Abstract:
The present invention provides a teaching aid system ( 10 ) for assisting students in applying trigonometric classroom lessons in real life applications both in indoor and outdoor settings. The teaching aid system consists of a pivoting scope ( 16 ) and an asymmetrically weighing gravity dial ( 18 ) that are pivotally mounted to a pair of support members ( 12 ). A tape measure ( 42 ) and an arithmetic electronic calculator ( 46 ) are attached on the support members ( 12 ) to enable students compute trigonometric formulations and applications of the same, when utilizing the system for real life objects either in indoor or outdoor settings. For determining dimensions of viewed objects, the student determines the distance from the viewed object using the tape measure ( 42 ), and the angles between the top and bottom of the viewed object using the scope ( 16 ) and gravity dial ( 18 ). Then applying the proper trigonometric formulae from a booklet or other conventional trigonometric formulae sources, the student can determine the height, elevations or slopes of objects.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     Not Applicable 
     FEDERALLY SPONSORED RESEARCH 
     Not Applicable 
     SEQUENCE LISTING OR PROGRAM 
     Not Applicable 
     BACKGROUND 
     1. Field of the Invention 
     The present invention relates to teaching devices and, in particular, to a teaching aid system for assisting students and users apply trigonometric lessons in real life applications. 
     2. Prior Art 
     In teaching young students, particularly those of advanced stature as early as elementary school, Applicant has found that the thirst and assimilation of classroom knowledge is enhanced by providing the opportunity to apply the lessons in ways related to daily experiences and observations. 
     In U.S. Pat. No. 5,732,474 issued to Cannon (1998), illustrates two dimensional nomographic device that uses the angular relationship between the moving arm and the angular scale. Two independent transparent slide indicators are mounted below the chart board one of which slides in the horizontal direction and is marked with an opaque vertical indicating line, the other of which slides in the vertical direction and is marked with an opaque horizontal line. There are no provisions in the device to actually enable the user to apply the trigonometric relationship to real time objects. 
     In U.S. Pat. No. 7,278,217 to Mills (2007), the aid comprises of a vertical support member and two semi-circular protractors, the protractors have same quadrant angulations preventing accurate angulations which extend beyond 180 degrees. The aid also does not allow 360 degree swivel of a simple barrel scope and angular inclination measurements, also the aid does not all allow 360 degree measurements. The aid needs setup and level adjustment, before taking measurements as it lacks angulations self alignment on any plane. It cannot self align its angulations to automatically indicate true horizontal and vertical. 
     The aid has a level that the user needs to refer to align to the horizontal before taking any measurements, also using the attached level increases chance of parallax errors and other inaccuracies. The aid has no resting means or supports, it may be only used as a handheld which will further the inherent inaccuracies. If the aid is used on uneven ground it can increase reading errors. The aid also highly depends on other external measurement gages such as a yard stick or tape measure for ground level or distance measurements. It is not a stand alone device and does not allow a user to learn all aspects of trigonometric ratios which involve cyclic gyrations. 
     In U.S. Pat. No. 3,322,340 issued to Frantland (1967) the instrument teaches the triangulations using trigonometric functions such as sine, tan and cosine but lacks the ability to engage the user to apply what he has learnt in simple manner. The invention comprises of a protractor scale and a vernier alignable therewith and operative in combination with a pair of micrometers, each having a vernier dial associated therewith and operated to indicate accurate calculations. The invention is primarily for the purpose of measuring geometrical figures as right-angle triangles, equiangular or equilateral triangles, isosceles triangles, and other polygonal figures when they can be broken down to right-angles triangles and when one side or more factor of right-angled triangle is known. The device is used as an instrument for triangulations and is not proposed to be used as a teaching aid or an educational device due to its complexity and inability to directly apply trigonometric relationships in real time. 
     In U.S. Pat. No. 1,955,392 issued to Shimberg (1934) the invention a trigonometric teaching device is used to demonstrate the changes in the trigonometric functions to angle changes by using a swinging member on a chart. The invention comprises of a swingable member, forming one movable side of the angle in connection with a suitable chart, properly ruled, and inscribed with a stationary line giving the other side of the angle whereby variations of the line functions corresponding to variations of an angle are illustrated on the chart. The invention uses a swinging member on a connected chart to animate the angular displacement; it does not associate it to any real time entity. The tool in its presented form lacks the application aspect altogether. 
     In U.S. Pat. No. 3,826,021 issued to Andrea (1974) is another two dimensional trigonometric visual demonstration tool that has a planar member having a unit circle inscribed with angulations. The planar member also includes a vertically extending, ordinate corridor, defined by the ordinate axis and scale associated shows the numerical values corresponding to secant, cosecant and other trigonometric functions. A transparent cursor member having a radius vector hairline is pivotally mounted at the origin of the unit circle. The device does not enable any application of trigonometric measurements on real time applications. 
     Similar U.S. Pat. No. 378,257 issued to Leschorn (1888), U.S. Pat. No. 3,359,653 issued to Redfern (1967), U.S. Pat. No. 3,556,397 issued to Anderson (1971) comprise of a pivoting arm or slide rulers attached to chart or protractor angulations. These inventions are for a student to understand the trigonometric relations in a class room and do not allow the learner to use them in real world or real world applications. 
     All the above invention&#39;s angular displacements need a point of reference and or a reference plane for angular displacement beyond the capability of the attached reference charts or connected planes. Also, the devices such as stated above lack the apparatus to enable them to automatically refer to true horizontal and vertical axis or plane of devices. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention provides a teaching aid system for assisting students, particularly young children, in applying trigonometric classroom lessons in real life applications both in indoor and outdoor settings. The teaching aid system consists of a pivoting scope and an asymmetrically weighing gravity dial that are pivotally mounted at the top of a pair of support members. A tape measure and electronic arithmetic calculator are attached on the support members to provide students solve trigonometric formulations with the system when using it to measure real life objects either in indoor or outdoor settings. For determining dimensions of viewed objects, the student determines the distance from the viewed object using the tape measure, and the angles between the top and bottom of the viewed object using the scope and gravity dial. Then applying the proper trigonometric formulae from a booklet or other conventional sources, the student can determine the height, elevations or slopes of objects. 
     Accordingly, it is an object of the present invention to provide a teaching aid system for enhancing trigonometric knowledge. 
     Another object is to provide a teaching apparatus allowing a student to determine physical aspects of structures using trigonometric lessons. 
     Another object is to provide a simple viewing device enabling students to comprehend trigonometric teachings in real life applications. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other features of the invention will become apparent upon reading the following description taken in conjunction with the accompanying drawing in which: 
         FIG. 1  shows the left orthogonal view of the system. 
         FIG. 2  shows the right orthogonal view of the system. 
         FIG. 3  shows the front view of the system. 
         FIG. 4  shows the left orthogonal view of the scope. 
         FIG. 5  shows the left side view of the scope. 
         FIG. 6  shows the exploded view of the system. 
         FIG. 7  shows an alternative embodiment of the system. 
         FIG. 8  shows a simple illustration of application of the system. 
         FIG. 9  shows a complex illustration of application of the system. 
     
    
    
     DRAWINGS-Reference Numerals 
       10  Teaching Aid System 
       12 L Left Forked Support Member 
       12 R Right Forked Support Member 
       14  Cylindrical Through Hole 
       16  Scope 
       18  Gravity Dial 
       20  Circular hole 
       22  Elongated Weight 
       24  Short Graduation 
       26  Primary Tube 
       28  Secondary Tube 
       30 L Left Shaft 
       30 R Right Shaft 
       32  Canted Slot 
       34  Peg 
       36  Image Branching Medium 
       38  Longitudinal Axis 
       40  Circular Protractor 
       42  Tape Measure 
       44  Tape Line 
       46  Arithmetic Calculator 
       48  Bracket 
       50  Single Tube Scope 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring to the drawings for the purpose of describing the preferred embodiment and not for limiting the same,  FIGS. 1 ,  2 ,  3  and  6  illustrates the preferred embodiment of a trigonometric teaching aid system  10  for providing students and users with real life applications of the principles of trigonometry.  FIG. 7  illustrates the alternate embodiment of the system. 
     The teaching aid system  10  comprises of a pair of forked planar upright support members  12 L and  12 R. All the elements of the embodiment are supported by support members  12 L and  12 R and are described in detail below. Both  12 L and  12 R on their top ends have a transverse cylindrical through hole  14 . A scope  16  and an asymmetrically weighing gravity dial  18  are pivotally connected between  12 L &amp;  12 R and are explained in detail below. 
     With reference to  FIGS. 4 and 5 , scope  16  comprises of a long hollow primary tube  26  with a longitudinal axis  38  a shorter hollow secondary tube  28 , an image dispersing medium  36 , a peg  34  and a shaft with two ends  30 L and  30 R on the left and right respectively. One end of hollow secondary tube  28  is perpendicularly inserted at the center of primary tube  26 . Tubes  26  and  28  have the same inner and outer diameters. A canted slot  32  is cutout on primary tube  26  right below the joining of secondary tube  28 . 
     The tubes are currently made of plastic and are adhesively attached. They can also be injection molded as one piece using conventional injection molding techniques. An image-branching medium  36  made of a semi-reflective glass sheet is inserted snugly in slot  32  cut in primary tube  26 . The acute angle between the plane of medium  36  and primary tube&#39;s longitudinal axis  38  is 45 degree caused by the canted arrangement of the slot. The purpose of the branching medium is to optically branch, including, partially reflecting an image beam passing through primary tube  26  to secondary tube  28 . This arrangement enables a user per their preference to easily view a target of interest either through the back end of primary tube  26  or through the top open end of secondary tube  28 . This arrangement also increases the usability of the system when it is resting on a ground level or if the user has to bend forward to view a target of interest using scope  16 . An elongated glass prism can also be used as an image-brancing medium to optically branch the image with minor adjustments to the linearity of the scope and the slot dimensions. 
     From the center or mid region of scope  16 , on primary tube  26  extends out a transverse shaft with two ends  30 L and  30 R on the left and right sides respectively. The shaft is perpendicular to both primary tube  26  and secondary tube  28  and is permanently attached at their intersection region on  26  using adhesives. The extremities of  30 L and  30 R are pivotally mounted on support members  12 L and  12 R respectively and positioned between them. The diameter of the shaft is slightly smaller than the diameter of hole  14  enabling the shaft to be pivotally inserted to it. This allows  16  to swivel a full 360 degrees; freely between support members  12 L and  12 R. A simpler version of the scope can also be made by just having one hollow primary tube and no interconnecting secondary tube. 
     With reference to  FIGS. 1 ,  3  and  6 , asymmetrically weighing gravity dial  18  is made of a flat dial, having a circular hole  20  in its diametric center; and its diameter is slightly larger than the diameter of shaft  30 L. Gravity dial  18  is pivotally mounted on  30 L in between  12 L and  26 . It can also be pivotally mounted between  12 R and  26 . A short elongated weight  22  is radially mounted on gravity dial  18  as shown in  FIGS. 1 ,  3  and  6 . The asymmetrical weight distribution caused by weight  22  on dial  18 , gives it a pendulum effect when it is pivotally attached to  30 L, and allows it to reproducibly orient to gravity to attain equilibrium. Dial  18  has equally spaced short graduations  24  on its outer surface along its circumference to indicate angulations. The radius of dial  18  is shorter than half the length of primary tube  26 . The dial helps a user to align scope  16  to the actual horizontal level irrespective to the system&#39;s resting or carrying plane. 
     With reference to  FIGS. 1 ,  4  and  5 , peg  34  is adhesively attached on the outer surface of the front left end of  26  on the side adjacent to  18 . The function of peg  34  is to help a user to accurately indicate the relative inclination of  26  against graduations  24 . This relative inclination can also be observed using simpler means such as grooves or markings on the outer surface of  26  adjacent to dial  18 . 
     A partially hollowed out conventional planar circular protractor  40  having graduations is permanently affixed on support member  12 L. The diameter of protractor  40  is relatively smaller than the diameter of dial  18 . It is attached such that its diametric center is concentric to dial  18 . This arrangement enables a user to find the aid&#39;s resting or carrying plane&#39;s inclination and its relative inclination to dial  18 . 
     A tape measure  42 , with a tape line  44  extending out of  42  is mounted upright on support  12 R using bracket  48  which is adhesively attached to the support member. It can also be mechanically fixed to support  12 R. The tape measure is mounted such that tape line  44  is able to extend out in front of system  10  and without interfering with any other parts, especially any other moving parts of the preferred embodiment. This provides a user of system  10  the means to measure the distance between system  10 , and a target of interest at a reasonable distance. 
     With reference to  FIG. 2 , a small conventional semi-circular framed electronic arithmetic calculator  46  is adhesively attached on support member  12 R. The calculator enables a user to conduct arithmetic calculations with observed angular inclinations of scope  16 , against dial  18  and the distance measured using tape measure  42 . With the help of a trigonometric table (not shown) and system  10  a user can conduct trigonometric calculations on real life objects. The teaching system  10  may be used in indoor and outdoor settings. 
     Operation-FIGS.  8 , 9   
     Use of the teaching system is preferably in conjunction with trigonometric formulas booklet. To explain the operation of the system, a simple determination of vertical height of an object  80  from ground level is used as illustrated in  FIG. 8 . The system  10  is either placed on ground or held at a stable plane, and whose height from ground level is known. The distance “D 1 ” between the object and the system is measured using tape measure  42 . Next, scope  16  is rotated to view the top of the object and the angle of upward inclination angle “A” is recorded by noting the graduation  24  on gravity dial  18  against peg  34 . 
     Using learned trigonometric functions, the user can determine the vertical height “H 1 ” of the object. For this example, the user can obtain the height of the object by multiplying the trigonometric tangent value of the measured inclination angle “A” with the measured distance “D 1 ” using calculator  46  and find the overall vertical height “H” of the object. To get an accurate measurement the height of system  10  from the ground is added to the final height calculations. 
     For advanced level users, a more complex application of system  10  is possible, where direct measurements are not convenient. The height of an object may also be determined with the teaching aid system where direct measurement to the object is not possible, for instance as shown in  FIG. 9  wherein the building  90  with height “H 2 ” is separated from the view location by a river  92  or other barrier. Therein, an initial location  94  is selected and marked. Following the above procedures, the angle “A 1 ” between the top on bottom of the building  90  is determined and the unknown distance between system and object is noted as “D 2 ”. Thereafter, the system  10  is moved further back to get a second inclination angle “A 2 ” at location  96  which is recorded and the distance “D 3 ” between initial location  94  and final location  96  is measured using tape measure  42 . By applying trigonometric formulation we know that Tan (A 1 )=H 2 /D 2  and Tan (A 2 )=H 2 /(D 2 +D 3 ). Next partially solving the first equation for D 2  and substituting it in the second equation to solve H 2  will result with the height of the building. The known height of the system  10  from the ground or resting plane must be added to get an accurate measurement of the height of the object. 
     ADVANTAGES 
     From the description above, a number of advantages of my trigonometry teaching aid system become evident, the significant advantages being:
         (a) Ease of use.   (b) A single stand-alone comprehensive tool for understanding and applying trigonometric principles in real life, when used in combination with a trigonometry formula table.   (c) A fun way to learn trigonometry by measuring real life objects.   (d) No-setup is required to measure the true horizontal and vertical angles.   (e) Due its application spectrum it can be used as a educational toy, educational device, school classroom assistive tool, and as an engineering scientific measurement tool.       

     DESCRIPTION OF THE ALTERNATIVE EMBODIMENT 
     The teaching aid system  10  may also be provided in simpler formats, for instance an alternate embodiment is shown in  FIG. 7 . In this alternate embodiment the scope is simplified. Scope  50  shown in  FIG. 7 , comprises of a single hollow tube and no additional mating tubes. Since it has no mating tube to branch the image beam passing through it, it is also void of the need of having an image branching medium. Lastly, the alternate embodiment also does not house the only electronic component in the aid, which is the electronic arithmetic calculator. All other elements are the same as the preferred embodiment.