Title of Invention

"A MANIPULATIVE DEVICE FOR VISUAL UNDERSTANDING OF THEOREMS RELATING TO TRIANGLES"

Abstract

This invention relates to a manipulative device for visual understanding of theorems relating to triangle wherein the device comprises a sheet (1) fixed on a wooden frame (2) with screw (3) wherein sheet has a smooth surface and is made of material selected from metal and plastic, said sheet (1) has slot coinciding with slot (8) of scale (5); Three scales (4,5,6) forming sides AB, BC, CA of a triangle ABC, which are rotatably joined together at A, B, C by nut-bolt means passing through holes provided at one end of each of the said scales wherein the scale (5) is fixed at one end 'A' by nut-bolt means (7) to the said sheet (1), wherein further scale (4) has a slot (10) at the middle and slot (11) at end B, wherein scale (5) has a slot (8) at end B, wherein scale (5) has a slot (8), at end B and slot (9) at middle, the slot (8) and (11) enabling to and fro motion of scale BC along the side AB of triangle by movement past nut-bolt means (13) and wherein scale (6) has slot' (15) at middle and slot (14) at end A and is movable to and fro along the nut-slot means (7); a scale (18) having groove (19) at one end and fixed at other end by nut 85 bolt means (20) within the slot (15) of scale (6) and said scale (18) being also movable in slot (10) of scale (4); three protractors (15,16,17) rotatably joined at the 'end points A, B, C of triangle with the help of nut & bolt means (7,13,12) respectively; three novel protractors (21,22,23) each comprising a protractor (30) and needle (31) provided along the periphery of protractor at 90° position and at right angle to the base of protractor, the said novel protractors being joined by nut & bolt means (24,25,20) at the middle slots of the sides of triangle; three detachable rubber threads joining vertices A, B, C of triangle to the nut 8s bolt means (20,24,25) in the middle slots of the sides AC, AB and BC of triangle.

Full Text

FIELD OF INVENTION This invention relates to a manipulative device for visual understanding of theorems relating to triangles. PRIOR ART Students at the schools are generally taught geometrical theorems without any visual teaching aid. The different theorems on triangles, quadrilateral and circle are orally explained by the teachers. The different theorems are proved by the teachers based on the conclusion drawn from number of steps. It is often drudgery for the students to understand the proof of theorems based on oral teaching of the approach and different reasoning steps involves committing to memory of the results of the related geometrical theorems. The students have also no way to see for themselves visually the relationship between different attributes of a geometrical figure. US Patent No. 5,732,474, discloses a visual and manipulative device for visual understanding of the relationships of all angles in a triangle, rectangle and other such geometric shapes relative to their side lengths. The basic unit (1) in the above stated device comprises of a disk (2) having indicia representing 360 degree compass. The disk is provided with a fixed leg (provided which has partly a sleeve portion and partly a non-sleeve portion. The non-sleeve part of second leg is attached to the center of the disk by a snap grommet. The sleeve portion is capable of accepting the fixed leg of another basic unit. For demonstrating theorems relating to triangles, three basic units are joined together as shown in figure 2, by inserting fixed leg of one unit into the sleeve portion of other basic unit forming an equilateral triangle. A limitation of the above device is that this device can be used to demonstrate trigonometric function by forming a right triangle by suitably joining three basic units. It can also be used to demonstrate relationship between sides and angles such as sides opposite to equal angles are equal, or side opposite to a greater angle is longer than side opposite to a smaller angle. The device cannot be used to demonstrate' theorems such as angle bisectors are concurrent, altitudes of a triangle are concurrent, perpendicular bisectors of sides are concurrent, medians are concurrent and proportionality theorems of triangles. Another limitation of the above device is that the manufacturing of the above device is relatively difficult. Still another limitation of the above device is that the device is not mounted on any supporting base due to which handing of the device is difficult. OBJECTS OF PRESENT INVENTION The primary object of present invention is to provide a manipulative device for visual understanding of theorems relating to triangles such as proportionality theorems, theorems relating to concurrency of angle Bisectors, perpendicular, bisectors medians etc. Another object of the present invention is to propose a device whose manufacturing is relatively easier and less expensive. STATEMENT OF INVENTION According to this invention there is provided a manipulative device for visual understanding of theorems relating to triangle wherein the device comprises a sheet fixed on a wooden frame with screw wherein sheet has a smooth surface and is made of material selected from metal and plastic, the said sheet has slot coinciding with slot of scale, three scales forming sides AB, BC, CA of a triangle ABC, which are rotatably joined together at A, B, C by nut-bolt means passing through holes provided at one end of each of the said scales wherein the scale is fixed at one end 'A' by nut-bolt means to the said sheet, wherein further scale has a slot at the middle and slot, at end B, wherein scale has a slot at end B, wherein scale has a slot, at end B and slot at middle, the slot and enabling to and fro motion of scale BC along the side AB of triangle by movement past nut-bolt means and wherein scale has slot' at middle and slot at end A and is movable to and fro along the nut-slot means; a scale having groove at one end and fixed at other end by nut & bolt means within the slot of scale and said scale being also movable in slot of scale; three protractors rotatably joined at the end points A, B, C of triangle with the help of nut & bolt means respectively; three novel protractors each comprising a protractor and needle provided along the periphery of protractor at 90° position and at right angle to the base of protractor, the said novel protractors being joined by nut 85 bolt means at the middle slots of the sides of triangle; three detachable rubber threads joining vertices A, B, C of triangle to the nut & bolt means in the middle slots of the sides AC, AB and BC of triangle. DESCRIPTION OF FIGURES The present invention will now be illustrated with accompanying drawings which are an illustrative embodiment of the invention and are not intended to be taken restrictively to imply any limitation on the scope of the present invention. In the accompanying figures:- Fig. l(a): shows the construction of the device known is the art as per US Patent No. 5,732,474; Fig. l(b): shows the construction of triangle as per US Patent No. 5,732,474; Fig. 2: shows the construction of the device of the present invention; Fig. 3(a): shows the scale with slot at middle and groove at one side, which constitutes one of the sides of the triangle; Fig. 3(b): shows the scale having one groove each on one side, which constitute line EF of the triangle as shown in Fig. 2; Fig. 4: shows the construction of novel protractor provided with a needle on the periphery of the protractor at 90° position. Fig. 5: shows the arrangement of the device for use of device for demonstrating proportionality theorems. Fig. 6(a): shows the arrangement of the device for use for demonstrating the theorems regarding concurrency of attitudes. Fig. 6(b): shows the arrangement of the device for use for demonstrating theorems on concurrency of right bisectors. Fig. 7: shows the arrangement of the device for use for demonstrating concurrency of medians of a triangle. Fig. 8: shows the arrangements of the device for use for demonstrating theorems regarding concurrency of angle bisectors of a triangle. DESCRIPTION OF INVENTION W.R.T. DRAWINGS Referring to fig 2, the device of the present invention is mounted on a sheet (1) of metal or plastic having smooth surface, preferably acrylic sheet. This sheet is fixed on a wooden frame (2) with the help of screws (3). Three scales (4,5,6) having construction as shows in Fig. 3(a) are joined together at A,B,C, with the help of nut and bolt means. The scale (5) is fixed at one end 'A' by nut 85 bolt means (7) to the acrylic sheet. The scale (4) has a slot (10) at the middle, slot (11) at the end 'B' and a hole at end 'C' where it is rotatably joined by nut and bolt means (12) to the scale (6). The said acrylic sheet (1) has a slot coinciding with slot (8) of scale (5). The scale (4) can slide to and fro along the slot (8) of scale (5) by nut and bolt means (13). The scale (4) can also move to and fro in its slot (11) along the screw (13). The scale (6) has one end 'C'joined to scale (4) by nut and bolt means (12) and has slot (14) at other end 'A' and slot (15) at middle. The scale (6) is movable to and fro along the nut and bolt means (7) in its slot (14) at the end 'A'. A scale (18) (construction as shown in fig.3)(b) having groove (19) at one end V and fixed at other end 'E' to the middle slot (15) of scale (6) with the help of nut and bolt means (20). The scale (18) is also movable to and fro in the slot (10) of scale (4). Three protractors (15,16,17) are rotatably fixed at the end points A,B,C of the triangle with the help of nut and bolt means (7,13,12) respectively. A set of three novel protectors (21,22,23) having construction shown in fig. (4) comprising a protractor (20) provided with needle (31) at the periphery of protector at position of 90°, are provided in the middle slots of each of scales (4,5,6). Three rubber threads are detachably (not shown in figure) joined to the vertices of triangle by the nut & bolt means (20,24,25) in the middle slots of sides (6,5,4) respectively. These rubber threads can be detached and used when required. The device can be used to demonstrate several theorems. Some of the theorems which can be demonstrated by the device are as follows :- 1- Basic proportionality Theorem (Thales Theorem):- In a triangle, a line drawn parallel to one side, to interest the other sides in distinct points, divides the two sides in the same ratio. 2. Converse of Theorem (1):- If a line divides any two sides of a triangle in the same ratio, the line must be parallel to the third side. 3. The line segment joining the mid points of any two sides of a triangle is parallel to the third side and equal to half of it. 4. The line drawn through the mid point of one side of a triangle, parallel to another side intersects the third side at its mid point. 5. Attitudes of a triangle are concurrent. 6. Perpendicular bisectors of the sides of a triangle are concurrent. 7. Medians of a triangle are concurrent. 8. Angle bisectors of a triangle are concurrent. WORKING ;- In order to demonstrate Basic Proportionality Theorem (Thale's Theorem) that in a triangle a line drawn parallel to one side divides the other two sides in the same ratio, remove novel protectors (having construction as shown in Fig.4) from the nut-bolts at points F and G leaving only one novel protractor at point 'E'. Also remove the rubber threads. The arrangement will be left as shown in Fig. (5). Now adjust the position of scale EF and the nut-bolt A and E and F such that ZCAB=ZCEF, which are corresponding ANGLES, thereby making line EF| | AB (EF parallel AB). This line EF intersects the sides AC and BC of AABC at points (Nut-Bolts) E and F. By measuring the length AE,EC,BF and FC, it will be observed that EC:AC= FC:BF. By changing the position of nut-bolts E&F or by changing the length of side AC or BC of AABC, the same result will be proved, thereby demonstrating theorem. In order to demonstrate the converse of the above theorem that if a line divides any two sides of a triangle in the same ratio, the line must be parallel to the third line, we fix the nut bolt E and F at the same distance from the nut-bolts A and B respectively such that EC : AC = FC : BF. In this position measure the ANGLES ZCEF and ZCAB by means of protractors at the points (nut-bolts) E and A. It will be seen that ZCEF=ZCAB. But these are corresponding ANGLES. This means line EF| | AB. By changing the position of nut-bolts E and F, the same result will be proved again. This demonstrates theorem. In order to prove the theorem that the line segment joining the middle points of any two sides of a triangle is parallel to the third side and equal to half of it, we adjust the position of nut-bolts E and F at the mid points of scales (sides of A) AC and BC, (as shown in Fig. 5) so that the line EF (scale) passes through the mid points of sides AC and BC of AABC. Now measure the ZCEF and ZCAB by adjusting the position of protractors at points E and A. It will be observed that ZCEF=ZCAB. But these are corresponding ANGLES. This means EF| |AB, where AB is the third side of AABC. Also note the length of segment EF and line AB. It will be seen that EF=1/2AB. By changing the length of scales (sides) AC and BC, but keeping the nut-bolts E and F at their respective mid points, the same result will be proved. This demonstrates the theorem. In used to demonstrate the converse of the above thereon that the line drawn through the mid point of one side of a triangle, parallel to another side intersects the third side at its mid point, we fix the nut-bolt E at the mid point of side AC. Now adjust the position of protractors of E and A to make ANGLES ZCEF=ZCAB, the scale EF being also adjusted accordingly. But these are corresponding ANGLES. This means line EF is parallel to AB. In this position it will be observed that the other end of line (scale) EF will be passing through the mid point of line (scale) BC. By changing the length of side AC and adjusting the position of nut-bolt E at its mid-point, the same result will be proved. This demonstrate the theorem. In order to demonstrate the theorem that altitudes of a triangle are concurrent, we remove the protractors from the nut-bolt A, B and C. Also remove the scale EF and rubber threads from the device. The arrangement left is as shown in fig.6(a). We adjust the position of all the three novel protractors (21,22,23) (having construction as fig. 4) in such a way that the needle part of these novel protractors passes through the respective opposite vertices A,B and C. In this position it will be seen that all the three needles of these said novel protractors(21,22,23) which represent attitudes, are passing though the same point Q, which is the point of concurrency. This proves the theorem that attitudes of a triangle are concurrent. Now shift the side BC towards side AC in the groove of scale (side) AB with the help of nut-bolt B. The point of concurrency Q will be disturbed. Again adjust the position of novel protractors (21,22,23) in such a way that the needles which represents altitudes pass through their respective vertices. In this position it will be seen that the three needles pass through a common point Q, (The point of concurrency). This proves the theorem. In order to demonstrate that the Perpendicular bisectors of the sides of a triangle are concurrent, we remove the protractors from the nut-bolts at points A,B,C, and also remove the scale EF along with nut-bolts E and F and the rubber threads from the device. The arrangement of device as left would be as shown in Fig. 6(b). The two novel protractors (22,23) (having construction as Fig. 4) are fixed at the mid-point E SB F of grooves (10,15) of scales AC and BC. The third novel protector (21) is kept movable in groove (9) of scale AB. We adjust the position of third novel protractor (21) in the groove of scale AB in such a way that it comes to the mid point G of scale AB. In this position it is observed that the needle part of all the three novel protractors (21,22,23) (having construction as (Fig. 4) are concurrent at point P. We change the shape of triangle ABC by shifting the side BC towards side AC with help of nut-bolt B in the groove of scale AB. We then bring the protractor to the mid point G of the decreased side AB of AABC. In this position, it will be observed that the needles of three novel protractors(21,22,23) are again concurrent at point 'P'. This demonstrates the Theorem. In order to demonstrate the theorem that medians of a triangle are concurrent, we attach three rubber threads as shown in Fig. 7 with rubber thread 31 joining A to F, rubber thread (32) joining B to E and rubber thread (33) joining G to C. Adjust the novel protractors (22,23), so that point E and F are the mid points of the sides AC and BC respectively. We then adjust the position of nut-bolt G along with novel protractor (21) till point (Nut-Bolt) G comes to the mid point of scale AB. In this position it will be observed that all the three medians (rubber threads) are concurrent at point O, which is the point of concurrency of medians. Now decrease the length of side AB by shifting the scale BC towards scale AC by moving the nut-bolt (B) in the groove of scale AB. Now the point of concurrency (O) will be disturbed. Now again adjust the position of nut-bolt (G) alongwith novel protractor till point (nut-bolt) G comes to the mid point of scale AB. In this position it will be again observed that all the three medians (rubber threads) are again concurrent at point (O). This demonstrates the theorem. In order to prove that Angle bisectors of a triangle are concurrent, we remove the novel protractors (21,22,23) from the nut-bolt E, F and G. Also remove the scale EF, from the device. The arrangement of device that will be left is shown in Fig. 8. We adjust the position of rubber threads AF, BE and CG (31,32,33) by moving the nuts F,E and G in their respective grooves such that ZBAC, ZABC and ZACB are bisected by the rubber threads along AF,BE and CG i.e. rubber threads along AF, BE and CG are angle bisectors of angles ZA, ZB and Z.C respectively. It will be seen that all the three rubber threads (bisectors) are concurrent at point N. We now shift the side BC towards side AC in the groove of scale AB with the help of nut-bolt (B). The point of concurrency (N) will be disturbed. We again adjust the position of rubber threads (Angle bisectors) AF, BE and CG such that ZBAC, ZABC and ZACB are bisected by rubber threads AF,BE and CG respectively. In this position it will be seen that the three rubber threads (bisector) pass through the common point N. This demonstrates the theorem that angle bisectors of a triangle are concurrent. It will be understood that the manipulative device of the present invention is insceptible to modifications, changes, adaptations by those skilled in the art. Such variant embodiments incorporating the features of the present invention are intended to be within the scope of the present invention, which is further set forth under the following claims: WE CLAIM; 1. A manipulative device for visual understanding of theorems relating to triangle wherein the device comprises:- (a) a sheet (1) fixed on a wooden frame (2) with screw (3) wherein sheet has a smooth surface and is made of material selected from metal and plastic and said sheet has slot' matching with slot (8) of scale (5). (b) Three scales (4,5,6) forming sides AB, BC, CA of a triangle ABC, which are rotatably joined together at A,B,C by nut-bolt means passing through holes provided at one end of each of the said scales wherein the scale (5) is fixed at one end 'A' by nut-bolt means (7) to the said sheet (1), wherein further scale (4) has a slot (10) at the middle and a slot (11) at end B, wherein scale (5) has a slot (8) at end B, wherein scale (5) has a slot (8), at end B and a slot (9) at middle, the slot (8) and (11) enabling to and fro motion of scale BC along the side AB of triangle by movement past nut-bolt means (13) and wherein scale(6) has slot' (15) at middle and slot (14) at end A and is movable to and fro along the nut-bolt means (7); (c) a scale (18) having groove (19) at one end and fixed at other end by nut & bolt means (20) within the slot (15) of scale (6) and said scale (18) being also movable in slot (10) of scale (4); (d) three protractors (15,16,17) rotatably joined at the end points A,B,C of triangle with the help of nut & bolt means (7,13,12) respectively; (e) three novel protractors (21,22,23) each comprising a protractor (30) and needle (31) provided along the periphery of protractor at 90° position and at right angle to the base of protractor, the said novel protractors being joined by nut 85 bolt means (24,25,20) at the middle slots of the sides of triangle; (f) three detachable rubber threads joining vertices A, B, C of triangle to the nut & bolt means (20,24,25) in the middle slots of the sides AC, AB, and BC of triangle; 2. A device as claimed in claim 1 wherein said sheet is made of acrylic. 3. A manually operable device for visual understanding of theorems relating to triangle, as herein substantially described and illustrated with accompanying drawings.

Documents:

862-DEL-2004-Abstract-30-04-2008.pdf

862-DEL-2004-Claims-30-04-2008.pdf

862-del-2004-claims.pdf

862-del-2004-Correspondence Others-(20-06-2012).pdf

862-DEL-2004-Correspondence-Others-30-04-2008.pdf

862-del-2004-correspondence-others.pdf

862-del-2004-correspondence-po.pdf

862-del-2004-correspondence.pdf

862-del-2004-description (complete)-30-04-2008.pdf

862-del-2004-description (complete).pdf

862-del-2004-description.pdf

862-del-2004-drawings.pdf

862-del-2004-form-1.pdf

862-del-2004-form-19.pdf

862-del-2004-form-2.pdf

862-del-2004-form1.pdf

862-del-2004-form19.pdf

862-del-2004-form2.pdf

862-del-2004-form26.pdf

862-del-2004-GPA-(20-06-2012).pdf

862-DEL-2004-GPA-30-04-2008.pdf

862-del-2004-gpa.pdf