FIELD OF INVENTION

[001] The present invention relates to a mathematical instrument and more particularly, related to an instrument for solving polygons.

BACKGROUND OF INVENTION

[002] Generally, size and shape of a polygon is defined by the size of the sides and the vertex angles of the polygon. If we know the size of one side (or the base) and the orientation or the angular reference of the remaining vertices of the polygon, the other elements of the polygon can be resolved or in short the polygon can be solved.

[003] However, students and professionals depend on laborious mathematical calculations of multiple triangles to solve polygon(s). Further, the graphical construction process of polygon(s) can be carried out by using the existing 180 degree protractor and the 6" (15 CM) linear scale using the multiple segments and the vertex angles measurements, which are very hard to procure in many situations.

[004] In conventional practices, if the length of the sides of a polygon are measured and included in a consideration or calculation, then the error of measurement will compound in multiplicative progression.

[005] In the conventional mechanism, the angle measurement can be done using a 6-inch 180- degree protractor in which a base line that passes through a center point is displaced from a drawing edge of the protractor by about 5mm. Thus, a user has to lift the protractor every time to measure the angles after the lines have been drawn, hence consumes a lot of user time.

[006] Yet in another conventional mechanism, a 360-degree protractor having a beveled drawing edge passing through the center point and a hollow window above the central line enables drawing of a line by the user. However, these protractors also consume a lot of user's time and are less efficient.

[007] Yet in another conventional mechanism, some drawing instruments provide a material shape at the point of origin and have a lot of drawbacks. For example, these drawing instruments align the drawing edge through the center line, but they fail to pass through the center point. [008] Further, conventionally an end user needs multiple instruments like compass, scale, set squares, protractors, etc. for solving geometric problems. It becomes very cumbersome and tiring to keep changing the instruments in between. This may further lead to higer error margins.

[009] Therefore, there arises a need for an instrument for solving geometry with greater accuracy and efficiency and further overcomes the associated drawbacks of conventional instruments.

SUMMARY

[0010] The present invention relates to an instrument for solving problems of geometry. The instrument includes a main scale slide rule jacket, a main protractor disc and a V disc. The main scale slide rule jacket includes a frame enclosing at least some hollow space. One or more main scale is provided with the main scale slide rule jacket. The main protractor disc is operationally coupled to the main scale slide rule jacket. The main protractor disc includes an angular scale. The V disc is movably disposed within the main protractor disc. The V disc includes at least one linear edge and an arc edge. The linear edge have a linear Vernier scale while the arc edge have an angular Vernier scale. The linear edge is configured to be used with the one or more main scale of the main scale slide rule jacket to get a least count of at least one or more decimal places. The arc edge is configured to be used with the angular scale of the main protractor disc to get a least count of at least one or more decimal places.

[0011] These and other aspects of the embodiments herein will be better appreciated and understood when considered in conjunction with the following description and the accompanying drawings. It should be understood, however, that the following descriptions, while indicating preferred embodiments and numerous specific details thereof, are given by way of illustration and not of limitation. Many changes and modifications may be made within the scope of the embodiments herein without departing from the spirit thereof, and the embodiments herein include all such modifications.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Example embodiments herein are illustrated in the accompanying drawings, throughout which like reference letters indicate corresponding parts in the various figures. However, the disclosure is not limited to specific methods and instrumentalities disclosed herein. Moreover, those in the art will understand that the drawings are not to scale. The example embodiments herein will be better understood from the following description with reference to the drawings, in which:

[0013] FIG. 1 is a diagram illustrating an instrument (or polygon solver) 100 for solving polygons, according to an embodiment as disclosed herein;

[0014] FIG. 2 is a diagram illustrating a Main Scale Slide Rule Jacket (MSSJ) 110 of a polygon solver 100, according to embodiments as disclosed herein;

[0015] FIG. 3 is a diagram illustrating a Main Protractor Disc (MPD) 130 of the polygon solver 100, according to embodiments as disclosed herein; and

[0016] FIG. 4 is a diagram illustrating a Vernier Sector Arc 150 of 59 degrees of the polygon solver 100, according to embodiments as disclosed herein.

DETAILED DESCRIPTION OF THE DRAWINGS

[0017] Prior to describing the invention in detail, definitions of certain words or phrases used throughout this patent document will be defined: the terms "include" and "comprise", as well as derivatives thereof, mean inclusion without limitation; the term "or" is inclusive, meaning and/or; the phrases "coupled with" and "associated therewith", as well as derivatives thereof, may mean to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have a property of, or the like; Definitions of certain words and phrases are provided throughout this patent document, and those of ordinary skill in the art will understand that such definitions apply in many, if not most, instances to prior as well as future uses of such defined words and phrases.

[0018] Wherever possible, same reference numbers will be used throughout the drawings to refer to same or like parts. Moreover, references to various elements described herein are made collectively or individually when there may be more than one element of the same type. However, such references are merely exemplary in nature. It may be noted that any reference to elements in the singular may also be construed to relate to the plural and vice-versa without limiting the scope of the disclosure to the exact number or type of such elements unless set forth explicitly in the appended claims.

[0019] Particular embodiments of the present disclosure are described herein below with reference to the accompanying drawings, however, it is to be understood that the disclosed embodiments are merely examples of the disclosure, which may be embodied in various forms. Well-known functions or constructions are not described in detail to avoid obscuring the present disclosure in unnecessary detail. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and as a representative basis for teaching one skilled in the art to variously employ the present disclosure in virtually any appropriately detailed structure.

[0020] A line may be defined as a straight and/or curve line with indefinite length (a line with no end points or a ray) or definite length (a line segment).

[0021] A polygon may be defined as a closed or open structure made up of one or more lines each having at least one angular relation with an adjacent line.

[0022] A drawing surface may be defined as a two-dimensional plane/surface.

[0023] A scale marking may be defined as a series of graduation marking corresponding to one of a length, angle, direction, etc. The scale marking may be associated with relevant scientific units (labels) including but not limited to centimeter, millimeter, degree, etc. The graduation marking may be closer to the drawing surface and the labels may be farthest from the drawing surface to minimize parallax errors. Other ways of marking to increase readability are within the scope of the teachings of the present invention.

[0024] The scale marking may also be provided with Vernier section having appropriate least count to get an accuracy of at least two decimal places. The scale marking may be etched or printed. In an embodiment, the scale marking are printed in black color.

[0025] The mathematical terminologies used in the present invention corresponds to their respective definition known in the art unless explicitly defined otherwise.

[0026] The embodiments herein provide an instrument for solving polygons and other problems of geometry (as described below). This instrument (polygon solver) is a one stop solution which combines the functions of a line and/or angle drawing, making, and measuring without having to switch from one instrument to another. The instrument of the present invention combines the utility/functionality of, for example, line scale, protractor and compass, etc.

[0027] The instrument of the present invention can be used, without limitation, in academic fields to graphically study and solve polygons, to create geological and geographic survey drawings of existing and planned new layouts and landscapes, to create engineering drawing in construction, and civil engineering, to navigate for obtaining the orientation and fixation of remote points without physically visiting them, measure angles of remote points, measure length of the Hamiltonian Salesman (TSM) route; work with polar coordinates, etc. For example, if the pole is treated as the observer's own location, then, by measuring an oriented base segment, the exact distance to and between any two remote points can be calculated by measuring angles to the remote points.

[0028] The instrument of the present invention provides line drawing solution of a polygon. The instrument can be used with only one known line (base) segment of the polygon and angular displacements of all the remaining points (vertices) from both ends of the said line (base) segment to solve the polygon. The instrument of the present invention requires only the measurement of a base segment, which can then be made/reproduced accurately and the remaining angles can be measured from a single reference axis, thereby reducing errors in solving the polygon.

[0029] The instrument of the present invention enables accurate drawing/measurements without any need of a physical anchor (usually a hole) on the drawing surface. This maintains the integrity of the drawing surface. The instrument of the present invention is a very simple to use instrument and can be easily adopted by a user. The instrument is also very durable and therefore can be used for many years without sacrificing the functionality of the instrument. The instrument can easily be scaled (up or down) to suit various user requirements.

[0030] The instrument of the present invention is a dedicated easy to deploy instrument without any special stationery (for example, printed graphs). Further, the instrument replaces multiple geometric instruments eradicating the time, effort loss and introduction of transfer errors due to changing between different instruments. The instrument increases the accuracy of input and output values during mathematical measurements. The instrument can act as a geometric box kit for every student, draftsman, technician, artisan, Goldman, surveyor, navigator, movement controller and/or security personnel.

[0031] Referring now to the drawings, and more particularly to FIGS. 1 to 5, similar reference characters denote corresponding features consistently throughout the figures.

[0032] Fig. 1 illustrates an exemplary embodiment of the instrument 100 of the present invention. The instrument 100 may be made of a thermal resistant material including but not limited to acrylic, plastic, glass, etc. In an embodiment, the instrument 100 is made of transparent high density polymer which is hard, inflexible and scratch resistant. In yet another embodiment, the instrument 100 is made of translucent high density polymer which is flexible, unbreakable and scratch resistant. In yet another embodiment, the instrument 100 is made of metal like stainless steel.

[0033] The instrument 100 includes a plurality of components including, but not limited to, a main scale slide rule jacket (MSSJ) 110, a main protractor disc (MPD) 130, a Vernier sector arc (V disc) 150, etc. The MSSJ 110 is akin to a housing or frame of the instrument 100 that seats or holds MPD 130. While further details of MSSJ 110 are disclosed in Fig. 2, the MSSJ 110 is a housing with a frame 110a at its edges and a hollow or semi-hollow space enclosed by the frame 110a. The MSSJ 110 thus functions to hold the entire assembly together and also to allow operational freedom to the MPD 130 and Vernier arc 150.

[0034] The MPD 130 is seated in the frame 110a of the MSSJ 110 and is capable of linear as well as rotational movement within the frame 110a. In an embodiment, the MPD 130 is in the form of a ring with the Vernier arc 150 provided in the ring. Further, details of MPD 130 and Vernier arc 150 are provided in Figs. 3 and 4 respectively.

[0035] Fig. 2 illustrates the MSSJ 110 of the instrument 100. The frame 110a of the MSSJ 110 may have any shape including but not limited to square, rectangle, pentagon, hexagon, etc. In an exemplary embodiment, the MSSJ 110 may have a thickness ranging from 1mm to 2mm. Alternately, the MSSJ 110 may have a size which may be scaled up or down based on the requirements of the user. In an embodiment, the MSSJ 110 is rectangle shaped and is 190mm long, 128mm wide and 2mm thick.

[0036] The MSSJ 110 may be partially or completely hollow to enable a user to draw on a drawing surface through the instrument 100. In an embodiment, an upper half 110b of the MSSJ 110 is hollow. The frame 110a of the MSSJ 110 may have one or more grooves 113 disposed along one or more edges (or rim) of the frame 110a. In an embodiment as shown in Fig. 2, two grooves 113 are disposed along the top and bottom edges respectively of the frame 110a. Alternatively or additionally, the grooves 113 are disposed along the side edges of the frame 110a (not shown).

[0037] The MSSJ 110 may be provided with one or more main scale (111) in the hollow space of the MSSJ 110. In an exemplary embodiment, the main scale 111 is disposed at the center of the MSSJ 110 running parallel to the grooves 113, i.e. the top and bottom edges of the MSSJ 110 either as an integrated unit or may be removable coupled. For example, the main scale 111 may be the edge of the semi-hollow portion provided within the frame 110a and thus, be an integrated unit. Alternately, if the frame 110a of the MSSJ 110 is hollow, a scale can be provided at the center extending from one side edge to another side edge of the frame 110a. Such scale can be permanently or removably attached to the MSSJ 110 by any conventional means like adhesives, etc. The main scale 111 may include one or more scale markings. The main scale 111 may enable a user to measure/draw lines accurately.

[0038] In an alternate embodiment, the edges of the MSSJ 110 may have scale markings including but not limited to length (in different and/or same units) and/or angular markings. The said markings help the user to use the instrument 100 as a set square.

[0039] Fig. 3 illustrates the MPD 130 of the present invention. The MPD 130 may have any shape including but not limited to square, rectangle, pentagon, hexagon, circle etc. The MPD 130 may be partially or completely hollow to enable a user to draw on a drawing surface through the instrument 100. In an embodiment, the MPD 130 is shaped like a ring (i.e., entirely hollow). The MPD 130 may have a size which may be scaled up or down based on the requirements of the user.

[0040] In an exemplary embodiment, the inner diameter of MPD 130 is 49mm and the outer diameter is 59mm. Similarly, the MPD 130 has an inner thickness of 1mm towards the inner diameter and an outer thickness of 2mm towards the outer diameter such that it creates a step 135. In other words, the thickness of the MPD 130 transitions such that the outer thickness is greater than the inner thickness of the MPD 130. In alternate embodiment, the transition may be abrupt (i.e., perpendicular) or gradual (i.e., with inclination).

[0041] The MPD 130 may include one or more scale markings. In an embodiment, the MPD 130 includes a clockwise and an anti-clockwise angular scale 133 ranging from 0 degrees to 360 degrees along its perimeter.

[0042] The MPD 130 may be operationally coupled to the MSSJ 110. The MPD 130 may slide and/or rotate with respect to the MSSJ 110. In an exemplary embodiment as depicted in Fig. 1, the MPD 130 is slidably and/or rotatably coupled within the grooves 113 of the MSSJ 110.

Other functionally equivalent means of coupling the MPD 130 with the MSSJ 110 are within the scope of the teachings of the present invention. In an exemplary embodiment, a center 131 of the MPD 130 may slide along the main scale 111 of the MSSJ 110. [0043] Further, as illustrated in Fig. 1, the V disc 150 may be movably disposed over the step 135 of the MPD 130 (i.e., within the MPD 130). The arc edges 153 may complement the transition of the MPD 130. In an embodiment, the V disc 150 rotates within the MPD 130 without any lateral movement with respect to the MPD 130.

[0044] As depicted in Fig. 4, the V disc 150 may include at least a linear edge 151 and an arc edge 153. The linear edge 151 may be used with the main scale 111 of the MSSJ 110 to get a least count of at least one or more decimal places. The linear edge 151 may overlap one or more scale 111 of the MSSJ 110. The arc edge 153 may be used with the angular scale 133 of the MPD 130 to get a least count of at least one or more decimal places. The arc edge 153 may overlap the angular scale 133 of the MPD 130.

[0045] The linear edge 151 and the arc edges 153 may include one or more scale markings. In an exemplary embodiment, the linear edge 151 includes a linear Vernier scale and the arc edge 153 includes an angular Vernier scale.

[0046] The V disc 150 may have any shape including but not limited to square, rectangle, pentagon, hexagon, circle etc. The V disc 150 may have a thickness which when added with the inner thickness of the MPD 130, may be equal to the outer thickness of the MPD 130. The V disc 150 may have a size which may be scaled up or down based on the requirements of the user. In an embodiment, the V disc 150 is arc shaped having a diameter of 54mm and is 1mm thick.

[0047] In an alternate embodiment, the V disc 150 is encircled by a circular ring (not shown) of for example, a width of 5mm. The circular ring may be rotatably disposed over the MPD 130, preferably over the step 135 of the MPD 130.

[0048] The V disc 150 may further include an interfacing edge 155. The interfacing edge 155 may enable a user to easily rotate the V disc 150 within the MPD 130.

[0049] The instrument/polygon 100 solver as described above, thus, includes a Slide Rule Main Scale jacket 110, the main scale 111 is marked with a scale marking, for example in centimeters up to millimeters (mm). An upper half 110b of the jacket 110 is hollow which enables a user to draw a line along a central main scale 111 edge. Further, it includes a groove 113 in the rim on top and bottom of the slide rule main scale jacket 110 to permit the Main Protractor Disc (MPD) 130 to rotate and slide along the main scale 111 of the slide rule main scale jacket 110. In an exemplary embodiment, the MPD 130 is of 360 degrees marked to a degree, clockwise (CW), with inner radius 4.9 cm and middle ring radius 5.4 cm and the outer most ring to accommodate the marking of degrees in numbers of 5.75cm. The MPD 130 includes a hollow cavity (not shown) to allow a Vernier Sector Arc 150 held restrained in place by the beveled edges inclined outwards.

[0050] In an exemplary embodiment, the polygon solver 100 can allow the lines and the angle rays to pass through the pole or the point of origin of the first instance. Unlike conventional mechanisms, the polygon solver 100 uses the angular Vernier arc to plot and read out angles of 1' i.e. one-minute angle by an angular Vernier arc. Unlike the conventional mechanisms, the polygon solver 100 uses the linear Vernier scale for plotting and reading off length of fractions of mm in graphics on paper in hand drawing. The polygon solver 100 enables geometrical drawing solution using polar coordinates on paper using a dedicated instrument. Further, the polygon solver 100 can measure and fix of any length or points. For example, the incentre, circumcenter, medians, altitudes off the drawing of micro measurements down to minutes, or even seconds. Further, it can be extended to smaller fractions of the mm. Further, the polygon solver 100 can also be used for construction of right-angled triangles with given parameters.

[0051] In an exemplary embodiment, the polygon solver 100 can find a solution to polygons by graphical intersection of rays, emanating from the two ends of a known base segment, and known angles measured with a fixed reference axis, as in the case of polar coordinates and enables reading off the values of the remaining sides and angles.

[0052] In the exemplary embodiment of Fig. 2, the Main Scale Slide Rule Jacket (MSSJ) 110 with dimensions of 16 x 11.5 cm has scale markings along the central line with a border of for example, 5 mm on top and bottom and 1 cm on the sides. The upper half 110b of the MSSJ 110 is hollow or contain a space to permit the user to draw uninterrupted angled rays. The top and bottom rims of the jacket 110 have grooves 113 to allow the center point 131 of the Main Protractor Disc (MPD) 130 to slide along the center main scale 111 of the Main Slide Rule jacket 110. In an embodiment, the MPD 130 with inner radius is 4.9 centimeters, outer radius is 5.75 cm (as shown in FIG.3) to be fitted into the grooves 113 of the MSSJ 110 designed to slide its center 131 along the main scale 111. In an embodiment, he MPD 130 is graduated CW from 00 to 360°.

[0053] The MPD 130 may further include a Vernier sector arc 150 (as illustrated in exemplary Fig. 4). In an exemplary embodiment, Vernier sector arc 150 of 59 degrees with markings of 60 equal divisions in conjunction with the MPD 130 has a least count (LC) of 1 minute angle and the straight diametric edge of 9.8 cm is marked with 50 equal divisions on each side of the center in 49 mm radial length and the linear radial Vernier in conjunction with main sliding scale has an LC of .02 mm.

[0054] In an exemplary embodiment, the V disc 150 is an angular Vernier scale marked on the rim of an arc 59° sector (as shown FIG.4), having a diametric edge of 9.8 cm on top and the narrow edge on the left joined to the 59° mark and the arc of 59 degrees is divided into 60 equal divisions and in conjunction with the MPD 130 angle markings will have the least count (LC) of 1' i.e., one minute angle. The one-degree angle includes 60 minutes. The diametric edge of the Vdisc 150 is graduated by 50 equal divisions on the radius of 4.9 cm or 49 mm and in conjunction with the main scale 111 has the LC of. 02mm. The Vdisc 150 remains restrained inside the hollow MPD 130 by beveled edges (not shown) inclined outwards. However, there is a negligible allowed slow motion restrained rotation of the V disc 150 in the hollow of the MPD 130.

[0055] Example 1: A polygon with a base of OA =2.34 cm and at point O with respect to Y axis as reference polar coordinates of Point A are (2.34, 100°13') , points B and C are (--, 40°) and (--, 20°) was to be made. At point A, the polar coordinates are points O, B and C are (2.34, 280°13'), (-, 340°) and (-, 320°).

[0056] The said polygon was constructed with the above said parameters by placing the instrument 100 on a drawing surface with 00 pointing up to imply the Y axis mark and join the 00 tol80° and 90° to 270° mark using a diametric edge which can be rotated through 360°. Intersection is point O using the diametric edge of the V disc 150 zero mark at 20°, 40° and 100°13'. For point A, placing the zero of Vdisc 150 to 100° mark and aligning to match the 13th division of the V disc 150 with the next degree line on the MPD 130 by slow rotation and marking the ray at the resulting zero of the Vdisc 150. Further, drawing and marking the rays at all the angle markings. Further, rotating the slide rule Main Scale jacket 110 to align with the ray OA and marking point A by sliding the Vdisc 150 center to the 2.3 cm mark and then aligning the second division of the Vdisc 150 Vernier scale with the next mm mark on the Main Scale 111 to bring the Vdisc 150 zero mark to 2.34 cm. Further, holding the Main Scale jacket (bracket) 110 in place and sliding the MPD 130 along the Main scale 111 and bringing the Vdisc 150 center to A. Further, keeping the Vdisc 150 center at A and MPD 130 and Vdisc 150 diametric edge at 100° 13' and then rotating the Main scale 111 to align the center line with the 90°-270° marks and the 00° i. e, Y axis at A is in place and the narrow edge of the Vdisc 150 diametric scale will stand at 280° 13'. Further, holding the Main Scale 111 and the MPD 130 in place and then rotating the Vdisc 150 edge to mark the reference angles of points B and C and drawing and marking the rays accordingly. The intersection of the B and C rays enables the fixation of points B and C. Further, joining the points OABC results in the polygon. In this case, a quadrilateral was generated. [0057] Example 2: A collimated, horizontally leveled bubble inclinometer is used to align the 00 angle marking of the instrument 100 towards the earths North, the angles measured to the points on ground can act as the angular displacement from the reference axis Y and can provide the corresponding polygon on the drawing board. The said arrangement enabled a user to read of the sides of the polygon and the vertex angles to provide the desired values. [0058] The scope of the invention is only limited by the appended patent claims. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the teachings of the present invention is/are used.