Abstract:
A multifunctional ruler and protractor tool with the ability to form and scale a near infinite number of geometric shapes. The tool comprises both a standalone ruler and protractor unit. Rulers are capable of being added to each other successively, creating straight ruler assemblies of virtually any length. The protractor unit can be slid onto a single ruler or a straight ruler assembly containing any number of consecutively connected rulers, and is capable of fastening another ruler to its sides by a quick connect/disconnect mechanism. The protractor component of the protractor unit pivots, allowing for the creation of angles between rulers that are laterally fastened and slidably engaged to it. The sliding lock on the protractor unit can arrest both rotational and translational motion of the protractor unit along any ruler, if it is manipulated to do so. Multiple rulers and protractors can be connected to form both open and closed, regular and irregular, polygons, and other sided geometric shapes. Geometric configuration can be scaled to larger or smaller sizes.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to sketching and measuring tools, rulers, protractors, devices for creating geometric shapes, and combinations thereof. 
     Many mechanical devices have been proposed and/or used for measuring and sketching straight lines, angles, and combinations of the same. The most common of these are straight rulers, stacked rulers with a fixed pivot, t-squares, adjustable t-squares, protractors, protractors with indicating arms, triangle rulers, squares rulers, adjustable fixed-length triangles with limited angle variability, and fixed-angle devices, such as scalable squares and frames. 
     However, most, if not all of these devices have limited intended uses: e.g., typical standalone rulers and T-squares are only useful in sketching and measuring straight lines; standalone protractors typically only allow for angle measurement and do not facilitate sketching; stacked rulers with a fixed pivot only allow for angle creation where at the location on the ruler where the fixed pivot point is located; fixed-length and variable-angle triangular sketch and measure devices can only be used over a small range of angles; scalable squares and frames have fixed angles and thus, are not useful for creating and scaling other shapes, etc. 
     More recently, combinations of rulers and protractors have appeared in the art, but these devices have limited intended uses, too. An example is the stacked, two-ruler configuration (U.S. Pat. No. 7,082,692 B2) with a sliding pivot element that fastens the two rulers of this assembly together and that is centralized in a slot that is common to the each of the stacked rulers; this configuration allows for an angle to be created at any metric point along the edge of each ruler where the rulers&#39; edges intersect each other. However, if an angle is created at a certain metric, e.g., the 5 inch mark, and the angle is subsequently changed, this change causes the point of intersection (vertex of the angle) between the two rulers to move along the metered edges of each ruler; i.e., the vertex of the angle moves away from the 5 inch mark. 
     A second issue with this type of design is that the two rulers with the pivot element are fixed to each other either permanently or semi-permanently, and these modes of attachment do facilitate rapid interchangeability between rulers (no quick connect/disconnect mechanism) or the addition of multiple rulers to create a super-assembly and thus, multi-sided shapes. Third, this stacked configuration causes each ruler to be raised off the sketching or measuring surface by a different height, which makes sketching and measuring along a stacked ruler&#39;s edge both inaccurate and difficult. 
     Perhaps, the most versatile of these devices that appears in the art is a ruler system composed of a central protractor piece that is permanently fastened to two rulers both of which emanate from the central protractor piece (U.S. Pat. No. 5,732,474). In this design, rulers act as legs and are allowed to rotate independently of each other: one ruler is hollow and acts as a sleeve; the other ruler is solid and acts as a male mating piece. This configuration allows for the male leg or insert of a second, same device to be inserted into the female leg or sleeve of a first device, and vice versa, thereby allowing for numerous shapes and mating configurations to be formed. 
     However, like the aforementioned devices, this device, too, has design issues that limit its intended uses. First, the length of the longest leg, regardless of whether the longest leg is the male or female mating member, is minimum separation distance that can be achieved between protractors when the male leg from one device is inserted into a female leg of another device. Second, the largest separation achievable between protractors must be less than the sum of the male and female legs added linearly, since the male leg must have, at least, some small amount of material inserted into the female leg in order to hold the configuration of parts together. Both of these facts attest to the limited scalability of this design. Third, the sleeve design itself creates a width-wise step along the edges of the mated rulers, which obscures both the sketching and measuring of straight lines. Further, this same mating design also creates an issue of overlapping ruler markings, where the marking on the male leg (insert) become either hidden or obscured by the markings on the female leg (sleeve), depending or a whether an opaque or transparent material, respectively, is used to construct these devices. Additionally, it is inevitable that the marking on the female and male legs must move past each other in opposite directions, regardless of the desired configuration; this creates a confusing situation when one attempts to make a linear measurement with any mated portions of a multi-device assembly of this type, since there is no significant meaning between distance of the measurement marking on oppositely moving and mated legs of different devices. As claimed in (U.S. Pat. No. 5,732,474), this device was only intended to be a visual aid, and it is mostly because of the said limitations. 
     Accordingly, there is a need for a design that resolves the deficiencies in the aforesaid devices and one that introduces a set capabilities not yet seen in the prior art. 
     SUMMARY OF THE INVENTION 
     A multifunctional ruler and protractor tool with the ability to form and scale a near infinite number of geometric shapes is provided. The tool comprises both a standalone ruler and a protractor unit. The ruler may have both empirical and metric markings, and multiple rulers may be capable of being added to each other, end to end, in succession, creating a straight ruler assembly of virtually any length. The protractor unit can be slid onto a single ruler or a straight ruler assembly containing any number of consecutively connected rulers, and is capable of fastening another ruler to the sides of the protractor unit by a quick connect/disconnect mechanism. Preferably but not necessarily, all rulers units coupled to the protractor unit lie in the same plane. 
     The protractor unit according to one embodiment comprises an assembly block, a translation block, the protractor component, and a sliding lock. The assembly block holds all of the components of the protractor unit together, and contains features that allow each component of the protractor unit to perform its intended function. The protractor component of the protractor unit pivots therein or therewith, allowing for the creation of angles between rulers that are fastened to the protractor component. The translation block arrests rotational motion of the protractor component when the sliding lock is manipulated to either lock rotation or both rotation and translation. The sliding lock can arrest translational motion of the protractor unit along any ruler, if it is manipulated to do so. 
     Multiple rulers and protractors can be connected to form both open and closed, regular and irregular, polygons, and other sided geometric shapes. Geometric configurations can be scaled to larger or smaller sizes by locking rotational motion of each protractor unit and adjusting the lengthwise position of protractor units along rulers. When a geometric configuration of ruler and protractor units is created using either empirical or metric distance measurements, the entire assembly can be flipped over to read the marking in the complimentary system. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         FIG. 1(   a ) is a top view of the most basic assembly of the preferred embodiment of the multifunctional ruler and protractor set according to at least one embodiment of the invention, where a protractor unit is slidably engaged to a ruler. 
         FIG. 1(   b ) is a left view of the tool shown in  FIG. 1(   a ). 
         FIG. 2  is a top view of the tool shown in  FIG. 1(   a ) with the protractor unit disassembled from the ruler. 
         FIG. 3(   a ) is a left view of the ruler shown in  FIGS. 1(   a ) through  2 . 
         FIG. 3(   b ) is a right view of the ruler shown in  FIGS. 1(   a ) through  2 . 
         FIG. 3(   c ) is a bottom view of the ruler shown in  FIGS. 1(   a ) through  2 . 
         FIG. 4(   a ) is a magnified, front view of the ruler shown in  FIG. 2 . 
         FIG. 4(   b ) is a magnified, top view of the front of the ruler shown in  FIG. 2 . 
         FIG. 4(   c ) is a magnified, top view of the back of the ruler shown in  FIG. 2 . 
         FIG. 4(   d ) is a magnified, back view of the ruler shown in  FIG. 2 . 
         FIG. 5(   a ) is a cross-sectional view of the ruler taken from the cutting plane V(a)-V(a)′ as shown in  FIG. 3(   a ). 
         FIG. 5(   b ) is a magnified, top view of the front part of ruler shown in  FIG. 5(   a ). 
         FIG. 5(   c ) is a magnified, top view of the back part of ruler shown in  FIG. 5(   a ). 
         FIG. 6(   a ) is top view of a two-ruler assembly, where the rulers are fastened to each other, consecutively. 
         FIG. 6(   b ) is left view of the two-ruler assembly shown in  FIG. 6(   a ). 
         FIG. 7(   a ) is a magnified, top view of the two-ruler assembly shown in  FIG. 6(   a ) showing the fastening mechanism. 
         FIG. 7(   b ) is a magnified, top view of the two-ruler assembly shown in  FIG. 6(   a ) with the two rulers disassembled and fastening mechanism exposed. 
         FIG. 8  is an exploded view of the protractor unit shown in  FIGS. 1(   a ) and  2 , exposing its components. 
         FIG. 9  is an isometric view of the assembly block, a component of the protractor unit, shown in  FIG. 8 . 
         FIG. 10  is a bottom view of the assembly block shown in  FIG. 9 . 
         FIG. 11  is a cross-sectional view of the assembly block taken from the cutting plane XI-XI′ as shown in  FIG. 10 . 
         FIG. 12  is a back view of the assembly block shown in  FIG. 9 . 
         FIG. 13  is an isometric view of the protractor component, a component of the protractor unit, shown in  FIG. 8 . 
         FIG. 14  is a bottom view of the protractor component shown in  FIG. 13 . 
         FIG. 15(   a ) is right view of the protractor component shown in FIG.  14 . 
         FIG. 15(   b ) is a detailed and magnified view of the shoulder element on the protractor component shown in  FIG. 14 . 
         FIG. 16(   a ) is cross-sectional view of the protractor component taken from the cutting plane XVI(a)-XVI(a)&#39; as shown in  FIG. 15(   a ). 
         FIG. 16(   b ) is cross-sectional view of the protractor component taken from the cutting plane XVI(b)-XVI (b)&#39; as shown in  FIG. 15(   a ). 
         FIG. 17  is an isometric view of the translation block, a component of the protractor unit, shown in  FIG. 8 . 
         FIG. 18  is a back view of the translation block shown in  FIG. 17 . 
         FIG. 19  is a bottom view of the translation block shown in  FIG. 17 . 
         FIG. 20  is a right view of the translation block shown in  FIG. 17 . 
         FIG. 21(   a ) is an isometric view of the top sub-component of the translation block shown in  FIG. 17 . 
         FIG. 21(   b ) is an isometric view of the bottom sub-component of the translation block shown in  FIG. 17 . 
         FIG. 22  is an isometric view of sliding lock, a component of the protractor unit, shown in  FIG. 8 . 
         FIG. 23  is a bottom view of sliding lock shown in  FIG. 22 . 
         FIG. 24  is a back view of sliding lock shown in  FIG. 22 . 
         FIG. 25(   a ) is an isometric view of the bottom sub-component of the sliding lock shown in  FIG. 22 . 
         FIG. 25(   b ) is an isometric view of the top sub-component of the sliding lock shown in  FIG. 22 . 
         FIGS. 26(   a ) through  26 ( b ) is a top view of at least one embodiment of at least one embodiment of the invention as a two-ruler assembly, showing how two rulers can be both slidably engaged and laterally fastened to a protractor unit and how different angles can be created between these rulers. 
         FIG. 26(   c ) is a magnified view of the protractor unit in  FIG. 26(   a ). 
         FIG. 26(   d ) is a magnified view of the protractor unit in  FIG. 26(   b ). 
         FIGS. 27(   a ) through  27 ( c ) are magnified isometric views of at least one embodiment of the invention as shown  FIGS. 26(   a ) through  26 ( d ) that illustrate how to laterally fasten a ruler to a protractor unit that already has a ruler slidably engaged to it. 
         FIGS. 28(   a ) through  28 ( c ) are magnified isometric views of the same two-ruler assembly shown in  FIGS. 26(   a ) through  26 ( d ) that illustrate how the sliding lock can be manipulated to either lock only the angle between rulers or to lock both the angle between rulers and translation of a protractor unit along the ruler that is slidably engaged to it. 
         FIGS. 29(   a ) is a top view of at least one embodiment of the invention according to the preferred embodiment that illustrates how open 3-ruler geometric configurations can be created. 
         FIGS. 29(   b ) is a top view of at least one embodiment of the invention according to the preferred embodiment that illustrates how simple triangular configurations can be created. 
         FIGS. 30(   a ) and  30 ( b ) are top views of at least one embodiment of the invention according to the preferred embodiment that illustrates how small rectangular configurations can be scaled to a larger sizes while holding the same common angles between rulers. 
         FIGS. 30(   c ) is a top view of at least one embodiment of the invention according to the preferred embodiment that illustrates how open quadrilateral configurations can be created. 
         FIGS. 31  is a top view of at least one embodiment of the invention according to the preferred embodiment that illustrates how closed and irregular, pentagonal configurations can be created. 
         FIGS. 32  is a top view of at least one embodiment of the invention according to the preferred embodiment that illustrates how open and irregular, hexagonal configurations with consecutive ruler attachments can be created. 
         FIGS. 33(   a ) is a top view of at least one embodiment of the invention according to the preferred embodiment that illustrates how closed octagonal configurations can be created. 
         FIGS. 33(   b ) is a top view of at least one embodiment of the invention according to the preferred embodiment that illustrates how open and spiral-like, octagonal configurations can be created. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Generally referring to  FIGS. 1(   a )- 2  and  FIG. 8 , the tool  1  is provided herewith that comprises two main, standalone components: the ruler unit  2  and protractor unit  3 . Preferably, the ruler  2  is an indivisible part, and the protractor unit  3  is itself an assembly comprising the following components: an assembly block  4 , a protractor unit  5 , a translation block  6 , and a sliding lock  7 . Together and in pluralities, the ruler  2  and the protractor unit  3  can be used to construct a myriad of different geometric and polygonal configurations ( FIGS. 26(   a )- 26 ( b ),  29 ( a )- 33 ( b )). 
     The ruler  2 ,  2 ′, as shown  FIGS. 1(   a )- 7 ( b ) and  26 ( a )- 28 ( c ), has a long body that in at least one embodiment is a quadrilateral solid in shape and is generally straight with a select length, width, thickness, and cross-sectional dimensions. The ruler  2 ,  2 ′ comprises one or more of the following major features: minor surfaces  10 ,  10   a ,  10   b ,  10   c ,  10 ′ and  10   b ′; center slot  9  and  9 ′; attachment holes  14 ,  14   a , and  14 ′; center tracks,  8 ,  8   a , and  8 ′; and material ends  13 ,  13   a , and  13 ′ with male  11 ,  11   a ,  11 ′ and female fastening features  12 ,  12   a ,  12 ′. 
     Additionally, rulers  2 ,  2 ′ may have two minor surfaces  10  &amp;  10   a ,  10   b  &amp;  10   c ,  10 ′ &amp;  10   b ′ on each top and bottom surface of the ruler  2 . Opposing surfaces  20  &amp;  20   a ,  10  &amp;  10   a ,  10   b  &amp;  10   c ,  10 ′ &amp;  10   b ′ are preferably parallel, except for the rotationally symmetrical ends  13 ,  13   a  as described herein. Also, the ruler  2 ,  2 ′ itself, may include at its ends  13 ,  13   a  and both the male  11 ,  11   a ,  11 ′ and female fastening elements  12 ,  12   a ,  12 ′ and all other features, may also be rotationally symmetric about the plane A-A′ as shown in  FIG. 2  and may be regularly symmetrical about the plane V(a)-V(a)′ as shown in  FIG. 3(   a ). 
     Each minor surface  10 ,  10   a ,  10   b ,  10   c ,  10 ′,  10   b ′, as shown in  FIG. 1(   a ) through  7 ( b ), has measurement markings near the ruler&#39;s edges  22 ,  22   a ,  22 ′,  22   a ′ that can be of any unit measurement system (e.g., empirical, metric, etc.), mixture of systems, patterns of different unit scales, or markings indicating proportions (e.g., golden ratio); preferably, these markings ascend in order from the tip of the female fastening element  12 ,  12   a ,  12  to the should  15 ,  15   a ,  15   b ,  15   c ,  15 ′ on the opposite end of the ruler  2 ,  2 ′. 
     Referring to  FIGS. 1(   a ) through  5 ( c ), the measurement markings on each minor surfaces  10 ,  10   a ,  10   b ,  10   c ,  10 ′,  10   b ′ that are on the same either top or bottom surface of the ruler  2 ,  2 ′ can be of different unit measurement systems; e.g., one can be in metric units, such as millimeters or centimeters, and the other in empirical units, such as inches. In general, when measuring marking on a ruler  2 ,  2 ′ are of different unit measurement systems, opposing minor surfaces  10 ,  10   a ,  10   b ,  10   c ,  10 ′,  10   b ′ along the same edge  22 ,  22   a ,  22 ′,  22   a ′ of a ruler  2 ,  2 ′ have measurement marking that are in the complimentary unit measurement system with respect to each other; e.g., if measurement markings on a top surface minor surface  10  along a side edge  22  are in millimeters (metric system), then measurement markings on the opposing surface  10   a  along the same edge  22  should be in inches (empirical system). 
     In one embodiment, center tracks  8 ,  8   a , and  8 ′ on the ruler  2 ,  2 ′, as shown in  FIGS. 1(   a ) through  4 ( c ), consist of recessed surfaces and side walls that are nearly as long as the ruler&#39;s itself; these tracks  8 ,  8   a , and  8 ′ have a select width and depth and are intended facilitate and cooperate with the movement of the assembly block&#39;s  4  center bodies  26 ,  26 ( a ) when the protractor unit  3  is slidably engaged to a ruler(s)  2 ,  2 ′. 
     Additionally, the recessed surfaces on the tracks  8 ,  8   a ( FIGS. 1(   a )- 4 ( c )) may also take part in the friction locking mechanism that is responsible for locking the sliding motion of a protractor unit  3  along a ruler&#39;s  2 ,  2 ′ length, assuming that a protractor unit  3  is slidably engaged to a ruler  2 ,  2 ′: when the sliding lock  7  is manipulated to the full lock position  147  as described below ( FIGS. 28(   a ) through  28 ( c )), the underside surfaces  42  and  42   a  on center bodies  26  and  26   a  of the assembly block  4  ( FIGS. 9-12)  press against the recessed surfaces of the center tracks  8 ,  8   a , and  8 ′ and thereby, creating friction a force that arrests the translational or sliding movement of the protractor unit  3  ( FIG. 1(   a )). The tracks  8 ,  8   a  may extend the entire length of the ruler  2 ,  2 ′ so that, when multiple rulers are attached to each other end to end, the protractor unit  3  may slide lengthwise from one to another of the rulers and may be locked at any point on the combined ruler set. 
     Referring to  FIGS. 1(   a ) through  5 ( c ), center slot  9 ,  9 ′ is a lengthwise slot that is preferably centered both widthwise and lengthwise on the ruler  2 ,  2 ′.The attachment holes  14 ,  14   a ,  14 ′ may be holes that are centered on the ruler&#39;s  2 ,  2 ′ triangular ends  13 ,  13   a ,  13 ′. The center slot  9 ,  9 ′ and attachment holes  14 ,  14   a ,  14 ′ may be extend entirely and/or part way through the thickness of the ruler  2 ,  2 ′. The center slot  9 ,  9 ′ and attachment holes  14 ,  14   a ,  14 ′ are intended to provide attachment points for accessories, and are optional. Further, if present, these holes  14 ,  14   a ,  14 ′ and slots  9 ,  9 ′ may be of any cross-sectional dimensions as long as they do obstruct, but rather cooperate with intended functions, movement, and dimensions of all other features and sub-features of the ruler  2 ,  2 ′ itself and that of all other assemblies  3  and components  4 ,  5 ,  6 ,  7  of those assemblies  3  when a protractor unit  3  is slidably engaged to a ruler  2 ,  2 ′ or both slidably engaged and laterally fastened to rulers as shown in  FIG. 26(   a )- 27 ( c ). 
     Referring to  FIGS. 2 through 7(   b ), the ends  13 ,  13   a ,  13 ′ of the ruler  2 ,  2 ′ are preferably straight, oriented diagonally relative to the lengthwise axis of the ruler  2 ,  2 ′ thereby giving the ends a triangular shape, but can also be of any shape as long as the shape allows the ruler  2 ,  2 ′ (i) to both laterally fasten at the ends to other rules and to slidably engage protractor units  3  as discussed herein and/or (ii) to cooperate with functions, movement, and dimensions of all other features and sub-features on the ruler  2 ,  2 ′ itself, and that of all other assemblies  3 ,  100  ( FIGS. 26(   a )- 26 ( b )) and components  2 ,  2 ′,  4 ,  5 ,  6 ,  7  of those assemblies  3 ,  100 , as well as with creation of other geometric assembly configurations ( FIGS. 29(   a )- 33 ( b )) as described herein. 
     Additionally, the ruler&#39;s ends  13 ,  13   a ,  13 ′, as shown in  FIGS. 2 through 7(   b ), have male  11 ,  11   a ,  11 ′ and female fastening elements  12 ,  12   a ,  12 ′ that facilitate connecting, locking, and disconnecting of a ruler  2 ,  2 ′ to and from the protractor component  5  of the protractor unit(s)  3  and/or to and from other rulers  2 ,  2 ′. The male fastening elements  11 ,  11   a , and  11 ′ and female elements  12 ,  12   a , and  12 ′, preferably, are both located on each of the ruler&#39;s  2 ,  2 ′ ends  13 ,  13   a ,  13 ′ and are separated from each other along the ends  13 ,  13   a ,  13 ′ by a space that is able to accommodate the full length of either fastening element  11 ,  11   a ,  11 ′,  12 ,  12   a ,  12 ′. These fastening elements  11 ,  11   a ,  11 ′, 12 ,  12   a , and  12 ′ have a select width, thickness, length, and cross-sectional dimensions and have a shape that is preferably rectangular and parallel to the diagonal profile of the ruler&#39;s ends  13 ,  13   a ,  13 ′; however, the shape of these fastening elements  11 ,  11   a ,  11 ′, 12 ,  12   a , and  12 ′ can also be of any shape as long as the shape facilitates and cooperates with action and mechanism of fastening rulers  2 ,  2 ′ to other rulers  2 ,  2 ′ and to the protractor component  5  of protractor units  3 . 
     Male fastening elements  11 ,  11   a , and  11 ′ on the ruler&#39;s ends  13 ,  13   a ,  13 ′, as shown in  FIGS. 2-7(b) , consist of a locking elements  20 ,  20   a ,  20   b ,  20   c , and  20 ′ and tracks  17 ,  17   a ,  17   b ,  17   c , and  17 ′ that in at least one embodiment are all generally rectangular in shape and that have a select width, thickness, length, and cross-sectional dimensions that facilitate and cooperate with both the sliding and locking of the locking elements  20 ,  20   a ,  20   b ,  20   c , and  20 ′ onto the tracks  16  and  16   a  of the female fastening elements  12 ,  12   a , and  12 ′ of other rulers  2 ,  2 ′ when a ruler  2 ,  2 ′ is fastened to another ruler  2 ,  2 ′. 
     Female snap features  19 ,  19   a ,  19   b ,  19   c , and  19 ′, as shown in  FIGS. 4(   b ) through  7 ( b ), are located on the inside wall of the locking elements  20 ,  20   a ,  20   b ,  20   c , and  20 ′ along the track  17 ,  17   a ,  17   b ,  17   c , and  17 ′ are intended to facilitate locking to the male snap feature  80  on the protractor component  5  after a male fastening element  11 ,  11   a , and  11 ′ on the ruler  2 ,  2 ′ has been inserted into the track  81  on the protractor component  5  for the purpose of fastening a ruler  2 ,  2 ′ onto a protractor unit  3 . 
     The snap features  18 ,  18   a ,  18   b , and  18 ′ ( FIGS. 4(   a ) through  7 ( b )) on the inside wall of the locking element  20 ,  20   a ,  20   b ,  20   c , and  20 ′ along the track  17 ,  17   a ,  17   b ,  17   c , and  17  are intended to facilitate locking to the snap features  25 ,  25   a ,  25   b , and  25   c  on the female fastening element  12 ,  12   a ,  12 ′ after a male fastening element  11 ,  11   a ,  11 ′ has been inserted into the track  16 ,  16   a  of the female fastening element  12 ,  12   a ,  12 ′ for the purpose of fastening rulers  2 ,  2 ′ consecutively to each other. 
     Female fastening elements  12 ,  12   a , and  12 ′ on the ruler&#39;s ends  13 ,  13   a , and  13 ′ ( FIGS. 2- 7(   b )) consist of a inner track  16 ,  16   a , locking elements  23 ,  23   a ,  23   b ,  23   c , and a slot  24 ,  24   a , as shown  FIGS. 5(   b )- 5 ( c ), all of which are preferably rectangular in shape, parallel to the profile of the ruler&#39;s  2 ,  2 ′ ends  13 ,  13   a ,  13 ′ and have a select depth, width, length, and cross-sectional dimensions that are to facilitate and cooperate with both the sliding and locking of locking element pairs  20  &amp;  20   a ,  20   b  &amp;  20   c  onto the tracks  16  and  16   a  of male fastening elements  12 ,  12   a ,  12 ′ of other rulers  2 ,  2 ′ when rulers  2 ,  2 ′ are being fastened to each other  2 ,  2 ′. 
     Snap features  25 ,  25   a ,  25   b , and  25   c  ( FIGS. 4(   a ) through  7 ( b )) on the locking elements  23 ,  23   a ,  23   b , and  23   c  of the female fastening elements  12 ,  12   a , and  12 ′ are intended to facilitate locking to the snap features  18 ,  18   a ,  18   b , and  18 ′ on the male fastening elements  11 ,  11   a , and  11 ′ after a male fastening element  11 ,  11   a ,  11 ′ on the ruler has been inserted into the track  16 ,  16   a  on the female fastening element  12 ,  12   a ,  12 ′ for the purpose of fastening rulers  2 ,  2 ′ to each other, consecutively. 
     Referring to  FIGS. 5(   a ) through  7 ( b ), to fasten a ruler  2 ,  2 ′ to another ruler  2 ,  2 ′ or to consecutively-connected ruler assemblies  100 , slide one set of the male locking elements  20 ,  20   a ,  20   b ,  20   c ,  20 ′, which are located on either end  13 ,  13   a ,  13 ′ of any ruler  2 ,  2 ′ into the track  16 ,  16   a  of the female fastening element  12 ,  12   a ,  12 ′ of another ruler  2 ,  2 ′, or vice versa, until the pertinent snap feature  18 ,  18   a ,  18   b ,  18   c ,  18 ′ of the male fastening elements  11 ,  11   a ,  11 ′ on one of rulers  2 ,  2 ′ fully engages the pertinent snap feature  25 ,  25   a ,  25   b ,  25   c  of the female fastening element  12 ,  12   a ,  12 ′ on the other or another ruler  2 ,  2 ′. Many rulers  2 ,  2 ′ can be connected in this same manner (e.g., six, ten, twenty, or thirty individual rulers can be connected end-to-end) for the purpose of creating long straight-edged assemblies. 
     To unfasten a ruler  2 ,  2 ′ from other rulers  2 ,  2 ′ or consecutively-connected ruler assemblies  100  ( FIGS. 5(   a )-( b )), pull rulers  2 ,  2 ′ diagonally away from each other in the direction of the length of the locking elements  20 ,  20   a ,  20   b ,  20   c ,  20 ′ until the snap feature(s)  18 ,  18   a ,  18   b ,  18   c ,  18 ′ of the male fastening elements  11 ,  11   a ,  11 ′ on one ruler  2 ,  2 ′ disengage the snap features  25 ,  25   a ,  25   b ,  25   c  of the female fastening element  12 ,  12   a ,  12 ′ on the other ruler  2 ,  2 ′ and until rulers  2 ,  2 ′ are completely spatially separated from each other as shown in  FIG. 7(   b ). 
     For consecutive-ruler assemblies  100 , as shown in  FIGS. 7(   a ) through  7 ( b ), where rulers  2 ,  2 ′ are fastened to each other, the tips of the female fastening elements  12 ,  12   a ,  12 ′ of one ruler  2 ,  2 ′ should contact or be in proximity to the pertinent set of shoulders  15 ,  15   a ,  15   b ,  15   c ,  15 ′ that are on the mating end  13 ,  13   a ,  13 ′ of the other ruler  2 ,  2 ′ as shown in  FIG. 7(   a ). 
     Additionally, when multiple rulers  2 ,  2 ′ are connected consecutively to each other to make larger linear ruler assemblies  100  ( FIG. 7(   a )- 7 ( b ))—all top, bottom, and side surfaces of individual rulers  2 ,  2 ′ should closely align, lie in the same plane, or be tangent to each other at their mating junction or contact points, as this will ensure that measurement markings on the minor surfaces  10 ,  10   a ,  10   b ,  10   c ,  10 ′, and  10   b ′ ( FIGS. 2-7(   b )) of one ruler  2 ′ add directly to the measurement markings on the other ruler(s)  2 , and that this addition, preferably, occurs in the same ascending or descending order as the measurement markings on the first ruler  2  or consecutive ruler assembly(s)  100 . Also, it is preferably that measurement markings on contiguous minor surfaces  10  &amp;  10 ′,  10   b  &amp;  10   b ′ in a consecutive-ruler assembly(s)  100  be of same unit measurement system (e.g., metric and metric). 
     Generally referring to  FIGS. 1-2 ,  6 ( a )- 8 , and  26 ( a )- 28 ( c ), the protractor unit  3  as previously stated, is an assembly composed of assembly block  4 , protractor  5 , translation block  6 , and sliding lock  7  components and is itself a standalone device that can be managed and handled independently of a ruler(s)  2 ,  2 ′. However, the protractor unit  3  can also be removably attached to the rulers so that the protractor unit  3  slidably engages rulers  2 ,  2 ′ and consecutive ruler assemblies  100 , and other rulers  2 ,  2 ′ and consecutive ruler assemblies  100  can be laterally fastened to the protractor unit&#39;s protractor component  5  ( FIGS. 26(   a )- 27 ( c ),  8 , &amp;  13 - 16 ( b )), as described herein. 
     Referring to  FIGS. 1-2  and  8 - 12 , in at least one embodiment the assembly block  4 , is the central component of the protractor unit  3 ; all other components  5 ,  6 ,  7  of the protractor unit  3  in this instance are assemble onto the assembly block component  4  in order to fully compose a protractor unit  3 . The assembly block component  4  is preferably fixed relative to the other components  5 ,  6 , and  7  of the protractor unit  3  when the components  4 ,  5 ,  6  and  7  are in the assembled state, while the other components  5 ,  6 , and  7  are free to move in the manner and under the conditions described herein. Cooperation between the components  4 ,  5 ,  6 , and  7  of the protractor unit  3  allows components  4 ,  5 ,  6 ,  7 , and the protractor unit  3  to function as intended and described herein. 
     The assembly block  4 , as shown in  FIGS. 9 through 12  is composed of a body that has a main block  56  and the following major features, all of which extend from the main block  56  and have select length, width, thickness, and cross-sectional dimensions: center bodies  26  and  26   a  and side bodies  29  and  30 . Additionally, the main block  56 , the said features  26 ,  26   a ,  29  and  30  and all sub-features of the assembly block  4  are symmetrical about the plane B-B′ ( FIG. 11 ) and accommodate and cooperate with the assembly of components  5 ,  6 , and  7  ( FIGS. 1-2  &amp;  8 ) onto the assembly block  4  itself, as described herein. 
     The main block  56  ( FIGS. 9-12 ) has an external shape that is generally rectangular, but that can also be of various shapes as long as the shape accommodates the internal cross-sectional shape and dimensions  46  of the assembly block  4 . It is preferred that the surfaces  28  and  28   a  be aligned with or be in proximity to the surfaces  60  and  60   a  of the protractor component  5  ( FIGS. 13-16(   b )) when the components  4 ,  5 ,  6 , and  7  ( FIGS. 1-2  &amp;  8 ) are in an assembled state  3 . The main block  56  is intended to impart mechanical stability to the center bodies  26  and  26   a  and side bodies  29  and  30  and to serve as a finger grip to facilitate handling of the protractor unit  3  as a whole, since assembly block  4  is intended to remain relatively fixed with respect to the pivoting aspect of the protractor unit  3  as compared to the rest of the components  5 ,  6 ,  7  in the protractor unit  3 . 
     The outer surface  50  ( FIGS. 9-12 ) of the assembly block  4  is preferably chamfered along the internal cross-section  46  in order to facilitate sliding onto to a ruler(s)  2 ,  2 ′ when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3 . The inner surfaces  59  and  59   a  are intended to be concentric with the outer surface  131  and  131   a  of the sliding lock  7  ( FIGS. 22-25(   b )) and should also provide enough clearance as to not obstruct the sliding lock&#39;s  7  lateral and rotational movement, which allows sliding lock  7  to slide to a lock or unlock position ( FIGS. 28(   a )- 28 ( c )), when components  4 ,  5 ,  6 , and  7  are in the assembled state  3 , regardless of whether the protractor unit  3  is mated to a ruler(s)  2 ,  2 ′. 
     Side body  30  ( FIGS. 9-12 ) is a body that extends from the main block  56  and is connected only to the main block  56 . Side body feature  30  is optional and a redundancy; its main purpose is to hold feature  31  in its intended spatial position as described below. Feature  31  of the side body  30  is a piece of material that curves off of the side body  30  and is intended to mate with feature  92  of translation block  6  ( FIGS. 17-21(   b )) when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3 ; feature  31  is also a redundancy that is intended to prevent lateral and rotational movement of the translation block  6  in the event that the guiding elements  35 ,  35   a  undergo material failure and are unable to properly mate and cooperate with the guiding elements  86 ,  86   a  ( FIGS. 17-21(   b )) of the translation block  6  when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3  and the sliding protractor component  3  is being handled independently of a ruler  2 ,  2 ′. 
     Side body  29  also extends outward from the main block  56  and is connected to both the main block  56  and the curved fastening elements  27  and  27   a . Side body  29  in cooperation with the curved fastening elements  27  and  27   a  imparts mechanical rigidity to center bodies  26 ,  26   a , especially by preventing center bodies  26 ,  26   a  from collapsing medially towards the center plane B-B ( FIG. 11 ) when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3  and the protractor unit(s)  3  is being handled independently from a ruler  2 ,  2 ′, or an assembly of rulers  100  ( FIG. 6   a - 6   b ), an example of which can be seen in  FIG. 2 . 
     Additionally, the inner walls of the side bodies  29  and  30  ( FIGS. 9-12 ) are intended to contact or be in proximity to the side walls  22 ,  22   a ,  22 ′ and  22   a ′ of the ruler  2 ,  2 ′ ( FIGS. 2-6(b) ) when the components  4 ,  5 ,  6 , and  7  are in an assembled state  3  and the protractor unit  3  is slidably engaged to a ruler  2 ,  2 ′, for example, when the ruler  2 ,  2 ′ is placed within the channel that extends through the main block  56  between the outer surface  50  at a top end of the block  56  and at a bottom end of the block  56  opposite the top end. As can be seen in  FIG. 9 , the outer surface  50  has an opening therein that is the approximate shape of the ruler  2 ,  2 ′. 
     Center bodies  26  and  26   a  ( FIGS. 9-12 ) are generally flat rectangular bodies that also extend outward from the main block  56  and contain the following major features: curved fastening elements  27  and  27   a , and guide elements  35 ,  35   a ,  40 , and  40   a . Center bodies  26  and  26   a  are intended to fit without interference in the center tracks  8 ,  8   a and  8 ′ of the ruler  2 ,  2 ′ when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3  and the protractor unit  3  is in the unlocked state ( FIG. 28(   a )) and slidably engaged (e.g., as in  FIG. 1(   a )) to a ruler  2 ,  2 ′ as described in detail below. 
     Guide elements  40  and  40   a  ( FIGS. 9-12 ) extend outward from the center bodies  26  and  26   a  and are preferably cylindrical in shape, but can also be of any shape as long as the shape and cross-dimensions cooperate with those of the guiding slots  145  and  145   a  on the sliding lock  7  ( FIG. 22-25(   b )) such that guide elements  40 ,  40   a  can slidably engage the curved guiding slots  145 ,  145   a , as shown in  FIGS. 28(   a ) through  28 ( c ). 
     Shoulder elements  47  and  47   a  ( FIGS. 9-12 ) are intended to be concentric with the guide elements  40  and  40   a  and have a larger cross-sectional width, as well as an equal, centered, and aligned width-wise cross-sectional shape as the round guide elements  40 ,  40   a ; shoulder elements  47  and  47   a  are also intend to extend outward from the center bodies  26  and  26   a  less than the guide elements  40  and  40   a . Further, shoulder elements  47  and  47   a  are intended to slidably engage and cooperate with the shape and cross-sectional dimensions of the shoulder elements  170 ,  170   a ,  171 ,  171   a ,  171   b ,  171   c ,  172 ,  172   a ,  172   b ,  172   c  on the sliding lock  7  such that the protractor units  3 ,  3 ′,  3 ″ on ruler-protractor assemblies, such as assemblies  200 ,  300 ,  301 ,  400 ,  401 ,  500 ,  600 ,  800 ,  801 , shown in  FIGS. 26(   a )- 33 ( b ), can be manipulated to the locked state by the mechanisms described in detail below. 
     Guide elements  35  and  35   a  ( FIGS. 9-12 ) extend outward from the center bodies  26  and  26   a  and preferably have a rectangular shape, but can also be of any shape as long as both its shape and cross-dimensions cooperate with those of the guide elements  86  and  86   a  of the translation block  6  ( FIGS. 17-21(   b )) such that guide elements  35 ,  35   a  can slidably engage the guide elements  86 ,  86   a  as discussed below and shown in  FIGS. 28(   a ) through  28 ( c ). Guide elements  35  and  35   a  are intended to prevent lateral and rotational movement of the translation block  6  when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3  and the sliding protractor component  3  is being handled independently of a ruler  2 ,  2 ′. 
     Curved guide elements  27  and  27   a  ( FIGS. 9-12 ) extend outward from the center bodies  26 ,  26   a  and have a curved shape and a constant thickness with an inner and outer radii that are concentric with respect to each other and that are respectively co-radial with the inner and outer radii of the rotational-guide slots  61 ,  61  on the protractor component  5  ( FIGS. 8  and  FIGS. 13-16(   b )) when the protractor component  5  is assembled onto the assembly block  4 . Further, the guide elements  27  and  27   a  are intended to mate and slidably engage the rotational-guide slots  61  and  61   a  when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3 , as shown in  FIGS. 26(   a ) through  26 ( b ), such that the protractor  5  is able to rotate unobstructedly about a virtual pivot  901  ( FIG. 10)  that is in fact the same point as or in proximity to the center point  901  of the imaginary circle  900  created by the radii of the curved guide elements  27  and  27   a  ( FIG. 10 ). 
     The magnitude of the radii on the curved guide elements  27  and  27   a  ( FIGS. 9-12 ) and the orientation of the circumference of the imaginary circle  900  ( FIG. 10 ) with respect to the center bodies  26 ,  26   a  are determined by the position of the center point  901  ( FIG. 10 ). Further, the position of the center point  901  is selected such that when a protractor unit  3  is both slidably engaged ( FIG. 1(   a ), for example) to a first ruler  2  and a second ruler  2 ′ is simultaneously, laterally fastened to the protractor unit  3 , as in assembly  200  ( FIGS. 26(   a )- 27 ( c )), the pivot point  901  lies in the center of circle created by the radius on the tip of the female fastening elements  12 ,  12   a ,  12 ′ on the laterally fastened unit ruler  2 ′ ( FIGS. 4(   b ) and  4 ( c )) and this same radius on the tip of the of the female fastening element  12 ,  12   a ,  12 ′ of the laterally fastened ruler  2 ′ is tangent or in proximity to the edge  22  of the slidably engaged ruler  2 . 
     Snap features  55 ,  55   a ,  55   b , and  55   c  ( FIGS. 9-12 ) may be located on the outer edge curved guide elements  27  and  27  that engage the recessed surfaces  67  and  67   a  ( FIG. 15(   b )) around the edges of the rotational-guide slots  61  and  61  a when protractor component  5  ( FIGS. 13-16(   b )) is assembled onto the assembly block  4  ( FIGS. 2 and 8)  and provide mechanical stability to center bodies  26 ,  26   a  of the assembly block  4  by preventing bodies  26 ,  26   a  from collapsing medially toward the plane B-B ( FIG. 11 ) when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3  and the protractor unit  3  is handled independently of any ruler  2 ,  2 ′. 
     Center bodies  26  and  26   a  ( FIGS. 9-12 ) and the curved guide elements  27  and  27   a  on the assembly block  4  are integral in locking the rotational motion of the protractor component  5  ( FIGS. 13-16(   b ) and  FIGS. 26(   a )- 26 ( d )) when (i) the components  4 ,  5 ,  6  and  7  are in the assembled state  3 , (ii) the protractor unit  3  is slidably engaged to a ruler  2 ,  2 ′, and (iii) the protractor unit  3  is in the angle-locked state  148  or fully-locked state  147  ( FIGS. 28(   a )- 28 ( c )), as is later described; the function of features  26 ,  26   a ,  27 , and  27   a  is made clear by describing the locking mechanism itself, which occurs as follows: as the sliding lock  7  is moved toward the angle-locked position  148  or fully-lock position  147 , the curved guiding slots  145  and  145   a  on the sliding lock  7  ( FIGS. 22-25(   b )) slide through the round guide elements  40 ,  40   a  on the assembly block  4  such that the curvature of slots  145  and  145   a  changes from the curve  151  and  151   a  to the curve  152  and  152   a ; this change in curvature causes the distance between the round guide elements  40  and  40   a  on the assembly block  4  and the surfaces  134  and  134   a  on the sliding lock  7  ( FIGS. 22-25(   b )) to increase; this increase in turn causes the sliding lock  7  to translate toward the translation block  6  ( FIGS. 17-21(   b )) and specifically, the surfaces  134  and  134   a  on the sliding lock  7  to push on the translation block  6 , causing the translation block  6  to translate toward the protractor component  5  and specifically, the surfaces  98  and  98   a  on the translation block  6  to push on the surfaces  73  and  73   a  on the protractor component  5  such that sufficient friction is created to arrest rotation motion of the protractor component  5 . 
     Additionally, each of the features  27 ,  27   a ,  35 ,  35   a ,  40 , and  40   a  ( FIGS. 9-12 ) should be positioned on the center bodies  26  and  26   a  at precise distances and orientations such that they  27 ,  27   a ,  35 ,  35   a ,  40 ,  40   a  can properly mate with their respective mating features  61 ,  61   a ,  86 ,  86   a ,  145 ,  145   a  ( FIGS. 8-25(   b )) and execute their intended functions, as described herein; so that the components  4 ,  5 ,  6 , and  7  can be assembled  3  in the manner as described herein, and the protractor unit  3  can simultaneously slidably engage ( FIG. 1(   a ), for example) and laterally fasten ( FIGS. 27(   a )- 27 ( c )) rulers  2 ,  2 ′ and function as intended. 
     Additionally, the top and bottom surfaces of the side bodies  29 , and  30  and outward-facing surfaces of the center bodies  26  and  26   a  ( FIGS. 9-12 ) with respect to the center plane B-B ( FIG. 11 ), should be level with or in proximity to each other and to the minor surfaces  10 ,  10   a ,  10   b ,  10   c ,  10 ′,  10   b ′ ( FIGS. 1(   a )- 7 ( b )) when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3  and the protractor unit  3  is slidably engaged to a ruler  2 ,  2 ′. Further, these same surface  26 ,  26   a ,  29 ,  30  should not obstruct the rotational movement of the protractor component  5  when the subcomponents  4 ,  5 ,  6 , and  7  are in the assembled state  3  and the protractor unit  3  is slidably engaged to a ruler  2 ,  2 ′. 
     Generally referring to  FIGS. 1(   a )- 2 ,  FIG. 8 , and  FIGS. 13-16(   b ), the protractor component  5 , a component of the protractor unit  3 , preferably has semicircular shape of either constant, variable, or linearly increasing or decreasing radius, that cooperates with the intended motions and functions of the protractor component  5  itself and the components  4 ,  6 , and  7  of the protractor unit  3  when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3  and the protractor unit  3  is either slidably engaged or laterally fastened to a protractor unit  3 , or both. 
     The protractor component  5  ( FIGS. 13-16(   b )), in one embodiment, contains the following major features: the rotational-guide slots  27  and  27   a , the female mating elements  65 - 65   i  and  65   l - 65   t , recessed surfaces  64  and  64   a , major outer  60  and  60   a  and inner surfaces  66  and  66   a , stabilizing blocks  70  and  77 , track  81 , snap features  80  and  80   a , and the surfaces  62 ,  62   a ,  71 ,  71   a ,  72 ,  72   a ,  73  and  73   a ; further, all of these features are preferably symmetrical about both the cutting planes XVI(a)-XVI(a)&#39; and XVI(b)-XVI(b)&#39; as shown in  FIGS. 15-16(   a ). 
     Component  5  ( FIGS. 13-16(   b )) assembles onto the assembly block  4  ( FIG. 8  and  FIGS. 9-12)  with components  6  and  7  such that: the protractor component  5  is able to rotate unobstructedly when the protractor unit  3  is in an unlocked state  149  ( FIG. 28(   a )- 28 ( c )); the inner surfaces  66  and  66   a  of the protractor component  5  are in contact with or in proximity to the outward-facing surfaces of the center bodies  26  and  26   a  ( FIG. 11)  and the minor surfaces  10 ,  10   a ,  10   b ,  10   c ,  10 ′ and  10   b ′ of the ruler  2 ,  2 ′ ( FIGS. 1(   a )- 7 ( b )); the rotational-guide slots  61 ,  61  a are be snapped into or over the snap features  55 ,  55   a ,  55   b ,  55   c  of the curved guide elements  27 ,  27   a  on the assembly block  4  ( FIGS. 9-12)  such that the snap features  55 ,  55   a ,  55   b ,  55   c  sit in the recessed surfaces  67 ,  67   a  ( FIGS. 13 &amp; 15(   b )) and the top surfaces of the curved guide element  27 ,  27   a  are level with or in proximity to the outer surfaces  60  and  60   a  of the protractor component  5 ; and the rotational-guide slots  61  and  61   a  are slidably engaged with the curved guide features  27  and  27   a  on the assembly block  4 . 
     Slot  63 , track  81 , and snap features  80  and  80   a  ( FIGS. 13-16(b) ) are intended to function in and cooperate with the lateral fastening of a ruler  2 ,  2 ′ to the protractor component  5  when the components  4 ,  5 ,  6  , and  7  are in the assembled state  3  ( FIGS. 27(   a )- 27 ( c )). The track  81  on the protractor component  5  ( FIGS. 16(   a )- 16 ( b )) has a select cross-sectional shape and dimensions that are to compliment those of any set of paired male locking elements  20  &amp;  20   a ,  20   b  &amp;  20   c  on the male fastening element  12 ,  12   a ,  12 ′ on the same end  13 ,  13   a ,  13 ′ of any ruler  2 ,  2 ′ ( FIGS. 1(   a )- 7 ( b )) such that these locking elements  20  &amp;  20   a ,  20   b  &amp;  20   c  are able to slide into the track  81  and allow any paired set of snap features  19 , &amp;  19   a ,  19   b  &amp;  19   c  on the same end  13 ,  13   a , 13 ′ of the ruler  2 ,  2 ′ to fully engage the male snap features  80  and  80   a  of the protractor component  5 . 
     Slot  63  ( FIGS. 13-16(   b )) has a select cross-sectional shape and dimensions that are to accommodate and allows the material between any set of paired tracks  17  &amp;  17   a ,  17   b  &amp;  17   c  on the male fasten elements  11 ,  11   a ,  11 ′ on the same end  13 ,  13   a ,  13 ′ of any ruler unit  2 ,  2 ′ ( FIGS. 1(   a )- 7 ( b )) to slide through and mate with slot  63  when the male locking elements  20 ,  20   a ,  20   b ,  20   c ,  20 ′ ( FIGS. 1(   a )- 7 ( b )) are slid into the track  81  to allow the female snap features  19 ,  19   a ,  19   b ,  19   c  and  19 ′ of the ruler  2 ,  2 ′ to fully engage the male snap features  80  and  80   a  of the protractor component  5  ( FIGS. 16(   a )- 16 ( b )). 
     Snap features  80  and  80   a  ( FIGS. 16(   a )- 16 ( b )) also have a select shape and cross-sectional dimension that allow it to engage any pared set of snap features  19 , &amp;  19   a ,  19   b  &amp;  19   c  on the same end  13 ,  13 ′ of the ruler  2 ,  2 ′ ( FIGS. 1(   a )- 7 ( b )). Additionally, when a protractor unit  3  is both slidably engaged to a first ruler  2  and laterally fastened to a second ruler  2 ′ ( FIGS. 26(   a )- 27 ( c ))—the snap features  19 ,  19   a ,  19   b ,  19   c , and  19 ′ on the laterally fastened ruler  2 ′ are to engage the snap features  80  and  80   a  on the protractor component  5  so as to hold the laterally fastened ruler  2 ′ at a position where the radius on the tip of ruler  2 ′ female fastening elements  12 ,  12   a ,  12 ′ ( FIGS. 1(   a )- 7 ( b )) is to be tangent or in proximity to the edge  22  of the slidably engaged ruler  2  ( FIGS. 27(   a ) and  27 ( b )) and such that the protractor component  5  of the protractor unit  3  is able to rotate unobstructedly, as in  FIGS. 26(   a ) through  26 ( d ), without allowing the snap feature  19 ,  19   a ,  19   b ,  19   c , and  19 ′ to disengage the snap features  80  and  80   a.    
     Surfaces  73  and  73   a  ( FIGS. 13-16(   b )) of the protractor component  5  are intended to have a radius that is constant, or that increases or decreases linearly in proportion to angular rotation, and an overall shape that compliments and is in proximity to the surfaces  98  and  98   a  on the translation block  6  ( FIGS. 17-21(   b )) such that the protractor component  5  is able to rotate unobstructedly ( FIGS. 26(   a )- 26 ( d )) when the components  4 ,  5 ,  6 , and  7  are in the assembled  3  and unlocked state  149  ( FIG. 28(   a )). Further, the surfaces  98  and  98   a  on the protractor component  5 , or the optional elastomeric or rubber material that may be adhered to these surfaces  98  and  98   a , should impart sufficient friction on surfaces  73 ,  73   a  (of the protractor component  5 ) to arrest the rotational motion of the protractor component  5  when the components  4 ,  5 ,  6 ,  7  are in the assembled state  3  and the protractor unit  3  is manipulated to the angle-locked or fully-locked state as described below. 
     Recessed surfaces  64  and  64   a  ( FIGS. 13-16(   b )) have a select and preferably constant depth and have a width that ranges from the surfaces  73  and  73   a  to the back walls  68  and  68   a . These surfaces  64  and  64   a  should be in proximity to the surfaces  95  and  95   a  on the translation block  6  ( FIGS. 17-21(   b )) and have sufficient depth to allow the surfaces  95  and  95   a  to slide unobstructedly over surfaces  64  and  64   a  when the components  4 ,  5 ,  6  and  7  are in the assembled state  3 , regardless of whether the protractor unit  3  is in a locked  147 , 148  or unlocked state  149  ( FIGS. 28(   a )- 28 ( c )). Further, these recessed surfaces  64  and  64   a  in cooperation with the surfaces  95  and  95   a , in addition to the snap features  55 ,  55   a ,  55   b ,  55   c  ( FIG. 11) , prevent the surfaces  60  and  60   a  on the component  5  from flaring outward away from the planes XVI(a)-XVI(a)&#39; and XVI(b)-XVI(b)&#39; when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3 . 
     Additionally, the back walls  68  and  68   a  ( FIGS. 13-16(   b )) on the protractor component  5  should not contact the surfaces  97  and  97   a  on the translation block  6  ( FIGS. 17-21(   b )) when the components  4 ,  5 ,  6 , and  7  are in the assembly state  3 , regardless of whether the components  4 ,  5 ,  6  and  7  are in motion and regardless of whether the protractor unit  3  is in a locked  148 ,  147  or unlocked state  149 . 
     Mating elements  65 - 65   i  and  65   l - 65   t  ( FIGS. 13-16(   b )) are optional and can be configured in patterns, pluralities, single sets or a set, or located anywhere about the surfaces  73  and  73   a . These features  65 - 65   i  and  65   l - 65   t  are preferably semi-circular in shape and are intended to mate with the feature  94  on the translation block  6  ( FIGS. 17-21(   b )) for the purpose of providing a method of tactilely feeling select common angles prior to locking said angles, when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3 . The mechanism by which this is accomplished is as follows: as the sliding lock  7  ( FIGS. 22-25(   b )) is moved so as to put the protractor unit  3  in either the angle-locked  148  or fully-locked state  147  , the translation block  6  itself and specifically, the block&#39;s  6  surfaces  98  and  98   a  move towards the surfaces  73  and  73   a  on the protractor component  5 , or towards the optional elastomeric or rubber material that may be adhered to the surfaces  73  and  73   a , in order to arrest the rotational motion of the protractor component  5 ; prior to the friction locking of protractor component&#39;s  5  rotation motion, stop feature  94  on the translation block engages the mating elements  65 - 65   i  and  65   l - 65   t  on the protractor component  5 , causing a perceivably loose and semi-permanent stop in the protractor component&#39;s  5  rotation. 
     The protractor component  5  ( FIGS. 13-16(   b )) also contains angle markings on each of its surfaces  60  and  60   a  which corresponds to the angle that is created between two ruler units  2 ,  2 ′ when one ruler  2  is slidably engaged to a protractor unit  3  and another ruler  2 ′ is laterally fastened to the same protractor unit  3 , as shown in  FIGS. 26(   a ) through  26 ( d ). The correct angle can be read by aligning the angle markings on the protractor component  5  with the reference markings  90  and  90   a  on the translation block  6  ( FIGS. 17-21(   b )). 
     Generally referring to  FIGS. 1(   a )- 2 ,  FIG. 8 , and  FIGS. 17-21(   b ), the translation block  6  a component of the protractor unit  3  has rectangular tubular internal  105  and external cross-sectional shape and dimensions that cooperate with the intended motions and functions of the translation block  6  itself and the components  4 ,  5 , and  7  of the protractor unit  3  when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3  and the protractor unit  3  is either slidably engaged to a protractor unit  3  or laterally fastened to a protractor unit  3 , or both. 
     The translation block  6  ( FIGS. 17-21(   b )) contains the following major features: the locking surfaces  98  and  98   a  ; recessed surfaces  95  and  95   a ; curved surfaces  89 ,  89   a ,  97 , and  97   a  ; mating feature  92  and  94 ; guiding elements  86  and  86   a ; mating tracks  88  and  88   a ; and gauge marking  90  and  90   a . Additionally, these features are all symmetrical about the plane C-C′, as shown in  FIGS. 18 . 
     Component  6  ( FIGS. 17-21(   b )) assembles onto the assembly block  4  with components  5  and  7  ( FIG. 8  and  FIGS. 9-12)  such that: the translation block  6  is able to translate unobstructedly towards or away from the protractor component  5  when the sliding lock is manipulated to one of the locked  147 ,  148  or unlocked states  149  ( FIGS. 28(   a )- 28 ( c )); the protractor component  5  is able to rotate unobstructedly when the protractor unit  3  is in an unlocked state  149 ; the sliding lock  7  is able to slide unobstructedly regardless of whether the protractor unit  3  is in a locked  147 ,  148  or unlocked state  149 ; the inner surfaces  96  and  96   a  of the translation block  6  are in contact with or in proximity to the outward-facing surfaces of the center bodies  26  and  26   a  ( FIG. 11)  and the minor surfaces  10 ,  10   a ,  10   b ,  10   c ,  10 ′,  10   b ′ of the ruler  2 ,  2 ′ ( FIGS. 1(   a )- 7 ( b )); the internal side walls of the translation block  6  are to be in close proximity to the side walls of the side bodies  29  and  30  of the assembly block  4  ( FIGS. 9-12) . 
     Surfaces  98  and  98   a  and  97  and  97   a  ( FIGS. 17-21(   b )) are to be concentric with each other and concentric with and compliment in both shape and cross-sectional dimensions the mating surfaces  73  and  73   a  and  68  and  68   a  on the protractor component  5  ( FIGS. 13-16(   b )) when the components  4 ,  5 ,  6  and  7  are in the assembled state  3 . Also, the surfaces  98  and  98   a  are to not engage the surfaces  73  and  73   a  so as to allow the protractor component  5  to rotate unobstructedly when the protractor unit  3  is in an unlocked state  149  ( FIG. 28(   a )), but are to engage the surfaces  73  and  73   a  of the protractor component  5  when the protractor unit  3  is manipulated to the locked state  147 ,  148  ( FIGS. 28(   b )- 28 ( c )), as described herein, such that surfaces  98  and  98   a  impart sufficient friction on surfaces  73  and  73   a  to arrest the rotational motion of the protractor component  5 . Additionally, the surfaces  98  and  98   a  may be coated or covered with a polymeric, elastomeric, or rubber material in order to increase the effectiveness of locking by friction, as described above. Also, the surfaces  97  and  97   a  should not contact the surfaces  64  and  64   a , regardless of whether the protractor unit  3  is in a locked state  147 ,  148  or not  149 . 
     Recessed surfaces  95  and  95   a  ( FIGS. 17-21(   b )) have a select and preferably constant depth and have a width that ranges from the surfaces  97  and  97   a  to the back walls  98  and  98   a  . These surfaces  95  and  95   a  should be in proximity to the surfaces  64  and  64   a  on the protractor component  5  ( FIGS. 13-16(   b )) and have sufficient depth to allow the surfaces  64  and  64   a  to slide unobstructedly over the surfaces  98  and  98   a  when the components  4 ,  5 ,  6  and  7  are in the assembled state  3 , regardless of whether the protractor unit  3  is a locked  147 ,  148  or unlocked state  149  ( FIGS. 28(   a )- 28 ( c )). Further, these recessed surfaces  95  and  95   a  in cooperation with the surfaces  64  and  64   a  prevent the surfaces  60  and  60   a  on the protractor component  5  from flaring outward away from the planes XVI(a)-XVI(a)&#39; and XVI(b)-XVI(b)&#39;, shown in  FIG. 15(   a ) when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3 . 
     Surfaces  89  and  89   a  ( FIGS. 17-21(   b )) on the translation block  6  are to be concentric with and compliment in both shape and cross-sectional dimensions the surfaces  142 ,  142   a , and  142   b  on the sliding lock  7  ( FIGS. 22-25(   b )) when the components  4 ,  5 ,  6  and  7  are in the assembled state  3 . Also, the surfaces  89  and  89   a  should not impart force on the surfaces  142  and  142   a  when the protractor unit  3  is in an unlocked state  149  ( FIG. 28(   a )), but should impart a force on the surfaces  142 ,  142   a , and  142   b  to cause the translation block  6  to translate towards the protractor component  5  and lock rotational motion, when the protractor unit  3  is manipulated to either the angle-locked  148  or full-locked  147  state ( FIGS. 28(   b )- 28 ( c )) in cooperation with the mechanisms as described herein. 
     Tracks  87  &amp;  88  and  87   a  &amp;  88   a  ( FIGS. 17-21(b) ) are optional and parallel or concentric with the surfaces  89  and  89   a  on the translation block  6  itself and compliment the shape of the tracks  137  &amp;  136  and  137   a  &amp;  136   a  on the sliding lock  7  ( FIGS. 22-25(   b )), respectively, such that tracks  87  &amp;  88  and  87   a  &amp;  88   a  slidably engage the tracks  137  &amp;  136  and  137   a  &amp;  136   a , and the sliding lock  7  is able to slide unobstructedly so that sliding lock  7  can effect either a locked  147 ,  148  and unlocked state  149  ( FIGS. 28(   b )- 28 ( c )) in the protractor unit  3 , as described herein, assuming the components  4 ,  5 ,  6 , and  7  are in the assembled state  3  and the sliding protractor  3  is slidably engaged or laterally fastened to a ruler  2 ,  2 ′, or both slidably engaged and laterally fastened to rulers  2 ,  2 ′. 
     Features  86  and  86   a  ( FIGS. 17-21(   b )) on the translation block  6  are optional; if present, however, these features  86  and  86   a  preferably have a rectangular shape, but can also be of any shape as long as both its  86  and  86   a  shape and cross-dimensions cooperate with those of the guide elements  35  and  35   a  on the assembly block  4  ( FIGS. 9-12)  such that they  86  and  86   a  can slidably engage the guide elements  35  and  35   a  and guide the translation block  6  to translate to and from the protractor component  5  ( FIGS. 1(   a )- 2  &amp;  8 ) without lateral or rotational movement when the sliding lock  7  is manipulated to cause the protractor unit  3  to be in either a locked  147 ,  148  or unlock state  149  ( FIGS. 28(   a ) through  28 ( c )), assuming that the components  4 ,  5 ,  6  and  7  are in the assembled state  3  and that when the sliding protractor component  3  is being handled independently of any ruler  2 ,  2 ′. 
     Feature  92  ( FIGS. 17-21(   b )) of translation block  6  is optional, but if present has a shape and cross-sectional dimensions that is to cooperate with that of feature  31  on the assembly block  4  ( FIG. 9-12)  such that these features  92  and  31  are able to mate and remain mated when the translation block  6  translates to or away from the protractor component  5  ( FIGS. 13-16(   b )) when the sliding lock  7  ( FIGS. 22-25(   b )) is manipulated to lock  147 ,  148  or unlock  147  the protractor unit  3  ( FIGS. 28(   a )- 28 ( c )). This feature  92  is also a redundancy that is intended to prevent lateral and rotational movement of the translation block  6  in the event that the guiding elements  35  and  35   a  on the assembly block  4  undergo material failure and are unable to properly mate and cooperate with the guiding elements  86  and  86   a  of the translation block  6 . 
     Stop feature  94  ( FIGS. 17-21(   b )) on the translation block  6  is optional, and if present, stop feature  94  preferably has a semi-circular in shape that that compliments that of the mating elements  65 - 65   i  and  65   l - 65   t  and is intended to mate with the mating elements  65 - 65   i  and  65   l - 65   t  for the purpose of providing a method of tactilely feeling select common angles on the protractor component  5  ( FIGS. 13-16(   b )) when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3  and the protractor unit  3  has both a ruler  2 ,  2 ′ slidably engaged and laterally fastened to the protractor unit  3  ( FIGS. 26(   a )- 26 ( d )); the mechanism by which this occurs has been described previously. 
     Marking  90  and  90   a  ( FIGS. 17-21(   b )) on the translation block are intended to act as reference marks for reading the angle marking on the protractor component  5  ( FIGS. 13-16(   b )) that corresponds to the angle that is created between rulers  2 ,  2 ′ that are slidably engaged and laterally fastened to the same protractor unit  2  ( FIGS. 26(   a )- 26 ( d )). 
     The translation block  6  ( FIGS. 17-21(   b )) is also, preferably, composed of two symmetrical halves  6   a  and  6   b  as shown in  FIGS. 21(   a ) and  21 ( b ), the purpose of which is to facilitate the assembly of the translation block  6  onto the assembly block  4  ( FIGS. 9-12) . These two halves  6   a  and  6   b  can be put together into one part  6  by mating the features  110 ,  110   a ,  110   b , and  110   c  on the subcomponent  6   a  with the features  115 ,  115   a ,  115   b , and  115   c  on the subcomponent  6   b  such that the surfaces  116 ,  116   a  and  116   b  and surfaces  111 ,  111   a , and  111   b , respectively, are in contact or in proximity to each other. An adhesive can also be used to achieve a cohesive bond of appropriate strength between the two halves  6   a  and  6   b.    
     Generally referring to  FIGS. 1(   a )- 2 ,  FIG. 8 , and  FIGS. 22-25(   b ), the sliding lock  7 , a component of the protractor unit  3 , has rectangular internal tubular  105  shape and external cross-sectional shape with curved front  134 ,  134   a ,  142 ,  142   a , and  142   b  and back surfaces  131  and  131   a  that the compliment the shape of the back surface of the translation block  6  that facilitate sliding; the shapes of the surfaces  131 ,  131   a    134 ,  134   a ,  142 ,  142   a , and  142   b  should cooperate with the intended motions and functions of the sliding lock  7  itself and the components  4 ,  5 ,  7  of the protractor unit  3  when the components  4 ,  5 ,  6 , and  7  ( FIG. 8)  are in the assembled state  3  and the protractor unit  3  is either slidably engaged ( FIG. 1(   a )) or laterally fastened to a protractor unit  3 , or both ( FIGS. 26(   a )- 27 ( c )). 
     The sliding lock  7  ( FIGS. 22-25(   b )) contains the following major features: curved guiding slots  145  and  145   a ; tracks  136 ,  136   a ,  137 , and  137   a ; the shoulder elements  170 ,  171 ,  171   a ,  172  and  170   a ,  171   b ,  171   c ,  172   a ; unlock, angle lock, and full lock markings  149   a ,  148   a , and  147   a , respectively. Additionally, these features are all symmetrical about the plane D-D′ as shown in  FIGS. 24 . 
     Sliding lock component  7  ( FIGS. 22-25(   b )) assembles onto the assembly block  4  ( FIGS. 9-12)  such that: the translation block  6  ( FIGS. 17-21(   b )) is able to translate unobstructedly towards or away from the protractor component  5  ( FIGS. 13-16(   b )) when the sliding lock  7  is manipulated to one of the locked  147 ,  148  or unlocked  149  states ( FIGS. 28(   a )- 28 ( c )); the sliding lock  7  is able to slide unobstructedly regardless of whether the protractor unit  3  is in a locked  147 ,  148  or unlocked state  147 ; the inner surfaces  138  and  138   a  of the translation block  6  are in contact with or in proximity to the outward-facing surfaces of the center bodies  26 ,  26   a  ( FIG. 11)  and the minor surfaces  10 ,  10   a ,  10   b ,  10   c ,  10 ′,  10   b ′ of the ruler  2 ,  2 ′ ( FIGS. 1(   a )- 7 ( b )); the curved guiding slots  145  and  145   a  are slidably engaged to the guide elements  40  and  40   a  on the assembly block  4 , and the shoulder elements  47  and  47   a  are slidably engaged to the shoulder elements  170 ,  171 ,  171   a ,  172  and  170   a ,  171   b ,  171   c , and  172   a , regardless of whether the protractor unit  3  is in a locked  147 ,  148  or unlocked  149  state; the internal sides walls  139  and  141  of the sliding lock  7  act as a stop to the lateral and rotational sliding motion of the sliding lock  7  when the side surfaces  139  and  141  contact the side walls  22 ,  22   a , and  22 ′ of ruler  2 ,  2 ′ ( FIGS. 1(   a )- 7 ( b )). 
     Guiding slots  145  and  145   a  ( FIGS. 22-25(   b )) are slots that are preferably curved in shape, but that can also be of any shape as long as they  145 ,  145   a  perform their intended function as described herein. These guiding slots  145 ,  145   a  are intended to slidably engage the guide elements  40  and  40   a  on the assembly block  4  ( FIGS. 9-12)  such that the sliding lock  7  is able to slide laterally and rotationally without obstruction when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3  and in order to place the protractor unit  3  in either a locked  147 ,  148  or unlocked state  149  ( FIGS. 28(   a )- 28 ( c )). 
     The position and cross-sectional dimensions of the guide slots  145  and  145   a  ( FIGS. 22-25(   b )) and orientation of curved surfaces  152  and  152   a , which characterize the guiding slots  145  and  145   a , is such that they are concentric with the surfaces  73  and  73   a  ( FIGS. 13-16(   b )) on the protractor component  5  when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3  and such that when the slots  145  and  145   a  are slid through the guide elements  40  and  40   a  on the assembly block  4  ( FIGS. 9-12) , the engagement of the guide elements  40  and  40   a  with the curved surfaces  152  and  152   a , regardless of where along the surfaces  152  and  152   a  this engagement occurs, is such that the sliding lock  7  is situated on the assembly block  4  so as to impart a force on the translation block  6  and the translation block  6  is situated on the assembly block  4  so as to impart a force on the protractor component  5 . The force that the translation block  6  imparts on the protractor component  5  creates friction and that friction is sufficient to arrest rotation motion of the protractor component  5 , as previously described. Also, when the guide elements  40  and  40   a  engage the curved surfaces  151  and  151   a , the components  4 ,  5 ,  6 , and  7 , when in assembled, do not cooperate to effect rotational locking of the protractor component  5 . 
     Shoulder elements  170 ,  171 ,  171   a ,  172  and  170   a ,  171   b ,  171   c ,  172   a  ( FIGS. 22-25(   b )) on the sliding lock  7  consist of recessed surfaces of varying depth and are intended to slidably engage and cooperate with the shoulder elements  47  and  47   a  on the assembly block  4  ( FIG. 9-12)  such that the shoulder elements  170 ,  171 ,  171   a ,  172  and  170   a ,  171   b ,  171   c ,  172   a  along with shoulder elements  47  and  47   a  and center bodies  26  and  26   a  are able to lock the translational movement of the protractor unit  3  when the protractor unit  3  is slidably engaged to a ruler  2 ,  2 ; the mechanism is described in greater detail below. The depths and positions of these shoulder elements  170 ,  171 ,  171   a ,  172  and  170   a ,  171   b ,  171   c ,  172   a  should cooperate with the shoulder elements  47  and  47   a  on the assembly block  4  such that these elements  170 ,  170   a ,  171 ,  171   a ,  171   b ,  171   c ,  172 ,  172   a  able to perform their intended functions. 
     Unlock, Angle Lock, and Full Lock markings  149   a ,  148   a , and  147   a  ( FIGS. 22-25(   b )), respectively, are reference labels on the sliding lock  7  ( FIGS. 22-25(   b )) that indicate whether the system is either in an unlocked  149  ( FIG. 28(   a )), angle-locked  148  ( FIG. 28(   b )), or full-locked state  147  ( FIG. 28(   c )), which occurs when the sliding lock  7  is slid laterally and rotationally on the assembly block  4  ( FIGS. 9-12)  as previously described and such that the guide elements  40  and  40   a  on the assembly block  4  are positioned as close to the center positions of these markings  149   a ,  148   a , and  147   a  as material constraints permit. The action of sliding the sliding lock  7  such that the guide elements  40  and  40   a  are in proximity to any these positions  149   a ,  148   a , and  147   a , causes the protractor unit  3  to achieve the particular state  149 ,  148 ,  147  that is indicated by the respective reference marking: when the guide elements  40  and  40   a  are in proximity to the Unlock reference marking  149   a , the protractor unit  3  is in the unlocked state  149 , and thus the protractor unit  3  is free to translate and the protractor component is free to rotate; when the guide elements  40  and  40   a  are in proximity to the Angle Lock reference marking  148   a , the protractor unit  3  is in an angle-locked state  148 , and thus, while the protractor unit  3  is free to translate, the protractor component  5  ( FIGS. 13-16(   b )) is not free to rotate; and when the guide elements  40  and  40   a  are in proximity to the Full Lock reference marking  147   a , the protractor unit  3  is in a fully-locked state  149 , and thus, the protractor unit  3  is not free to translate, nor the protractor component  5  is not free to rotate. 
     Tracks  136  &amp;  137  and  136   a  &amp;  137   a  on the sliding lock  7  ( FIGS. 22-25(   b )) are optional and parallel or concentric with the surfaces  142 ,  142   a , and  142   b  on the sliding lock  7  itself and compliment the shape of the tracks  87  &amp;  88  and  87   a  &amp;  88   a  on the translation block  6  ( FIGS. 17-21(b) , respectively, such that the tracks  136  &amp;  137  and  136   a  &amp;  137   a  slidably engage the tracks  87  &amp;  88  and  87   a  &amp;  88   a , and the sliding lock  7  is able to slide unobstructedly, so that sliding lock  7  can lock  147 ,  148  or unlock  149  ( FIGS. 28(   a )- 28 ( c )) the protractor unit  3  as described herein, when the components  4 ,  5 ,  6 , and  7  are in the assembled state and the sliding protractor unit  3  is slidably engaged or laterally fastened to a ruler  2 ,  2 ′, or both. 
     The sliding lock  7  ( FIGS. 22-25(   b )) is also, preferably, composed of two symmetrical halves  7   a  and  7   b  as shown in  FIGS. 25(   a ) and  25 ( b ), the purpose of which is to facilitate the assembly of the sliding lock  7  onto the assembly block  4  ( FIG. 9-12) . These two halves  7   a  and  7   b  can be put together into one part  7  by mating the features  185 ,  185   a ,  185   b , and  185   c  on the subcomponent  7   a  with the features  180 ,  180   a ,  180   b ,  180   c  on the subcomponent  7   b  such that the surfaces  186  and  186   a  and surfaces  181  and  181   a , respectively, are in contact or in proximity to each other. An adhesive can also be used to achieve a cohesive bond of appropriate strength between the two halves  7   a  and  7   b.    
     Referring to  FIGS. 1-2  and  FIGS. 8-25(   b ), the internal cross-sectional shape and dimensions  46 ,  76 ,  105 ,  160  ( FIGS. 8-25(   c )) of the components  4 ,  5 ,  6 , and  7 , respectively, are to accommodate and compliment the cross-sectional shape and dimensions of the ruler  2 ,  2 ′ such that when the components  4 ,  5 ,  6  and  7  are in the assembled state, these internal cross-sections  46 ,  76 ,  105 ,  160  allow the protractor unit  3  to slide unobstructedly along the length of a ruler  2 ,  2 ′ or consecutive assembly of rulers  100  ( FIGS. 1(   a )- 7 ( b )). Additionally, the top  28 ,  60 ,  85 ,  130  and bottom outer surfaces  28   a ,  60   a ,  85   a ,  130   a  of the components  4 ,  5 ,  6 , and  7 , respectively, are to be proximally coplanar or coplanar when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3 . 
     Referring to  FIGS. 1(   a ) through  25 ( b ), all fastening features described herein can be of any type, shape or configuration, and either member of each pair can be either the male or female member of the fastening unit, as long as the members of each pair complement each other and allow the parent components and assemblies  2 ,  3 ,  4 ,  5 ,  6 , and  7  to cooperate with each other and function as intended and as described herein; e.g., locking elements  20 ,  20   a ,  20   b ,  20   c , and  20 ′ and tracks  16  and  16   a ; tracks  17 ,  17   a ,  17   b ,  17   c , and  17 ′and locking elements  23   a  and  23   c ; snap features  18 ,  18   a ,  18   b , and  18 ′ and snap features  25 ,  25   a ,  25   b , and  25   c ; locking elements  20 ,  20   a ,  20   b ,  20   c , and  20 ′ and track  81 ; snap features  19 ,  19   a , and  19 ′ and snap features  80  and  80   a ; snap features  55 ,  55   a ,  55   b , and  55   c  and features  67  and  67   a ; slots  61  and  61   a  and elements  27  and  27   a ; slots  86  and  86   a  and features  35  and  35   a ; slots  145  and  145   a  and elements  40  and  40   a , etc. Further, additional fastening fasteners, elements, or features, such as a pin(s), screws and bolts, rivets, grooves, cams, snap features, taper fits, etc., may be added to any of the above fastening pairs or components in order to complete the intended fastening units or achieve the intended cooperation between components and assemblies  2 ,  3 ,  4 ,  5 ,  6 , and  7 . 
     When the components  4 ,  5 ,  6 , and  7  are in the assembled state or states ( FIGS. 8 and 26(   a )- 33 ( b )), they compose the protractor unit  3 ,  3 ′,  3 ″ which itself may be a standalone device that can be manipulated so as to engage and interact with rulers  2 ,  2 ′ ( FIGS. 1(   a )- 5 (c)), consecutive ruler-unit assemblies  100 , ( FIGS. 6(   a )- 7 ( b )), and protractor-ruler assemblies  200  ( FIGS. 26(   a )- 26 ( c )) to create ruler-protractor super-assemblies, such as assemblies  200 ,  300 ,  301 ,  400 ,  401 ,  500 ,  600 ,  800 ,  801  ( FIGS. 29(   a )- 33 ( b )). 
     A single protractor unit  3 ,  3 ′,  3 ″ can simultaneously fasten a maximum of two rulers units  2 ,  2 ′,  2 ″ ( FIGS. 1(   a )- 4 ( b )), two ruler assemblies  100  ( FIG. 6(   b )- 7 ( b )), or two configured protractor-ruler assemblies  200 ,  300 ,  301 ,  400 ,  401 ,  500 ,  600 ,  800  ( FIGS. 26(   a )- 33 ( b ))—by two different methods: by the first method, the protractor unit  3 ,  3 ″, 3 ″ can be slid onto ruler  2 ,  2 ′,  2 ″ such that the internal cross-sections  46 ,  76 , 105 , and  160  ( FIGS. 8-25(   b )) of the components  4 ,  5 ,  6 , and  7  ( FIG. 8)  mate with the external cross-section and shape of a ruler(s)  2 ,  2 ′,  2 ″, or assemblies containing the same, such that the protractor unit  3 ,  3 ′,  3 ″ is slidably engaged to a ruler  2 ,  2 ′,  2 ″, as shown in  FIG. 1(   a ) and in the same manner, the protractor unit  3 ,  3 ′,  3 ″ can also be unfastened from a ruler  2 ,  2 ′,  2 ″ being slid of one  2 ,  2 ′,  2 ′″; by the second method, the protractor component  5  ( FIGS. 13-16(   b )) can laterally fasten a ruler  2 ,  2 ′,  2 ″ to itself  5  as shown in  FIGS. 27(   a ) through  27 ( c ) by use of a semi-permanent snap mechanism and in the same manner, unfasten a ruler  2 ,  2 ′,  2 ″ from itself  5 , as described in detail below. 
     Referring to  FIGS. 27(   a ) through  27 ( c ), to laterally fasten a ruler  2 ′ to a protractor unit  3 , slide a set of male locking elements  20 ,  20   a ,  20   b ,  20   c ,  20 ′ ( FIGS. 2-5(   b )), which are located on top and bottom surfaces of the male fasten elements  11 ,  11   a ,  11 ′ on either end  13 ,  13   a ,  13 ′ of any ruler unit  2 ′ into the track  81  of the protractor component  5  ( FIGS. 13-16(   b )) on a protractor unit  3  until the pertinent female snap feature  19 ,  19   a ,  19 ′ of the ruler  2 ,  2 ′ fully engage the male snap features  80  and  80   a  of the protractor component  5 . The engagement between the snap features  19 ,  19   a , and  19 ′ and snap features  80   80   a  is preferably semi-permanent. Also, assuming that the protractor unit  3  is slidably engaged to a first ruler  2 , it is intended that - the radius on the tip of the female fastening elements  12 ,  12   a ,  12 ′ on the second and laterally fastened unit ruler  2 ′ ( FIGS. 27(   a )- 27 ( c )) - be tangent or in proximity to the edge  22  of the slidably engaged ruler  2  such that the protractor component  5  of the protractor unit  3  is able to rotate unobstructedly when the components  4 ,  5 ,  6 , and  7  ( FIG. 8)  are in the assembled  3  and unlocked state  149  ( FIG. 28(   a )), as described herein. 
     Further, the particular end  13 ,  13   a ,  13 ′ of a ruler  2 ,  2 ′ ( FIGS. 2-5(   b )) that is to be mated with a protractor component  5  ( FIGS. 13-16(   b )) is typically chosen by selecting the unit measurement system that is preferred for the intended use, since as previously described, the measurement markings are on each minor surfaces  10  &amp;  10   b ,  10   a &amp;  10   c of the same top and bottom surfaces of a ruler  2 ,  2 ′ are of different unit measurement systems (e.g., empirical or metric). 
     To unfasten a ruler  2 ,  2 ′ from a protractor unit  3  ( FIGS. 27(   a )- 27 ( c )), pull the ruler  2 ,  2 ′ away from the center of the protractor component  5  ( FIGS. 13-16(   b )) until the snap features  19  and  19   a  ( FIGS. 4(   a )- 4 ( d )) of the ruler  2 ,  2 ′ disengage from the snap features  80  and  80   a  of the protractor component  5  and such that the locking elements  20 ,  20   a ,  20   b ,  20   c  on the ruler  2 ,  2 ′ ( FIGS. 2-4(   b )) are fully removed from the track  81  of the protractor component  5 . 
     The protractor unit  3  can also be locked at any position along the ruler&#39;s  2 ,  2 ′ length ( FIGS. 28(   a )- 28 ( c )), when the protractor unit  3  is manipulated to the fully-locked state  147  and while the protractor unit  3  is slidably engaged to a ruler  2 ,  2 ′. This fully-locked state  147  ( FIG. 28(   c )) can be achieve by sliding the sliding lock  7  ( FIGS. 22-25(   b )) to the full lock position  147   a  ( FIG. 23) . The mechanism by which this locking occurs is as follows: as the sliding lock  7  is moved toward the full lock position  147   a , the curved guiding slots  145  and  145   a  on the sliding lock  7  slide through the round guide elements  40  and  40   a  on the assembly block  4  ( FIGS. 9-12 ), causing the shoulder elements  170  and  170   a  on the sliding lock  7 , which engage the shoulder elements  47 ,  47   a , to slide away from the shoulder elements  47  and  47   a  until they engage the sloped shoulder elements  171 ,  171   a ,  171   b , and  171  c; as the sloped shoulder elements  171 ,  171   a ,  171   b , and  171   c  are slid past the shoulder elements  47  and  47   a , the shoulder elements  47  and  47   a  are forced towards each other due to intended material interference between the shoulder elements  47  and  47   a  and the sloped shoulder elements  171 ,  171   a ,  171   b , and  171   c ; this causes the center bodies  26 ,  26   a  (assembly block  4 ) and under surfaces  42 ,  42   a  to move toward and interfere with the material of the center tracks  8 ,  8   a ,  8 ′ of the ruler  2 ,  2 ′. This material interference creates sufficient friction to arrest the translation motion of the assembly block  4  and thus, the protractor unit  3 . Once the sloped shoulder elements  171 ,  171   a ,  171   b , and  171  c on are fully slid past the shoulder elements  47  and  47   a  on the assembly block  4  and engage the shoulder elements  172 ,  172   a ,  172   b , and  172   c  the sliding lock  7 , the medial displacement of the shoulder elements  47  and  47   a  is at maximum, as is the friction force, and remains so until the system is manipulated to an angle locked  148  ( FIG. 28(   b )) or unlocked state  149  ( FIG. 28(   a )) as described herein. 
     In order to lock the rotation of the protractor component  5  ( FIGS. 13-16(   b )) and any ruler  2 ,  2 ′ that is laterally fastened to the protractor component  5  ( FIGS. 27(   a )- 27 ( c )) when the components  4 ,  5 ,  6 , and  7  are in the assembled state  3 , the sliding lock  7  ( FIGS. 22-25(   b )) should be slid to either the Angle Lock  148   a  or Full Lock  147   a  position ( FIGS. 22 &amp; 23) ; this action causes the components  4 ,  5 ,  6 , and  7  to cooperate by the previously described mechanisms to arrest the rotational motion of the protractor component  5  and any ruler  2 ,  2 ′ that is laterally fastened to the protractor component  5 . 
     The use of the protractor unit  3 ,  3 ′ in conjunction with the other rulers  2 ,  2 ′ as described herein is the overall basis of at least one embodiment of the invention; thus, when the protractor unit  3 ,  3 ′,  3 ″ is both slidably engaged and laterally fastened to rulers  2 ,  2 ′, as shown in  FIGS. 26(   a )- 26 ( b ) and  29 ( a )- 33 ( b ), the protractor unit&#39;s components  4 ,  5 ,  6 , and  7 , all subcomponents of these components  4 ,  5 ,  6 , and  7 , and all bodies, features and sub-features of these components  4 ,  5 ,  6  and  7  cooperate with each other and each other&#39;s movement such that these components  4 ,  5 ,  6 , and  7  are able to function as intended and as described herein. 
     Generally referring to  FIGS. 26(   a ) through  33 ( b ), rulers  2 ,  2 ′,  2 ″ and protractor units  3 ,  3 ′,  3 ″ can be configured in pluralities to create myriad of different and complex geometric assemblies; e.g., assemblies  200 ,  300 ,  301 ,  400 ,  401 ,  500 ,  600 ,  800 ,  801 . The inner edges  22 ,  22   a ,  22 ′ of rulers  2 ,  2 ′,  2 ″ in these geometric assemblies create geometric and polygonal shapes. Both open-shaped assemblies  300 ,  401 ,  600 ,  801  and closed-shaped assemblies, such as triangles  301 , squares  400 , pentagons  500 , octagons  800 , etc., can be created. Additionally, any geometric assembly can be varied by: (i) changing the angle between and two rulers  2 ,  2 ′,  2 ″ ( FIG. 26(   a )- 26 ( b )) or sets of rulers  2 ,  2 ′,  2 ″ within the geometric assembly; (ii) by changing the scale or size of the geometric shape that characterizes a particular assembly, which can be done by sliding the protractor units  3 ,  3 ′,  3 ″ along any ruler  2 ,  2 ′,  2 ″ that the protractor unit  3 ,  3 ′,  3 ″ is slidably engaged to (e.g., the square assembly  400  in  FIG. 30(   b ) is larger than the square assembly  400  in  FIG. 30(   a ), but both create square shapes); (iii) rulers  2 ,  2 ′,  2 ″ can be consecutively fastened to other rulers  2 ,  2 ′,  2 ″ in ruler-protractor assemblies to form complex assemblies  600 ; and (iv) multiple protractor units  3 ,  3 ′,  3 ″ can slidably engage the same ruler  2 ,  2 ′,  2 ″ or assembly of consecutively-fastened rulers  100  ( FIG. 6(   a )- 6 ( b )) to form even more complex assemblies, super assemblies, and so on. 
     Also, when rulers  2 ,  2 ′,  2 ″ are configured in the said assemblies, such as assemblies  200 ,  300 ,  301 ,  400 ,  401 ,  500 ,  600 ,  800 , and  801 , the respective top and bottom surfaces of all rulers  2 ,  2 ′,  2 ″ within each assembly should closely all align or lie in the same plane, as should the respective top and bottom surfaces of all protractor units  3 ,  3 ′,  3 ″ and all components  4 ,  5 ,  6 ,  7  of protractor units  3 ,  3 ′,  3 ″. 
     Additionally, when geometric assemblies, such as assemblies  200 ,  300 ,  301 ,  400 ,  401 ,  500 ,  600 ,  800 , and  801 , are created by selecting the same unit measurement system marking (e.g., inches) to be near the inner edges  22 ,  22   a ,  22 ′ of each ruler  2 ,  2 ′,  2 ″ in the assembly, the entire assembly  200 ,  300 ,  301 ,  400 ,  401 ,  500 ,  600 ,  800 ,  801  can be flipped over so that the marking along the internal edges of each ruler  2 ,  2 ′,  2 ″ can then be read in the complimentary system (e.g., centimeters). 
     Last, it should be understood that the descriptions and examples of the invention stated herein are merely meant to be illustrative, rather than restrictive, as manifold variations of this invention, all components of this invention, and all features and sub-features of those components can reasonably be anticipated anyone skilled in the art. 
     Second Embodiment 
     In another embodiment, each of the components  2 ,  2 ′,  2 ″,  3 ,  3 ′,  3 ″,  4 ,  5 ,  6 , and  7  would function as previously described, but with a few exceptions: (i) the ruler  2 ,  2 ′,  2 ″ as shown in  FIGS. 1(   a )- 7 ( b ) and  FIGS. 26(   a )- 33 ( b ), would not contain the tracks  8 ,  8 ′, and  8   a , and rulers  2 ,  2 ′,  2 ″ external cross-sectional shape would not be rectangular as shown in  FIGS. 4(   a ) and  4 ( d ), but circular, center bodies  26  and  26   a  on the assembly block  4  ( FIGS. 9-12)  would not be recessed from the main block  56 , but an extension of the main block&#39;s  56  itself such that the surfaces  28  and  28   a  on the main block  56  are tangent with the outward facing surfaces of the center bodies  26  and  26   a , respectively, and such that the under surfaces  42  and  42   a  of the center bodies  26  and  26   a  do not interrupt the internal cross-sectional dimension  46  of the assembly block  4 , but are tangent with the surfaces  48  and  48   a  of the main block; the internal cross-sectional shapes and dimensions  46 ,  76 ,  105 ,  160  ( FIGS. 8-25(   c )) of the components  4 ,  5 ,  6 , and  7 , respectively, should be tubular and should accommodate or otherwise compliment the external cross-sectional shape and dimensions of the ruler  2 ,  2 ′,  2 ″ such that when the components  4 ,  5 ,  6  and  7  are in the assembled state of the protractor unit  3 ,  3 ′,  3 ″, these internal cross-sections  46 ,  76 ,  105 ,  160  allow the protractor unit  3 ,  3 ′,  3 ″ to slide unobstructedly along a ruler  2 ,  2 ′ or consecutive assembly of rulers  100  ( FIGS. 1(   a )- 7 ( b )). 
     The external cross-sectional shapes of the components  4 ,  5 ,  6 , and  7  under this embodiment are generally circular, too, and should substantially accommodate all features, sub-features, bodies, and the internal cross-sectional shapes  46 ,  76 ,  105 ,  160  of each component  4 ,  5 ,  6 , and  7 , respectively, as described herein. 
     The variation in the external cross-sectional shape of the ruler  2 ,  2 ′,  2 ″ and internal cross-sectional dimensions  46 ,  76 ,  105 ,  160  of the components  4 ,  5 ,  6 , and  7 , not only allows the protractor unit  3 ,  3 ′,  3 ″ to slidably engage the ruler  2 ,  2 ′,  2 ″, it confers an additional benefit: the siding protractor unit  3 ,  3 ′,  3 ″ itself can now be rotated around the ruler  2 ,  2 ′,  2 ″ in to the 3 rd  dimension and slide along a ruler  2 ,  2 ′,  2 ″; thus, rulers  2 ,  2 ′,  2 ″ can be laterally fastened to protractor unit  3 ,  3 ′,  3 ″ in the 3 rd  dimension, while the protractor unit  3 ,  3 ′,  3 ″ is still able to rotate in order to create angles between slidably engaged and laterally fastened ruler  2 ,  2 ′,  2 ″. 
     Additionally, rulers, under this embodiment, would have both linear distance measurement markings (e.g., centimeters, inches, etc.) and angle measurement markings at select locations on the circumferential surface of their cylindrical shape (circular cross-section) so that these marking do not interfere with each other. The former are to be oriented longitudinally along the ruler, and the later are to be oriented circumferentially about the circumferential surface of the ruler. Further, the said angle marking indicate the angle of rotation between the ruler and the protractor unit when the protractor unit is rotated about the longitudinal axis of a slidably engaged ruler(s). 
     Lateral fastening of a ruler  2 ,  2 ′,  2 ″ to the protractor components  5  ( FIGS. 27(   a )- 27 ( c )) of protractor units  3 ,  3 ′,  3 ″ would still work in the manner previously described, as would the fastening of rulers  2 ,  2 ′,  2 ″ to rulers  2 ,  2 ′,  2 ″ to create consecutive ruler assemblies  100  ( FIG. 6(   a )- 7 ( b )). Rulers  2 ,  2 ′,  2 ″ would contain the same fastening features, elements, and sub-features at each of their ends  13 ,  13   a ,  13 ′ The triangular-shaped ends  13 ,  13   a ,  13 ′ of each ruler  2 ,  2 ′,  2 ″ could still have a rectangular cross-section for mating purposes, or can be circular, as long as all of the male and female mating features on the rulers  2 ,  2 ′,  2 ″ ends  13 ,  13 ′,  13 ″ are adjusted appropriately to cooperate with fastening to other the rulers  2 ,  2 ′,  2 ″ for purpose of creating consecutive-ruler assemblies  100  and to the protractor components  5  for the purpose of creating ruler-protractor assemblies  200  ( FIGS. 26(   a )- 27 ( c )). 
     The protractor component  5  ( FIGS. 13-16(   b )), under this embodiment, would also have a swivel or rotatable block preceding the fastening features and mechanism responsible for laterally fastening the protractor unit to rulers. Rotation of the said block would break the plane of the protractor component and would allow rulers to be twisted into the 3 rd  dimension when rulers are laterally fastened to protractor components. Further, rotation of this block also allows all three degrees of rotation—i.e., rotation about the x-, y-, and z-axis, to be covered by the design, so that there are no orientation related mating issues between rulers and protractor units when they are mating to each other in the 3 rd  dimension. Additionally, the rotating block or the part of the protractor component that it is attached to can also have angle markings on its external surfaces so that the angle of rotation can be measured or selected as well. 
     Additionally, components  4 ,  5 , and  6 , as well as all features, sub-features, and bodies of these components  4 ,  5 , and  6  and assemblies would function in the same general manner as previously described. The sliding lock  7  (FIGS.  22 -= 25 ( b )), however, due to its circular internal and external cross-sectional shape, under this embodiment, would function differently than previously described: instead of sliding to achieve angle locking  148 , full locking  147 , and unlocking ( FIGS. 28(   a )- 28 ( c )) of the protractor unit when the protractor unit is slidably and laterally engaged to rulers, the sliding lock would rotate to achieve locking and unlocking of the protractor unit. The mechanism by which the sliding lock achieves these locked and unlocked states would remain the same as those described in the first embodiment. 
     The curved slots  145  and  145   a  on the sliding lock  7  ( FIGS. 22-25(   b )), under this embodiment, would still slidably engage the guide elements  40  and  40   a  on the assembly block  4  ( FIGS. 28(   a )- 28 ( c )), but would not be mirror images of each other  145  and  145   a , as described in the first embodiment; instead they  145  and  145   a  would be rotational symmetrical to each other, as would the orientation of the shoulder elements  170 ,  171 ,  171   a ,  172  and  170   a ,  171   b ,  171   c ,  172   a , respectively. All other aspects of the sliding lock remain the same and function as described in the first embodiment. 
     Ultimately, geometric assemblies, such as assemblies  200 ,  300 ,  301 ,  400 ,  401 ,  500 ,  600 ,  800 , and  801 , can be made even more complex by rotating either the protractor unit or the rotating block on the protractor unit, or both, into the 3 rd  dimension. 
     Third Embodiment 
     In another embodiment, all components  2 ,  2 ′,  2 ″,  4 ,  5 ,  6 , and  7  (FIGS.  1 ( a )- 25 ( b )), as well as their features and sub-features, and assemblies  3 ,  3 ′,  3 ″,  100 ,  200 ,  300 ,  301 ,  400 ,  401 ,  500 ,  600 ,  800 ,  801  ( FIGS. 26(   a )- 33 ( b )) would function in the same manner as previously described in the first two embodiments; however, the only difference would be that features  27  and  27   a  on the assembly block  4  ( FIGS. 9-12)  and features  61  and  61   a  on protractor component  5  ( FIGS. 13-16(   b )) would not be positioned at a radius  900  ( FIG. 10) , but rather the center point  901  of the circle corresponding to the radii of the surfaces  73  and  73   a  of the protractor component  5 , and features  27 ,  27   a  and  61 ,  61   a  would not slidably engage each other as in the first two embodiments, but rotationally engage each other. The position of the pivot point, which is in fact intended to be the same point as the center point  901  of the circle  900  created by the surfaces  73  and  73   a , is to be selected as described in the first embodiment.