Title of Invention

'A GEOMETRICAL INSTRUMENT FOR CONSTRUCTING REGULAR POLYGONS'

Abstract A geometrical instrument for constructing regular polygon. The said instrument comprises a lightweight transparent sheet having two horizontal sides (CD, AF) of which the side (CD) is the base of the instrument (2) having two vertical sides (CB, DE) and joining to said top horizontal line (AF) at an angle of 30° and 45° respectively said instrument (2) having plurality of vertical lines (a1, a2 k1 k2) at a predetermined steps starting from a point ( C ) at the left hand side of the base of the said instrument, said vertical lines are provided with pin holes (5, 6, 7, 8, 9) for five to nine sided polygons said instrument is operated by rotatably fixing at any one of the said pin holes (5, 6, 7, 8, 9) at any one of the vertical lines (b2 b1 j1 j2) with a holding device (3) having a pin with a flat head.
Full Text The invention relates to a geometrical instrument for constructing regular polygons namely Pentagon, hexagon, heptagon,octagon etc. of given side lengths in convenient incremental steps.
Presently regular polygons are usually constructed by using set-squares and compass. Such construction methods are given in Text Books like " Elementary Engineering drawings" by N.D. Bhatt.
There are disadvantages associated with the present system of constructing polygons.
One of the main disadvantages is that it is time consuming and inaccurate and requires lot of practice and memorization of the construction process or steps.
Another disadvantage with the present system of constructing polygons is that it is necessary to follow the step by step construction methods given in the text books and omission of any one such steps usually results in irregular polygons.
Yet another disadvantage with the present system of constructing polygons is that it is necessary to use at least two instruments, namely set square or ruler and compass and unwanted construction lines are to be erased after completion of the figure thereby deteriorating the appearance of the drawing.
Still another disadvantages associated with the present system of constructing polygons is that it demands a lot of effort and time to construct regular polygons.
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Therefore the main object of the present invention of a geometrical instrument for constructing regular polygons which is simple and accurate and requires minimum construction time.
Another object of the present invention of a geometrical instrument for constructing regular polygon which is small enough to carry in the instrument box presently being used.
Yet another object of the present invention of a geometrical instrument for constructing a regular polygon of standard sizes and can be adapted for a specific size. The same instrument can be used for at least 8 sizes of polygons having 5 to atleast 9 sides. The sizes and sides can be further adapted simply by drilling a pin hole at a suitable point of the instrument.
Still another object of the present invention of a geometrical instrument for constructing a regular polygon is that there is no fixed construction method to be followed and once the user is conscious of how to use it, the operation gets very simple and easy.
Further object of the present invention of a geometrical instrument for constructing a regular polygon is that after construction of the polygon there are no superfluous lines to be erased and as such the drawing is neat and clear.
According to the present invention there is provided a geometrical instrument for constructing regular polygon comprising a lightweight transparent sheet having two horizontal sides of which one side is the base of the instrument having
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two vertical sides that join to the said top horizontal line at an angle of 30° and 45° respectively, said instrument having plurality of vertical lines at a predetermined steps starting from a point at the left hand side of the base of the said instrument, said vertical lines are provided with pin holes for five to nine sided polygons said instrument is operated by rotatably fixing at any one of the said pin holes at any one of the vertical lines with a holding device having a pin with a flat head.
This invention particularly provides a geometrical instrument for constructing regular polygon comprising a lightweight transparent sheet having two horizontal sides (CD, AF) of which the side (CD) is the base of the instrument having two vertical sides (CB, DE) and joining to said top horizontal line (AF) at an angle of 30° and 45° respectively, said
instrument having plurality of vertical lines (a1, a2 k1 k2) at a
predetermined steps starting from a point ( C ) at the left hand side of the
base of the said instrument, said vertical lines are provided with pin holes
for five to nine sided polygons, said instrument is operated by rotatably
fixing at any one of the said pin holes at any one of the vertical lines (b2 b1
j1 j2) with a holding device having a pin with a flat head.
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The nature of the invention, its objective and further advantages residing in the same will be apparent from the following description made with reference to non-limiting exemplary embodiments of the invention represented in the accompanying drawings.
Figure 1 - shows a polygon for relationship between radius and the
quantities 11 n and G.
Figure 2 - shows the top, side and front views of the instrument. Figure 3 - shows details of the holding device and the center pin
holes on the main device. Figure 4 - shows details of another embodiment of the holding
device. Figure 5 - shows details of the centre pin holes of the main device
corresponding to the holding device of Figure 4.
Summary of the present invention:
A regular polygon being a figure with one unique centre, the shape and size depends upon the following quantities.
(i) The number of sides of the polygon (say, n)
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(ii)The length of each sides of the polygon ( say, 1), and (iii)The included angle of each sides at the centre (say, ).
For a given polygon, the above quantities namely (1' and 'n' are known and
Since every regular polygon can be contained inside a circle with common centre, hence it is natural to assume that a relationship between the radius of the circle or the polygon and the quantities 1, n and must exist. On this basis an assumption is made that the length of the side of a polygon is approximately equal to the arc subtended by the angle ' ' and with this approach, the following relationships are derived.
( See Fig. 1).
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Length of each sides of the polygons,


Meanwhile several possible solutions were generated and based upon eqn.- (2) , a prototype of the choosen solution was made and tested. It was found that the device could not draw the desired polygon and the first failure was encountered.
On re-examining the above equation and carefully studying the Fig. (1), the errors are easily detected and the correct relationship between the said quantities are as follows:

Now using eqn - (4) and corrected to two decimal places,
the different lengths of the altitute (x) for different polygons
are obtained in table - 1 below.
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TABLE - 1 : LENGTH OF ALTITUDES (x)

PRACTICAL USE OF THE INVENTED INSTRUMENT:-.
The instrument sequences may be followed to efficiently use the device to construct the reuired polygon whose no. of sides and length of the sides are given.
(i) Out of the eight possible side lengths vi. 10mm, 20mm, 25mm, 30mm, 35mm, 40mm, 50mm and 60mm select the perpendicular at the mid-centre of the desired side length. This perpendicular with holes along it are the corresponding altitude of the triangles inside the desired polygon.
The pin- holes on these perpendiculars are numbered as 5, 6, 7, 8 etc. and. hole No. 5 corresponds to the centre of a pentagon no. 6 corresponds to the centre of a hexagon of the given side lengths and so on.
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(ii) Insert the centre pin at the appropriate centre hole and keeping the device at the desired position, draw the first side of the polygon about the division edge (CD) equal to the reuired side length.
(iii) Keeping the position of the centre pin fixed, rotate the device about it such that the end point of the first side line already drawn becomes the starting point for drawing the second side of the polygon.
Repeat process step (iii) till the polygon is closed with the required number of sides. When the polygon is closed the construction is completed and thus regular polygons would be obtained. ALTERNATIVE WAYS OF USING THE INVENTION:
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As we can see from eqn - (iii) , there are three variables, viz r, 1 and 9 and in the chosen solution, the instrument is based on the length of the altitude given by


However, it is also possible to construct similar polygons by using the included angle (9) as the base (concept-E is based on this method). This instrument is more complicated requires many parts and is more delicate than the chosen concept. DESCRIPTION OF THE PRESENT INVENTION:
(Figure 2) illustrate an instrument which is made from
acryllic sheet of around 2mm to 5mm in thickness. The present
embodiment of the instrument of 3mm thickness is for
construction of polygons of sies 10mm to 60mm in steps of 10mm
i.e. 10, 20, 30, 40, 50 and 60mm and 35mm and 25mm. Each
vertical lines erected on the edge of the base of the instru
ment (CD), namely, b1, b2 , c1 c2 j1 j2 have five pin
holes each for a polygon having the number of sides 5 to 9.
In the horiontal base ( reference line) CD has a margin for accuracy at both ends of about 2mm each (i.e. Ca2 =k2D = 20mm) and the total length between a2k2 is exactly to be 60mm. The whole length a2k2 is graduated at an equal interval of 5 mm each and altitude lines like b1b2 c1c2, d1d2, e1e2, f1f2 and g1g2 are erected on the base CD on the LHS of the device as can be seen in Fig. (2). Now the altitude line b1 b2 is for all polygons having side length of 10mm ( ie. a2c2) and the pin holes numbered 5, 6, 7, 8 and 9 are for pentagon, hexagon, heptagon, octagon and Nanogon respectively. Similarly the altitude line C1C2 is for all polygons having side length of 20mm (ie. a2e2) and so on. To enable the user recognize the desired side lengths easily .


triangles like -o-10, -o-20, -0-60, etc. are also
printed on the instrument to read 10mm, 20mm, 60mm,
etc. It is not necessary that the letters , ,
and the altitude lines b1b2, C1C2' jl'J2 be shown
on the instrument.
Similarly, the other two altitude lines on the RHS of the device namely, h1 h2 and j1j2 are erected on the base CD at a distance of 17.5mm and 12.5mm from k2 to represent the centre or altitude lines for polygons of 35 mm and 25 ram side lengths respectively. On all these altitude lines namely, b1b2,
C1c2 , d1 d2 j1 j2, the pin holes for the device with
maximum diameter ( d -eg - To construct a polygon of 10mm side length of 7 sides polygon i.e. heptagon), the following steps may be followed.
(1) Hold the main device on a piece of paper where the figure
is to be drawn in the desired position.
(2) Draw the first line ( a2c2) of 10mm
(3) Holding the main device in the previous position, now insert
the pin of the holding device at the hole numbered 7 on the
altitude line b1 b2 and rotate the main device alone about the
pin till the point a2 of the instrument coincides with the
end point of the previously drawn line.

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Now draw the second line of the open polygon.
(4) Repeat the above step No. (3) till the polygon is closed and a regular heptagon would be obtained.
Figure 3 - and 4 shows details for two types of holding device pin and the centre pin holes on the instrument.
The invention described hereinabove is in relation to non-limiting embodiments and as defined by the accompanying claims.
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WE CLAIM:
1. A geometrical instrument for constructing regular polygon,
comprising a lightweight transparent sheet having two horizontal
sides (CD,AF) of which the side (CD) is the base of the instrument (2) having two vertical sides (CB, DE) and joining to said top horizontal line (AF) at an angle of 30 and 45 respectively said instrument (2) having plurality of vertical lines ( a1a2..... k1k2) at a predetermined steps starting from a point (C) at the left hand side of the base of the said instrument, said vertical lines are provided with pin holes ( 5 ,6,7, 8,9) for five to nine sided polygons, said instrument is operated by rotatably fixing at any one of the said pin holes
( 5,6,7,8,9) at any one of the vertical lines ( b2 b1. j1j2)
with a holding device (3) having a pin with a flat head,.
2. A geometrical instrument as claimed in claim 1 wherein
the said instrument is for side lengths 10mm, 20mm, 30mm, 40mm,
50mm, 60mm, 35mm and 25mm for polygons of 5 to 9 sides.
3. A geometrical instrument as claimed in claim 1 wherein
the instrument is made of transparent material such as acrylic.
4. A geometrical instrument as claimed in claim 1 wherein
the holding device has a pin which just fits inside the pin
holes of the instrument with no play.
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5. A geometrical instrument for constructing regular
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polygons as herein described and illustrated in the accompanying drawings.
A geometrical instrument for constructing regular polygon. The said instrument comprises a lightweight transparent sheet having two horizontal sides (CD, AF) of which the side (CD) is the base of the instrument (2) having two vertical sides (CB, DE) and joining to said top horizontal line (AF) at an angle of 30° and 45° respectively said instrument (2) having
plurality of vertical lines (a1, a2 k1 k2) at a predetermined steps
starting from a point ( C ) at the left hand side of the base of the said instrument, said vertical lines are provided with pin holes (5, 6, 7, 8, 9) for five to nine sided polygons said instrument is operated by rotatably fixing at any one of the said pin holes (5, 6, 7, 8, 9) at any one of the
vertical lines (b2 b1 j1 j2) with a holding device (3) having a pin
with a flat head.

Documents:

00929-cal-1999-abstract.pdf

00929-cal-1999-claims.pdf

00929-cal-1999-correspondence.pdf

00929-cal-1999-description(complete).pdf

00929-cal-1999-drawings.pdf

00929-cal-1999-form-1.pdf

00929-cal-1999-form-13.pdf

00929-cal-1999-form-18.pdf

00929-cal-1999-form-2.pdf

00929-cal-1999-form-3.pdf

00929-cal-1999-letters patent.pdf

00929-cal-1999-p.a.pdf


Patent Number 203361
Indian Patent Application Number 929/CAL/1999
PG Journal Number 11/2007
Publication Date 16-Mar-2007
Grant Date 16-Mar-2007
Date of Filing 25-Nov-1999
Name of Patentee KAMLIANTHANG GUITE DEPT.
Applicant Address Imphal Takyelpat - 795001 Manipur
Inventors:
# Inventor's Name Inventor's Address
1 KAMLIANTHANG GUITE DEPT. Imphal Takyelpat - 795001 Manipur
PCT International Classification Number B 43L 13/00
PCT International Application Number N/A
PCT International Filing date
PCT Conventions:
# PCT Application Number Date of Convention Priority Country
1 NA