Abstract:
A multi-functional measuring device made of lightweight material planed on one edge in a succession of ascending and descending steps representing dimensional increments. Successive steps ascend over one-half the length of the device and, at the mid-point, level off and begin to descend in dimensional increments for the remaining length, providing a visual image and tactile profile for the user. Centerline notches are cut on both the upper and lower edges, and are used to locate the center point of an object. High and low profiles are cut into specific locations to allow for visual and tactile determination of specific subdivision dimensions. A notch is provided at each end of the device to accommodate linear measurements exceeding the length of the device. The lower face surface is punctuated with a series of holes. Small diameter holes, marking dimensional increments, are arranged in a straight line parallel to the lower edge, opposite the ascending and descending steps. Large diameter holes, marking additional dimensions, are arranged in an alternating pattern with the small diameter holes.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     None  
       STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT  
       [0002]     None  
       REFERENCE TO SEQUENCE LISTING, A TABLE, OR A COMPUTER PROGRAM LISTING COMPACT DISK APPENDIX  
       [0003]     None  
       BACKGROUND OF THE INVENTION  
       [0004]     1. Field of the Invention  
         [0005]     The field of this invention is measuring devices. Vast multitudes of measuring devices have been created and used through the course of time to measure not only linear dimensions but also non-linear dimensions. Measuring devices allow the user to qualify spatial relationships observed in a two dimensional format. Systems of measurement are based on either the English system with the foot as the base unit of measure or the metric system with the meter as the base unit of measure. The English system is divided into fractional parts and the metric system is divided into decimal portions of the meter.  
         [0006]     The present invention relates to a measuring apparatus and methods for measuring and proportioning linear distances, more particularly to tactilely accessible measuring devices for teaching recognition and understanding of units of measure. This device has features designed to facilitate education of beginner measuring device users regarding the concepts of measurement. It also has features intended to make acquisition of such skills equally simple for vision-impaired or tactilely oriented learners.  
         [0007]     2. Description of the Related Art  
         [0008]     Various measuring devices and measuring teaching devices have been used from the start of civilization. Current devices for measurement and teaching measurement vary from a simple graduated ruler to electronic devices capable of extremely accurate measurement. The measuring devices of interest which relate to this invention include devices that allow for feel of the graduations, that can be used to teach beginners how to effectively use a measuring device, and, which facilitate ease of use.  
         [0009]     Various rulers have been designed to serve as teaching aids for instruction in units of measure. For example, U.S. Pat. No. 4,614,042 issued Sep. 30, 1986 describes a measuring and instructional ruler for use by persons having learning impairments or physical handicaps. The device has a base panel with one-inch subdivisions delineated by both visual and tactile features. This device also has a top panel which slides on the base panel and has a series of tabs, which are marked in increasing fractions of an inch. The device is used by placing the edge of the base panel on one end of an object to be measured and setting the edge of the sliding top panel against the other end of the object. A reading is then taken from the top panel tabs to the subdivisions on the base panel.  
         [0010]     Among the limitations of this invention are the following; use for relatively short distances, the embodiment demonstrates only a compact size requiring the user to manipulate thin panels, addresses only fractions of an inch, and its limitation to illustrating the significance of inch and lesser graduations.  
         [0011]     U.S. Pat. No. 5,746,001 issued May 5, 1998 discloses a ruler which comprises a teaching aid for instruction in fractional and decimal units of linear measure. It consists of an elongated rectangular body with beveled edges and a central slide. The slide allows a student to determine and verify the fractional portion of a distance measured. Limitations of this patent are; the device only teaches fractional units of measure, cannot respond to distances not allowing lengthwise registration of the device, cannot accomplish center locating or bifurcating functions, and for the flexible embodiment, the assisted reading (labeled graduations) are not direct reading (applied to the observed distance).  
         [0012]     Another patent, U.S. Pat. No. 5,881,469 issued Mar. 16, 1999 discloses a measuring and instructional ruler which is comprised of a base panel with standard units of measure delineated thereon and a transparent sheet with the fractional increments of the same standard units of measure as the base panel. The transparent sheet is positioned over the base panel allowing the student to see the relationship between the unit of measure and the fractional increments thereof. Limitations include; requiring changing to different scales (overlays) to access varying degrees of resolution, only addresses conventional desk-top type ruler applications, and the useful range of graduations must be relocated to the area of interest to number a measurement reading.  
         [0013]     Still another, U.S. Pat. No. 6,192,594 B1 describes a ruler that is a triangular shaped prism with three faces and twelve scaled working edges, four located on each prism face. A reference mark from one scale can be interrelated to another scale by turning the prism over to show the new scale in turn allowing a user to learn the interrelationship between fractions, mixed numbers, and decimals. A limitation of this invention is that it addresses unconventional odd common denominators, which can be simulated by applying any conventional ruler obliquely between two parallel demarcations. Its construction of twelve scales over one-half length on each prism face limits the functionality of this device versus a conventional draftsman or architect scale or the device proposed herein; also, this invention has no tactile characteristics. This invention allows the user to learn interrelationships between fractions, decimals, and mixed numbers, based on the English system only.  
         [0014]     The Monck patent (U.S. Pat. No. 6,243,959 B1) concerns a ruler device for use in measuring distance and construction of linear objects. It is also used during linear measurement instruction as well as demonstration of the relationship between units of measure and fractional equivalents of these units. Similar to U.S. Pat. No. 5,881,469, this invention consists of a base panel having units of measure and a transparent top panel with fractional increments. The top panel is overlaid on the base panel to demonstrate the relationship between units of measure and fractional equivalents of these units. Limitations for this invention include; the requirement of full discrimination of several colors, the degree of resolution is limited by graduation line width, application to non-distance units such as time, angles, and volumes requires the compilation of a graph, and with regard to compass points or trigonometric functions, it only covers circles to the extent of circular templates the user builds.  
         [0015]     The aforementioned patents are focused on a single use as an instructional aid. Still another device, a tactile measuring device, is described in U.S. Pat. No. 6,529,122 B1. This invention utilizes two conductive workpieces, which bear on one another and measure an object through conductivity of a closed cell foam workpiece. This invention does not include visual use and requires an electrical source.  
         [0016]     A common shortcoming with all these measuring devices is that each requires the user to have previous knowledge and understanding of the function and use of a ruler. Users must be able to accurately read and comprehend the whole unit and sub-unit demarcations on a ruler. All the above mentioned patents focus primarily on fractional increments to demonstrate the relationship between such sub-units and the base unit of measure.  
         [0017]     In summary, various measuring and instructional ruler devices have been invented that offer functionality for certain applications. However, none of these offer the multitude of uses and teaching aids that the current invention provides.  
       BRIEF SUMMARY OF TH INVENTION  
       [0018]     The present invention provides a multi-functional, measuring device for use during the instruction of linear measurement, having sufficient resolution for everyday tasks. This device comprises a measuring device for use as a proportioning reference tool, for use in estimating, measuring and construction of spatial objects, for use during the instruction of measurement concepts, for use in indexing to provide multiple layout points. Additionally, it has use as an instrument to demonstrate the relationship between a given unit of measure and said standard units of measure.  
         [0019]     This patent addresses a device that reinforces teaching and understanding of units of measure by incorporating various tactile as well as visual qualities of said units of measure to enhance their representation and application to spatial relationships resulting in better acquisition of resultant quantities by the device user. It is suitable for widespread use among sighted and non-sighted students and the general populace.  
         [0020]     It is an object of this invention to provide a measuring device to be used in the measurement of distance and objects and to use when drawing.  
         [0021]     It is further an object of this invention to provide an educational tool which will facilitate instruction in the use of conventional tools of measurement.  
         [0022]     It is still another object of this invention to provide a measuring tool of the aforesaid nature of sufficient construction and low cost that it may find widespread use amongst educators and persons.  
         [0023]     These objects and other beneficial objects and advantages of this invention will be apparent from the following description of the preferred embodiment in accordance with the present invention described as a measuring tool comprising a lightweight piece of material with two faces, two long edges, two short edges, and a distal length. The longitudinal upper long edge is shaped in a succession of ascending increments of five centimeters to the midpoint where these steps level off and descend in five-centimeter increments for the remaining length. The total length of the preferred embodiment of this invention is one meter with a V-shaped notch located at the fifty-centimeter mark on both of the long edges and at each short edge of the measuring device. On one edge of this device, alternating raised and depressed profile areas, each equaling one centimeter in length, are cut into the face of each five-centimeter step and along the upper long edge of the stair-step arrangement of the device. The profile areas begin at one end of the device and continue along its entire length.  
         [0024]     A plurality of equally spaced holes, in straight-line arrangement, is punctuated along the lower face surface of the tool, parallel to the straight edge. All of the holes demarcate five-centimeter increments. Counter-bored holes are interspersed among the simple holes at ten-centimeter increments along the wide side of the measuring device. The holes, steps, profile areas and V-shaped notches provide locations to insert or affix pins or writing instruments which permit the measuring device to perform functions otherwise accomplished by beam compasses, dividers, trammel points, scribers and “shadow posts” used for triangulation observations.  
         [0025]     Said device can be used to measure the distance between two points, to measure objects, or to replicate two-dimensional constructs.  
         [0026]     Said device can be used as a centering device, whereby one proceeds visually and tactically, to locate either the upper or lower “V” notch at the center (fifty-centimeter) mark when positioning the device versus two fixed points. The “V” notches are oriented transverse to the device face and extend fill width across their respective upper or lower edge of the device.  
         [0027]     It may be used as a guide to locate a centerline and to arrange objects symmetrically about a point or a line. Either a centerline notch or the fifty-centimeter hole may be used as a fulcrum location to use the device as a balancing arm.  
         [0028]     Said device can be used to measure lengths greater than one meter by winding non-stretchable cordage, wire, or similar item around the device horizontally, and securing in “V” notches, end for end. The “V-shaped” notches at the proximal and distal ends are oriented transverse to the device face and extend full width across their respective device end. The elevation of these notches, above the device lower edges situates them collinear with the plurality of equally spaced holes.  
         [0029]     Said measuring device can be used as an educational aid to facilitate instruction in the use of conventional metric rulers for the sighted as well as the visually impaired. A user, sighted or non-sighted, can simultaneously count by ones, fives and tens to acquire an accurate measurement.  
         [0030]     Said device can be utilized as a demonstration tool or as a measuring tool in all circumstances that call for a measuring device. Such circumstances include elementary schools, technical schools, trade schools, prison, adult, and special abilities educational programs or in any household or business environment situation where there is a need for measurements.  
         [0031]     This embodiment is also a useful device for teaching principles of vector calculus. It is useful in teaching the use of a protractor and the relationship of trigonometric functions to angles on the protractor.  
         [0032]     This embodiment of the present invention is also useful in teaching polar geometry. Lessons may include learning the degrees of a circle corresponding to compass points, as well as the degrees of a circle between compass points. When presented using this measuring device, a student can readily understand the degree of a turn required to change direction of travel from a first compass point to a second compass point by linearly adjusting the device.  
         [0033]     This embodiment of the present invention can be modified to demonstrate fractional relationships in the English system of units by redefining the overall length to be equal to one yard (thirty-six inches). The incremental stair-step arrangement and incremental high and low profile areas will then be set equal to inches and fractions thereof.  
         [0034]     Said instructional measuring device can be used as an educational aid to facilitate instruction in use of conventional rulers.  
         [0035]     The present invention includes methods by which relationships between units of angular measurement can be demonstrated and taught with the present invention. The present invention also includes methods by which vector mechanics and navigation can be demonstrated and taught using the devices of the present invention.  
         [0036]     For angular measurements, the device can be used to draw a base and the major cord of a 180 degree semicircle, preferably in the form of a protractor, from which associated geometry and trigonometric functions can be rapidly and accurately determined.  
         [0037]     The holes and incremental steps can be used to lay out curves demonstrative of the relationship between angular measurements and trigonometric functions.  
         [0038]     Said device can be used as a linear or a circular layout tool, as a beam compass or a scribe. Parallel and/or radial cuttings can be produced using this device.  
         [0039]     Another embodiment of the present invention utilizes narrow slits cut across the upper edge and face of the device to serve as subdivisions of the ascending/descending step intervals.  
         [0040]     Another embodiment retains the alternating raised and depressed profile areas to designate these minor subdivisions, but extends their length fully across the device face and partially across its lower edge, rendering them accessible while the device variously is laid upon its edge or face. In this embodiment a thin portion of the lower edge remains intact (uncut) to serve as a straightedge.  
         [0041]     Additionally, other embodiments can be produced which may be more convenient to use. One of these embodiments is a flexible strip capable of being coiled between uses. The textural features are applied by forming in the substrate or disposition of high-build coatings. Another embodiment can be produced in a folding version when replicated on individual slats affixed to one another with either hinges or pivots. When aligned and deployed, this folding embodiment functions the same as its rigid counterpart.  
         [0042]     For low-cost, educational, imaging, temporary or other uses, this invention can be produced in various lightweight or low volume versions using processes such as stamping, molding, printing, and the like.  
         [0043]     Where a specific range of use is desired, overall size limitations are imposed, or finer resolution is sought, small-scale versions can be produced to accommodate those variations.  
         [0044]     This inventive concept can be produced on material sections capable of retracting to longer or shorter extensions by mechanisms such as telescoping shapes. Telescoping variants can be equipped with locking features that enable the measuring device to be set at and replicate a range demonstrative of a specific measuring value.  
         [0045]     Curvilinear, girth, and other irregular measurements can be made and demonstrated or taught with the use of a non-stretchable auxiliary cord or other similar item, which is then compared to the scales provided on the measuring device. The cord itself can be marked (graduated) or unmarked. Attaching a similar cord to the measuring device provides convenience for the foregoing illustrated exercise and can be utilized to extend the range of this measuring device.  
         [0046]     Wrapping cordage about the measuring device allows the transference and replication of the measuring device features upon the cord. Such an auxiliary cord also can be stored conveniently in a compartment within the measuring device or stowed while remaining attached, in its own package compatible with the user&#39;s handling of the measuring device.  
         [0047]     When positioned in the recesses and holes provided on this measuring device, ancillary trammel points or pins allow the device to be used as a center finder, scribe, beam compass, or pitch (angle) layout device. Such ancillary reference points, when properly affixed, permit the measuring device to be used for distance estimation and remote length sensing by application of the geometric principles of triangulation.  
         [0048]     This inventive concept is applicable to both the metric and English standard units systems. Original or job-specific measuring bases can also be applied and laid out with subdivisions, graduations, or highlights after the same fashion. In addition, the measuring device can be enhanced or converted to other scales or sizes by the addition of physical overlays featuring different graduations, resolution, or sizes. 
     
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS  
       [0049]      FIG. 1  is a perspective view of the preferred embodiment of the invention and shows the cross-section taken for  FIG. 2 .  
         [0050]      FIG. 2  is a cross-section of the multi-functional measuring and layout device showing the openings.  
         [0051]      FIG. 3A  is a partial view of a metric version showing the recesses and lands and dimensions of the various divisions.  
         [0052]      FIG. 3B  is another metric version showing slits extended across the face and full depth across the upper edge.  
         [0053]      FIG. 3C  is a portion of the device showing recesses extending almost fully around the device so that one can measure and mark along a straight edge.  
         [0054]      FIG. 4  is an English version of the device showing recesses and lands.  
         [0055]      FIG. 5  shows the device being used to measure the length of a string.  
         [0056]      FIG. 6  shows the device being used to locate the center of a plane.  
         [0057]      FIG. 7  shows the device being used to divide a plane into equal portions.  
         [0058]      FIG. 8  shows the device being used as a compass creating an arc.  
         [0059]      FIG. 9  shows the device being used as a balance. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0060]     As will be described below, the measuring and layout device has multiple advantages including the ability to be constructed in a simple manner and produced economically. Moreover, it can be made from durable, impact resistant and flexible material. The measuring device has numerous uses as a linear measurement aid and a linear units educational tool. It is designed with a series of elevated steps as well as a series of depressed and elevated increments representative of two differing degrees of resolution. All graduations are both visually and tactually discernable, thus making the measuring device useful for the sight impaired as well as the general population. Deployed near the bottom edge of the device is an array of holes that can be used for geometric and trigonometric measurements and layouts. The V-shaped notches on the top and bottom edges at a mesial location aid use of the device as a center finder, scribe, or balance. The V-shaped notches on the proximal and distal ends provide a simple attachment for additional linear measurement, such as non-stretchable cordage. The use of simplified basic units provides a versatile educational tool for new learners. Many others can take advantage of its simplified intuitive scales.  
         [0061]     Various embodiments are included with extended grooves running across the face of the device for enhanced layout, but terminating very near one edge, allowing a contiguous straightedge surface to remain intact. Parallax errors are avoided when tick marks are made to copy measurements.  
         [0062]     Another embodiment extends the finer graduations across all faces, but in the form of narrow slits versus recesses. This allows rapid acquisition of step increments and finer layout markings. Redesigning the tool using the English system for measuring makes another embodiment. In this embodiment, each of the raised lands and lowered recesses or the distance between slits delineated along the top edge will be equal to one-half inch. Each stepped distance is equal to two inches, with an overall dimension of thirty-six inches.  
         [0063]     Referring more particularly now to the drawings and reference numbers, wherein like numerals designate corresponding parts throughout the several views, in  FIG. 1  there is shown the preferred embodiment of the measuring device which is designated generally by the number  1  comprising a flat device one meter long and having various holes  12 ,  15 , recesses  4 , V-shaped notches  7 ,  9 ,  59  lands  3  and steps  6 . The holes  12 ,  15  are located at five-centimeter intervals. The holes  12 ,  15  differ from each other in that the first hole  12  from the edge of the measuring device is a straight hole sized for the approximate diameter of a writing instrument or pin. At both faces of the device, these holes  12  remain the same diameter, allowing for tactile identification. Holes  15  differ from the interspersed holes  12  as they are counter-bored at both faces of the device allowing for tactile identification of the different holes  12 ,  15 . Each of the holes  12 ,  15  are located at the same linear position along the device at the five-centimeter steps  6 . The straight holes  12  begin five-centimeters from the edge of the device and are interspersed between the counter-bored holes  15 . The differing tactile feel of the holes  12 ,  15  allow the user to differentiate ten-centimeter intervals as well as the five-centimeter intervals between holes  12 ,  15 . Steps  6  are located at five-centimeter intervals along one face of the device  1  and increase in height at each step  6  between each end of the device  1  to the center of the device which is identified by a notch  9 . The differing rise that occurs between each step  6  allows for quick visual or tactile identification of a five-centimeter interval. On either side of the centerline V-shaped notch  9 , the adjacent steps  6  are at the same comparable linear plane  10 . Partially along one side and partially across the top of the device  1 , one centimeter wide undercut recesses  4  are provided at a depth sufficient for both visual and tactile identification. These recesses  4  are interspersed between non-recessed lands  3  also one centimeter in width. Each step  6  interval is comprised of five one-centimeter divisions where the second and fourth one-centimeter division will be undercut recesses  4  and the first, third, and fifth one-centimeter divisions  3  will be full height lands and not undercut. Thus, two recesses and three lands comprise a five-centimeter step and the user can easily and quickly acquire one-centimeter resolution either before or after making coarse (five-centimeter) approximations.  
         [0064]     When pins or writing instruments are used as compass implements, scribes or trammel points, measurements beginning or ending at the measuring device ends  8  can be registered by use of the V-shaped notches  7  provided on either end. These features are also employed when extended measurements (beyond the measuring device&#39;s self-contained one meter range) are acquired with the assistance of a non-stretchable cord, wire, or any other non-stretchable item which can be wrapped around the V-shaped notches  7  and evaluated on the measuring device face to determine the total cordage length used.  
         [0065]     A typical cross-section II of the measuring device  1  from  FIG. 1  is shown in  FIG. 2 . In a straight line along the length of the device at five-centimeter intervals are placed straight holes  12  through the device  1  from face to face and the counter-bored holes  15  are enlarged at each face of the device  1 . The straight through holes  12  indicate ten-centimeter divisions starting at five centimeters from the end of the measuring device thusly; five centimeter, fifteen centimeter, twenty-five centimeter intervals and so on. Similarly, the counter-bored holes  15  also indicate ten-centimeter intervals alternating with the straight holes  12  starting ten centimeters from the end of the measuring device thusly; ten centimeter, twenty centimeter, thirty centimeter intervals and so on. The combination of the straight holes  12  and the counter-bored holes  15  will allow for any measurement in five-centimeter increments with the undercut recesses  4  and the non-recessed lands  3  shown in  FIG. 1  allowing for further refinement of measurement to one centimeter resolution.  
         [0066]     An enlarged sectional view of the device  1  is shown on  FIG. 3A  showing the undercut recesses  4  located in each five-centimeter step  6  which steps ascend from the proximal device end  8  to its mesial centerline, thereafter descending to the distal device end. Finer resolution (one centimeter) is obtained by use of the recesses  4 . Each one-centimeter wide recess is adjacent to one-centimeter (un-notched) lands  3 . Thus, two recesses  4  and three lands  3  occupy each five-centimeter step  6 . By reference to both  6  and  4  the user can record distances quickly to the nearest five centimeters and accurately to the nearest one centimeter.  
         [0067]     Each step  6  coincides with a straight hole  12  or a counter-bored hole  15  with varying combinations of these holes  12 ,  15  indicating either five- or ten-centimeter intervals. The axis of these holes  12 ,  15  is collinear with the centerline of the end-located V-shaped notches  7 .  
         [0068]     An alternative embodiment of the measuring device  1  is shown in  FIG. 3B . At one-centimeter intervals, narrow slits  18  spanning both the face and upper edge of the device  1  serve as visual and tactile graduations. At five-centimeter intervals, steps  6  are cut to facilitate acquisition of longer dimensions.  
         [0069]     The steps  6  coincide with simple holes  12  and counter-bored holes  15  connoting five centimeters and ten-centimeter intervals, respectively, for use in conjunction with pins or writing instruments. Those holes  12 ,  15  align with the V-shaped notches  7  at either end  8  of the measuring device.  
         [0070]     Each step  6  comprises four slits  18  separating five lands  21 . Thus five one-centimeter intervals are demarcated within each step  6 .  
         [0071]     Another alternative embodiment of the measuring device  1  is shown on  FIG. 3C . In this embodiment the ascending and descending steps  6  are cut at five-centimeter intervals above the upper edge. One-centimeter wide recesses  20  are cut in the second and fourth one-centimeter wide bands within each five-centimeter step. Thus two recesses  20  and three lands  3  comprise each five-centimeter step.  
         [0072]     In this embodiment, the recesses  20  extend across the measuring device face and almost fully across the measuring device lower edge. A narrow portion  13  of the lower edge remains intact (uncut). This embodiment permits the user to place the measuring device face up in a stable position and accurately transfer, to a work surface, measurements at least as fine as one centimeter. Accuracy is enhanced by the proximity of the recesses to the work surface. The thin uncut portion  13  of the edge preserves concurrent use of the measuring device as a straightedge without interference caused by the steps  6  or the recesses  20 .  
         [0073]     The simple holes  12  at five-centimeter intervals and counter-bored holes  15  at ten-centimeter intervals remain available for functions and uses employing pins or writing instruments. Similarly, the V-shaped notch  7  located at either end, aligned with the holes  12  and  15 , is available for those same functions and applications involving the non-stretchable cord.  
         [0074]     An alternative embodiment utilizing English units of measurement is shown on  FIG. 4 . The ascending steps  26 , start at each end of the measuring device and peak at the centerline. Individual steps connote two-inch intervals. Within each step is located two 0.5 inch wide recesses  24  and two uncut lands  25 , which together provide 0.5 inch resolution throughout the length of the measuring device.  
         [0075]     A V-shaped notch  7  is provided on each end  8  of the measuring device for alignment of the device upon a work surface and use with ancillary layout devices (pins and writing instruments) or non-stretching cordage when making extended range measurements.  
         [0076]     Collinear with those V-shaped notches  7  are located both simple holes  29  and counter-bored holes  33 , which denote four-inch (two, six, ten inches, et cetera) intervals and (four, eight, twelve inches, et cetera) intervals, respectively.  
         [0077]     Evaluating an extended range measurement is shown in  FIG. 5 . Measurements exceeding the normal length of the device  1  can be obtained by employing the device in conjunction with a length of non-stretching cord  36 .  
         [0078]     After comparison to a real object being measured, the cord is laid on the face of the measuring device  1  collinear with the end located V-shaped notches  7 .  
         [0079]     Then the length of the cord is evaluated by comparison with the ten-centimeter intervals connoted by counter-bored holes  15 . Smaller increments are evaluated by comparison with the five-centimeter increments designated by the simple holes  12  and the steps  6 . Still finer resolution is gained by evaluating the observed length using one-centimeter recesses  4  and lands  3 .  
         [0080]     In  FIG. 6 , the measuring device is shown being used as a center finding tool. To find the center of a plane, any one of the counter-bored holes at midpoint  45 , the upper V-shaped notch  9 , or the lower V-shaped notch  59  can be set coincident with the mid-line of a surface when the edges of that surface  39  and  42  are located at equal distances from the respective ends  8  of the measuring device  1 .  
         [0081]     The end  8  versus edges  39  and  42  distances can be set equal by comparison with the five-centimeter and ten-centimeter intervals designated by the simple holes  12  and counterbored holes  15  as well as the one-centimeter recesses  4  and lands  3 .  
         [0082]      FIG. 7  depicts a planer surface being divided into a number of columns or intervals irrespective of the gradations provided by the measuring device utilized. The effective width increment is the projection of the measuring device gradation onto the plane.  
         [0083]     When the measuring device  1  is laid obliquely across a given width at two points, the oblique angle can be adjusted so that measuring device features divide that width into any number of convenient intervals. Any convenient feature, such as at the five-centimeter steps  9  or one-centimeter recesses  4  or lands  3 , can be utilized to draw tick marks then complete lines  48  denoting intervals or columns of the desired number, all equally spaced.  
         [0084]     When the end located V-shaped notches  7  are aligned with the width extrema, the simple holes  12  at five-centimeter intervals and the counter-bored holes  15  at ten-centimeter intervals, can be used to tick off those intervals desired.  
         [0085]     Polar geometry and trigonometric relationships can be drawn using the measuring device  1  to represent radii and chord distances. The measuring device  1  is shown facilitating a circular layout in  FIG. 8 . Other curvilinear layouts require repeated similar applications of the device. To construct an arc, a pin  49  is inserted into one simple hole  12  or counter-bored hole  15  or V-shaped notch  7 , and another pin or writing instrument  52  can be inserted or affixed elsewhere to define a curve by swinging the measuring device to a second position  30 .  
         [0086]     Other radii can be laid out by positioning the writing instrument at the desired five-centimeter step  6 , holes  12  or  15 , or one-centimeter recess  4 .  
         [0087]     A graduated axially symmetric beam can be used to evaluate masses versus one another and applied forces versus a known mass or combination of masses. The measuring device  1  is symmetric and can be used as a balance as shown on  FIG. 9 . In this application, any roller, pivot or knife-edge, for example, a pencil  54  or other suitable object can be positioned at the mesial bottom edge V-shaped notch  59  or centerline hole  12  to serve as a fulcrum. Then two masses  56  and  58  can be compared.  
         [0088]     When balanced, the moment arms corresponding to two masses can be derived from information obtained by recording the distance denoted by intervening simple holes  12  and counter-bored holes  15 , spaced five centimeters apart, and recesses  4  which are one centimeter wide and one centimeter apart (separated by lands  3 ) and one centimeter remote from step  6  transitions.  
         [0089]     With moment arms known, the proportion of the two masses can be calculated. When one mass is known, the other mass can be mathematically derived; and the measuring device  1  functions as a weigh scale. In a similar fashion, a known mass or masses  56 ,  58  can be utilized to evaluate a force applied elsewhere to the measuring device (at remaining typical location  56  or  58 ) by acquisition of the same distinguishing moment arms and the same mathematical proportioning. In this application the measuring device  1  functions as a dynamometer.  
         [0090]     These foregoing descriptions of the various embodiments should be taken as illustrating, rather than limiting, the present invention. As will be readily appreciated, numerous variations and combinations of the features set forth above can be utilized without departing from the present invention as set forth in the claims. Such variations are not regarded as a departure from the spirit and scope of the invention, and all such modifications are intended to be included within the scope of the following claims.