that the terms “including”, includes“, “having”, “has”, “with”, or variants thereof are used in the detailed description and/or claims, such terms are intended to be inclusive in a manner similar to the term “comprising”. Modifications and alterations will occur to others upon reading and understanding the preceding detailed description. It is intended that the invention be construed as including all such modifications and alterations.