User:Uday warang/Shree yantra

'‘Sriyantra’' Geometrical Constructions Chapter 1 Design 1

The figure of ‘sriyantra’ is a mystic diagram consisting of nine triangles intermingled in each other in such a way that there are 18 intersecting points of three lines each (i.e. sides of triangles) in the figure. One of the nine triangles is equiangular and eight are isosceles ones. The circular figure of Sriyantra is divided by a vertical diameter into two equal parts so that each part is a mirror impression of the other. For convenience we draw the figure of semi circle only and complete it by joining the mirror impression.

The vertical diameter of the semi circle is divided into 3 unequal parts. There is however some symmetry in their measurements. Let us take that the vertical diameter is of 100 unites.

a)The top portion is of 38.017152130056 unites. b)Bottom                    “  33.333333333333  “ c)Middle                    “   28.649514536611  “ d)Difference                (a -b) and (b-c) remains almost the same, i.e.4.6838187967223. This figure is also a common factor of three numerical figures at (a), (b) and (c). By dividing (a), (b) and (c) by the common factor we get 8.116700021926, 7.116700021926, and 6.116700021926 respectively. This shows that there is a numerical symmetry in geometrical drawings also.

Step-by-     Step construction is as under. The figures at pages 4 to 6 may be seen. Step1. -      Draw a semi circle with vertical diameter of 100 units. Let the center point be referred as 1, the top and bottom and points of the diameter by referred as 2 and 3 respectively.

Step 2.-        Divide the diameter into three equal parts. From the lower marking point draw a horizontal line 4-5 to meet Circumference in point 5. Step 3.-         Erase the marking points. Now take a marking point 6 on the diameter at a distance of 38.017152130056 units from the top end point of the diameter. Draw a horizontal line 6-7 from the said point 6 meet the circumference in point 7. Step 4-       Divide the diameter into nine equal parts and from the first marking Point from the lower and point of the diameter draw a horizontal line 8-9 as shown in the figure. Step 5-           Erase the marking points. Join points 2 and 5. Line 2-5 will intersect Intersect line 6-7 in point 10. Step 6. – Join points 3 and 7. Line 3-7 will intersect line 4-5 in point 11. Step7.-     Join points 8 and 10. Line will intersect line 4-5 in point 12. Step8.- Join points 6 and 12 and extend line 6-12 to meet the line 8-9 in point 9. Trim Out if any part of this line remains beyond point 9. Line 6-9 intersects line 3-7 In point 13. Step 9.- Draw a horizontal line from point 1 to meet line 6-9 in point 14. Step10.- Extend line 1-14 by about 10 units. From point 14 draw a line upward of               about 40 units making an angle of 60 degrees with the newly extended line. Step11.- Extend the newly drawn line from point 14 down wards to meet the diameter In point 15 and upward to intersect line 6-7 in point 16 and further to               Intersect line 6-7 in point 16 and further to intersect line 2-5 in point 17. This line will meet the circumference near point 2. Through point 17 draw a                Horizontal line to meet the diameter in point 19. Extend lines 19-17 and 8-10 to meet each other in point 20. Step 12. - Join points 11 & 16 and extend the line 11-16 to meet the diameter in point 21. Step 13.- From point 21 draw a horizontal line to meet the line 15-17 in point 18. Trim out if any part of this line remains beyond point 18. Step 14.- Draw horizontal line through point 13 to meet the diameter in point 22. Extend lines 22- 13 and 21- 11 to meet each other in point 23. Step 15.-  Draw a horizontal line from point 15 to intersect line 6-12 in point 24 and Meet the line 8-10 in point 25. Step 16.- Join points 25 and 19. Line 25-19 will intersect line15-16 in point 26. Step 17.- Through point 26 draw a horizontal line to meet the diameter in point 27 and to meet the line 21-11 in point 28. Step 18.-  Join point 28 and 22. Line 28 -22 must pass through the intersecting point 24. Step 19.-  Extend line 1-14 to meet line 19-25 in point 29. Join points 29 and 4. Step 20. – Erase all the reference numbers. Join the mirror impression of the semi Circular figure on the opposite side of the diameter and erase the line of the diameter. Thus the method by ‘ Saunhar Krama a’ is complete. The ‘ Bindu’ is invisible at the mind point of the base line of the inner most equilateral triangle.

Sriyantra Geometrical Constructions Design 2 There is a very little difference in Design No. 1 and 2. In design portion. In design No 2 measurement of small bottom is taken as 1/3rd of the bottom portion. In design No 2 Measurement of small top portion is taken as 1/3rd of the top portion. Therefore there is suitable change in the measurements of the top, bottom and middle portions. The circular figure of Sriyantra is divided by a vertical diameter into two equal parts so that each part is a mirror impression of the other. For convenience we draw the figure of semi circle only and complete the same by mirror impression. The vertical diameter of the semi circle is divided into 3 unequal parts. There is however some symmetry in their measurements. Let us take that the vertical diameter is of 100 unites. a)The top portion is of 37.7547753276364 units. b)Bottom                    “ 33.3333333333333 “ c)Middle                     “ 28.9118913390303” d)Difference           (a-b) and (b-c) remains almost the same i.e.4.4214419943030 “.

This figure is also a common factor of three numerical figures at (a), (b) and (c). By dividing (a), (b) and (c) by the common factor we get 8.539018577261, 7.539018577260 and 6.539018577260 respectively. This show that there is a numerical symmetry in them and thus we get symmetry in geometrical drawing also.

Step- by – step construction is as under. The figures at pages 10 and 11 may be                     seen. Step 1. -   Draw a semi circle with vertical diameter of 100 units. Step 2-     Let the center point be referred as 1, and the top and bottom end point of the diameter be referred as 2 and 3 respectively. Divide the diameter into three equal parts. From the lower marking point draw a                  horizontal line 4-5 to meet circumference in point 5. Step 3.-     Erase the marking points. Now mark a point 6 on the diameter at a                   distance of 37.7547753276364 units from the top end point of the diameter. Draw a horizontal line 6-7 from the said new point 6 to                   7 from the said new point 6 to meet the circumference in point 7. Step 4.-      Join points 2 and 5. Line 2-5 will intersect line 6-7 in point 8.Join Point 3 and 7. Line 3-7 will intersect line 4-5 in point 9. Step 5.-      Segregate segment 2-6 from the other part of the diameter and divide the segment into three equal parts and the first marking point from the upper end point of the diameter be referred to as 10. Draw a                     horizontal line of about 25 units length from point 10. Step 6.-       Erase the marking points join points 10 and 9. Line 10-9 will Intersect line 6-7 in point 11. Step7.-       From point 11 draw a line upward of about 40 units making an angle Of 60degrees with the line 11-7. Extend the newly drawn line from Point 11 upward to intersect line 2-5 in point 12 and further to meet the horizontal line from point 10 in point 13. And also extend the said line down wards to meet the diameter in point 14. Step 8.-   Draw a horizontal line from point 1 to meet line 11-14 in point 15. Join points 6 and 15 and extend line 6-15 to intersect the line 4-5 in point 16 and further to intersect line 3-7 in point 17. Step 9.-   Join points 8 &16 and extend the line 8-16 both ways to meet the Diameter and the circumference. Step10.-   Through point 12 draw a horizontal line to meet the diameter in point 18. Extend lines 18-12 and 16-8 to meet each other in point 19. Step 11.-  The pint where the line 8-16 meets the diameter be marked as 20. Extend line 6-17 and draw a horizontal line from point 20 to meet Each other in point 21. Step 12.-   Draw a horizontal line from point 14 to intersect line 6-16 in point 24 and further to meet the line 8-16 in point 25. Join points 25 and 18 . Line 25-18 will intersect line 12-14 in point 26. Step 13.-    Through point 26 draw a horizontal line to meet the diameter in                     Point 27 and to meet the line 9-10 in point 28. Extend line 1-15 to                    Meet line 25-18 in points 29 and Step 14.-     Erase all the reference numbers, join the mirror impression of the Semi circular figure on the opposite side of the diameter and erase the line of the diameter. Thus the construction of design No 2 is                     complete by ‘saumhar Krama.’ The ‘Bindu’ is at the mid point of                       base line of the innermost equilateral triangle.

Sriyantra Geometrical Constructions Design 3 The special feature of this figure is that the ‘ Centroid’ point of the innermost smallest equilateral triangle and the center of the circle outside the figure of nine triangles are one and the same. Hence the ‘Bindu’ (Bindi point) is visible and some worshipers insist on the same. In view of the above there is a change in the measurement and mathematical symmetry cannot be proved. Step- by step method of drawing the figure is as under. It can see the figures at pages 14,15.

Step 1.-  Draw a semi circle with vertical diameter of 100 units. Let the mod point of the diameter be referred to as 1 and the top and bottom end points of the diameter be referred to as points 2 and 3 respectively. Step 2.-  At a distance of 36.5 units from the bottom end point of the diameter draw a                 horizontal line 4-5 so that point 4 will be on the diameter and point 5 will be on                 circumference Step 3.-  Similarly at a distance of 35.0008956789403 units from the top end point of the Diameter draw a horizontal line 6-7 so that point 6 will be on the diameter and Point 7 on the circumference. Step 4.-   Join points 2 and 5. line 2-5 will intersect line 6-7 in point 8. Step 5.-   Similarly join points 3 and 7. Line 3-7 will intersect line 4-5 in point 9. Step 6.-   Segregate segment 2-6 of the diameter from other part of the diameter and Divide the same into 3 equal parts. Let the upper marking point be referred as                 10. Join point 10 and 9. Line 10-9 will intersect line 6-7 in point 11. Step7.-     Starting from point 11 draw a line upward (of about 20 units) making an angle of 60 degrees with line 11-7. Extend the said line downward to meet the diameter in point 12 and upward to intersect line 2-5 in point 13. Draw a                   horizontal line from point 10 and extend line 12-13 to meet each other in                    point 14. Step 8.-     Segregate segment 1-12 from the other part of the diameter and divide the same into two equal parts. With point 1 as center and radius equal to ½ of                   the segment 1-12 draw a circle. Extend line 2-6 to meet the circle in point 15. Draw a horizontal line from point 15 to meet line 12-13 in point 16. Join points 6 and 16. Step 9.-     Extend line 6-16 to intersect line 4-5 in point 17 and further to intersect line 3-7 in point 18 and to meet the circumference near point 19. Step 10-    Join points 17 and 8. Through point 13 draw a horizontal line to meet the Diameter in point 20. Extend lines 20 -13 and 17-8 to meet each other in                   Point 21. Step 11-    Through point 18 draw a horizontal line to meet the diameter in point 22. Extend line 22-18 and 10-9 to meet each other in point 23. Step 12.-    Extend line 8-17 to meet the diameter in point 24. through point 24 draw a                    Horizontal line to meet ( the extended ) line 6- 18 in point 19. The portion of                     Line 6-18, if any, beyond point 19 may be trimmed out. Step 13.-   Draw a horizontal line from point 12 to intersect line 6-19 in point 25 and to                    Meet line 8-17 in point 26. Join points 26 and 20. Line 26-2- will intersect Line 12-13 in point 27. Through point 27 draw a horizontal line to meet the Diameter in point 28 and to meet line 10-23 in point 29. Step 14.-    Join points 29 and 22. This line 29-22 must pass through the intersecting Point 25. Step 15.-    Extend line 15-16 to meet line 26-20 in point 30. Join points 30 and 4. Step 16.-    Erase all the reference numerical from 1 to 30 and join the mirror impression Of the semi circle on the opposite side of the diameter. Erase the line of the Diameter. A ‘ Bindu’ may be marked at the center by a circle of a suitable Size. This completes the construction.

Sriyantra Geometrical Constructions Design 4 The special feature of this figure is that the mind point of the altitude of the innermost smallest equilateral triangle and the center of the circle outside the figure of nine triangles are one and the same. Hence the ‘Bindi’ (Bindi point) is visible and some worshipers insist on the same. In view of the above there is a change in the measurement and mathematical symmetry cannot be proved. Step by step method of drawing the figure is as under. Please see page 18,19. Step 1.-  Draw a semi circle with vertical diameter of 100 units. Let the mind point of the diameter be referred to as 1 and the top and bottom end point of the diameter be                 referred to as point 2 and 3 respectively. Step 2.-   At a distance of 37.5 units from the bottom end point of the diameter draw a                 horizontal line 4-5 so that point 4 will be on the diameter and point 5 will be                 on the diameter and point 5 will be on circumference. Step 3.-   Similarly at a distance of 33.860162697716 units from the top end point of the diameter draw a horizontal line 6-7 so that point 6 will be on the diameter and point 7 on the circumference. Step 4.-    Join points 2 and 5. Line 2-5 will intersect line 6-7 in point 8. Step 5.-    Similarly join points 3 and 7. line 3-7 will intersect line 4-5 in point 9. Step 6.-    Segregate segment 2-6 of the diameter from other part of the diameter and divide the same into 3 equal parts. Let the upper marking point be referred as                   10. join point 10 and 9. Line 10-9 will intersect line 6-7 in point 11. Step 7.-     Erase the marking points. Starting from point 11 draw a line upward ( of                   about 20 units) making an angle of 60 degrees with line 11-7. Extend the said line downward to meet the diameter in point 12 and upward to intersect line 2-5 in point 13. Draw a horizontal line from point 10 and extend line 12-13 to meet each other in point 14. Step8.-      With point 1 as center and radius equal to the segment 1-12 draw a circle. The circle with intersect the diameter in point 15. Draw a horizontal line from Point 15 to meet line 12-13 in point 16. Join points 6 and 16. Step 9.-      Extend line 6-16 to intersect line 4-5 in point 17 and further to intersect line 3-7 in point 18 and to meet the circumference near point 19. The diagrams of                    page 19 should be enlarged (zoomed) Step 10.-    Join point 17 and 8. Through point 13 draw a horizontal line to meet the Diameter in point 20. Extend line 20- 13 and 17-8 to meet each other in point 21. Step 11.-    Through point 18 draw a horizontal line to meet the diameter in point 22. Extend line 22-28 and 10-9 to meet each other in point 23. Step 12.-     Extend line 8-17 to meet the diameter in point 24. Through point 24 draw a                    Horizontal line to meet the extended line 6-18 in point 19. The portion of                    Portion of line 6-18, if any, beyond point 19 may be trimmed out. Step 13.-     Draw a horizontal line from point 12 to intersect line 6-19 in point 25 and to                     Meet line 8-17 in point 26. Step 14.-     Join point 26 and 20. Step 15.-    Line 26-20 will intersect line 12-13 in point 27. Through point 27 draw a                   Horizontal line to meet the diameter in point 28 and to meet line 10-9 in                      Point 26. Step 16.-     Join point 29 and 22. This line 29-22 must pass through the intersecting Point 29. Step 17.-      Extend line 15-16 to meet line 26-20 in point 30. join points 30 and 4. Step 18.-      Erase all the reference numerical from 1 to 30 and join the mirror Impression of the semi circle on the opposite side of the diameter. Erase Line of the diameter. A ‘Bindu’ may be marked at the center by a circle of a                             Suitable size. This completes the construction.

Sriyantra Geometrical Constructions Design 5 The special feature of this design is that the apex point of the innermost smallest equilateral triangle and the center point of the outside circle are one and the same. Measurements are accordingly changed. Step-by-step method is not given here. Those who have gone through the previous four methods can easily draw the figure referring to the drawing at respective pages.

Sriyantra Geometrical Constructions Design 6&7 Designs No 6& 7 are based on single measurements. Successive step-by-step construction of the figures is shown in the diagrams at pages 24, 25 & pages 26 to 28. Readers who will study the methods given in previous pages will not find any difficulty in understanding the methods of construction of these figures.

Sriyantra Chapter II Srusti yoga krama Methods of construction of sriyantra by Saunharkrama have been show from Design 1 to 5. The method of construction of sriyantra by srustikrama is being explained below. With the method explained below all the designs from 1 to 5 can be drawn by Srustikrama. The diagram at page 33 to 37 may please be seen. It is necessary to have measurement of line segments of lines indicated by nine alphabets ‘a’ to ‘i’ in the figure at page 33. After getting the measurement of nine segments, five proportions as stated in the first column of the Ready Reckoner (page 34) are worked out. Five Sriyantras of different specifications are drawn first by Saumharkrama and then measurement of nine segments of line from each figure are taken. Five proportions are worked out for each figure. The method of drawing the figure is common for all the five figures. One has to take corresponding proportions are given in five columns. The CAD version now available to the author is old one and is not giving satisfactory service. Readers,/ Interested persons however are requested to try the method on any recent version of computer CAD. However it is wonderful and beyond imagination as to how our forefathers could think of such a complicated figure in the absence of computer and such advance instruments. Step-by-step method of construction of Sriyantra by Srustikrama is given below. Please see page 35 to 37. Step 1.- Draw a horizontal straight line of suitable length (say about 20 cm). Step 2.- Taking the end points of the said lines as centers and radius equal to the length Of the line draw arcs of circles (below the line) intersecting each other. Step 3.-  Join the end points of the horizontal line and the intersecting point of the arcs so                             So that an equilateral triangle is drawn. This is called a first ‘ Shakt’ triangal. Step 4.-  Draw a vertical altitude of the triangle (i.e. the line from the vertex point to the                  mid point of the base). Step 5.-   Taking the vertex point as base reduce/shrink the length of altitude by scale 0.5700483009966(*). Note: (*)  For drawing different  figures corresponding scales shown in the ready reckoner are used. With the help of computer only the length of the line already drawn can be reduced by the given scale. (It is not cut or trimmed out). Similarly the length can be increased to required scale. Step 6.-    From the upper end point of the reduced altitude draw a horizontal straight line both ways. This line will be terminated both sides by the sidelines of the First/ shakti triangle. Step 7.-   Taking the mid point of the said line (i.e. the top end point of the reduced                  altitude) as base, extend the said line both ways by scale 2.4054114340112 (*). Step 8.-   Taking the top end point of the reduced altitude as base, extend the altitude downwards by scale 1.959159702694(*). Step 9.-   By joining the end points of the extended horizontal line and the extended Vertical (altitude) line, complete the second triangle. The equilateral triangle Inside this second triangle is known as Adya (Shakti ) triangle/ (Trikona). Step 10-   Through the vertex point of the first triangle (and also of the Adys Trikona) Draw a horizontal straight line both ways. This line will be terminated by the sidelines of the second triangle. Step11.-   Taking the mid point of the said line as base, extend the said line both ways by                   Scale 1.4520088415275(*). Step 12.-   Join the end point of the said extended line upward to the intersecting point of                     the sides of the first triangle and base line of the second triangle. Step 13.-   Extend the said lines upward to meet each other in one point beyond the first (initial) horizontal line. Thus the thirs (i.e. first Shiva) triangle is completed. In this figure there is chain of eight small triangles. Therefore it is called as                   ‘Astar’ or Astar Cakra. Step 14.-    Join the side vertices of the second triangle and the side vertices of the first Triangle by oblique lines (sea figure 14). Step 15.-     Extend the oblique lines upward to meet each other in one point. Step 16. -    Extend the horizontal line drawn through the vertex of the first triangle both ways and also extend the oblique lines (which were last extended upward) now horizontal line will meet each other and the second Shiva triangle will be completed (fig.-16). Step 17.-      Taking the mid point of the first line as base extend the first line both way by                      Scale 1.694932787628 (*). Join the end point of this extended first line and the vertices of the 4th and 6th smallest triangles out of ‘Astar Cakra’ ( fig.17). Step 18.-      Extend the last drawn oblique line down wards to meet each other in a point (fig. 18). Step 19.-      Extend the sidelines of the first Shakti triangle upward and also extend the sidelines of the first ‘ shiva’ triangle downwards. (Fig.19). Step.20.-      Draw horizontal lines through the top and bottom apex point of the ‘Astar’ to meet the line extended as explained in step 19 and to complete the said triangles (fig.200. Thus a chain of 10 small triangles is completed. This figure                      is called as ‘Antar Dashar. Step 21.-        Join the pairs of vertices in each quadrant (at the North-East, East-South, South- West and North- West directions) by oblique lines (fig.21). Step 22.-       Extend the oblique lines in the upper quadrants upward and in the lower                        quadrant downward to meet each other in respective point at the North and                        South directions (fig.22). Step 23.-         Now extend the said oblique lines in the upper quadrant downwards and in                         the lower quadrant upward to meet the horizontal line passing through the                          bottom and top apex point of the ‘Astar’ respectively and to complete the                         respective triangles ( see fig.23). Step 24.-         Once again extend further the sides of first ‘Shakti’ triangle upward and the                         sides of the first ‘ Shiva’ triangle downward to meet the horizontal lines                        passing through the apex point of ‘Antar Dashsr’ and to complete the chain of 10 small outer triangles. This outer chain of triangles is called ‘Bahir Dasher .(fig.24) Step 25 .-         Join the point of the pairs of vertices in all the four quadrants by oblique lines (fig.25). Step 26.-        Extend the said oblique lines in upper quadrant upward and in the lower quadrant downward respectively to meet each other at the North and South directions. (Fig.26) Step 27.-         Again follow similar procedure of extending the lines as explained in step Nos. 23 and 24. A chain of 14 small triangles will be completed. This chain Of triangles is called ‘Catur Dashar.’(Fig 27) Step 28.-         Draw a circle passing through the six outer points. Thus the figure of nine Bigger trianglesn inside the circle is completed by Srustikrama.

Sriyantra Chapter III Construction of ’’ Astadala, Shodashadala amala Bhoopura’

‘Sriyantra’ consists of nine elements namely 1) Bindu, 2) Trikona, 3) Astar, 4)Antar Dashar, 5) Bahir Dashar, 6) Catur Dashar, 7) Astadala kamala, 8) Shodashadala kamala and 9) Bhoopura. The methods of constraqting the first six elements by Saumhar karma and Sristi karma have already been explained in the previous pages. The method of constructing remaining three elements is now explained below. Step 1: - Let us take a Sriyantra diagram of six elements as already completed (Fig.1) Step 2: - Take a copy of the circle from the said diagram and draw its vertical radius from it              center point upward to the circumference Extend the said radius by three times its                own length, base point being the center of the circle. Step 3:-  From the center of the circle draw an oblique line upward making an angle of 45               degrees with the line of the vertical radius. Trim out or erase the line of the vertical radius inside the circle. Divide the extension part of the line lying out of               the circle in to 17 equal parts (Fig. 3). Draw 4 concentric circles passing through the 3rd, 6th, 7th and 8th marking points from the initial circle. Draw 3 horizontal line from the ninth, tenth and eleventh marking points to meet the oblique line. ( Fig.3) Step 4:-  Divide the horizontal line drawn from the eleventh marking point up to the oblique line into 5 equal parts (by 4 horizontal marking points). (Fig.4). Draw a                draw a horizontal line from the top end point of the extended vertical radius. Draw a vertical line from the intersecting point of the oblique line and the horizontal line from point 11. These two lines will intersect and terminate each other. Draw six horizontal lines from the remaining six vertical marking points to vertical line already drawn. Through the first horizontal marking point draw a vertical line both ways to meet the first and the last horizontal lines. From the third horizontal marking point draw a vertical line upward to meet the last horizontal line. This vertical line should be trimmed between the 11th and 12th horizontal lines. At a small distance from this vertical line draw a vertical line draw a vertical parallel line of equal length. (Fig.4). Step 5:-  Erase all the vertical and horizontal marking points. Out of the 9 horizontal line trim out only 6 horizontal line from bottom between the extended radius and the first vertical line. (Fig.5) small parts of 6 horizontal lines from top between the two vertical line be erased or trimmed out so that a set of six lines will be                segregated or amputed from the other parts of horizontal lines. The block of 6 horizontal line now segregated from the other part may be rotated by 90 degrees and the same block will now be turned as vertical line. (Fig.5) This block of 6 vertical lines may be divided in to two blocks of 3 lines each. They will appear like cricket stumps. Step 6:-   Move the block of 3 vertical lines (Like stumps) and paste the same at the bottom end point of the first vertical line meeting the first horizontal line                   (Fig.6). Similarly move the second block of three line and paste the same at the Intersecting point of the vertical line starting from the third horizontal marking Point and the horizontal line starting from the 12th vertical marking point (Fig.6) Step 7 & 8: - A specimen copy of ‘ Sriyantra’ may be kept available for ready reference. After careful and proper study of the diagram and by repeated use of the command ‘Trim’ the required drawing can be achieved. Note:-     It is really wonderful and beyond our imagination as to how our forefathers could think of such a complicated diagram in the absence of modem instruments, implement and machines like ‘Computer (CAD)’. It becomes a subject for research as to whether our forefathers had the knowledge of ‘Computers or                similar machines and their use. The method herein explained is with the help of a               Computer. Step 9:-   A copy of the drawing completed up to step 8 may be taken for further alteration, additions etc. The drawing between the first vertical line and the oblique line may be trimmed out or erased. (Fig.9) Step 10:-  The border of drawing covering the vacant portion of the second, third, forth and half of first quadrant may be restricted to half of first quadrant only as                  shown in Fig. No 10. Step 11: - The border of the drawing may be again reduced to 1/8 0f circle. (Fig.11) Step 12:-  Each of the three inner arcs may be divided into two equal parts and one part may be trimmed out.(Fig.12) Note:-       In figures No 13 to 16 the normal size dose not give a clear impression. It gives a cloudy, clumsy and awkward impression and hence zoomed copy is shown, but the proportional size of the figure is not changed in comparison to the other parts of the diagram. Step 13:-  Now we are concerned with a four-sided figure, One of which is vertical straight line, other an oblique line and two concentric arcs. (We are not concerned with                  still outer two arcs.) Divide each of the inner and outer arcs into two equal parts. Draw a straight line joining the midpoints of the arcs. The figure is now divided Into four quadrants. Each of the straight lines be divided into 8 equal parts. By                   the help of ‘arc’ command draw 4 parallel concentric arcs passing through the first, third, fifth and seventh marking points from the inner arc. Step 14:-  Divide each of the three arcs into 8 equal parts. In the second quadrant draw a                     Straight line dividing the quadrant into two equal parts. Mark the mid-point of                              This line. Erase all the other marking points. Now once again divide the inner And outer arcs each into 16 equal parts. Retaining only one marking points on the arcs should be erased. Draw a straight line joining the retained marking points.

Step 15:-  Divide the middle line into 4 equal parts. Retaining the marking point near the Innermost arc erase the two other marking points on the middle line. Taking ‘mirror’ command select the first line near the vertical line and using the second line near the vertical line as base draw the mirrored line near the middle line. Similarly taking ‘mirror’ command once again select the first line near the vertical line and using the middle line as base draw the mirrored line near the oblique line. Taking ‘Arc’ command and using three points namely 1) intersection of vertical line and outer arc 2) intersection of line near the vertical line and the arc near the outer arc and 3) mid point of the middle line (second line from the vertical line), draw one forth part of Shodashadala Kamala. Similarly taking ‘Arc’ command and using three points namely 1) midpoint of the middle arc and mid-point of the middle line 2) intersection of nearer line and nearer arc 3) Mid-point of the middle line (second line from the vertical line), draw one forth part of Shodashadala Kamala. Thus half petal of Shodshadala Kamala is completed. Other half can be joined by mirror impression. By adopting similar procedure half petal of Astadala kamala can be deawn.(Fig. 15) Step 16:-  Retaining the four borderlines and the curved lines of petals all other lines be Erased. By using mirror impression two petals in the outer arcs and one petal in the inner arcs can be drawn. Step 17:-  By appropriately amalgamating Fig. 10 and Fig. 16, Fig. 17 can be achieved. step 18,19 and 20:- By skilful and appropriate use of ‘mirror’ command Fig. 18,19 and 20 can be achieved. Step 21:-  By amalgamating Fig. No. 1,8 and 20 final diagram can be achieved. Maximum care Should be taken to see that the circles and the straight lines are continuous and without break. Similarly it is necessary to see that the circles and straight lines are not copied one over the other repeatedly. Thus the construction of the outer three elements of Sriyantra is completed.

Sriyantra Chapter IV Traditional Rangavali fashion

About 2/3 generations ago there was a fashion in joint Hindu families of decorating the house every morning by drawing some figures with white stone powder on the ground. ‘ Sriyantra’ is one of the figures, which were generally used in such decorations. It is a mystic geometrical figure of nine triangles intermingled in each other and bounded by a circle. Sau. Shubhada Shreepad Tatke (c/o Shree Anandswami. 22/14 D. Near Ranade High School, Zawbawadi, Thakurdwar. Mumbai. 400002 ) who had received the lesson of drawing figure from her grand mother in law in tradition demonstrated method in the past. The successive step-by-step method is as under. Step-1: With the help of a glass, vessel, cup or a circular disk of a suitable size a draw a                   circle with white stone powder. ‘Rangavali’ mark the end point of the vertical diameter on the circumference. (See Fig. 1)

Step 2: With help of foot-rule mark second point on the vertical diameter (without actively            drawing the line of diameter) dividing the same from top to bottom in the proportion approximately or either 8:6:7 or 8.5:6.5:7.5 draw two lines thought this point perpendicular to the diameters and reaching the circumference. (Fig.2)

Step 3: Draw 2 lines parallel to the above lines in the top portion diving the same into 3 approximately equal parts. Similarly draw 2 lines parallel to the above lines in the bottom portion dividing the same into 3 approximately equal parts. (See Fig. 3)

Step 4: Draw 3 lines in the middle portion, Parallel to the above lines. The length of these seven (2+2+3) lines is to be decided by repeatedly drawing the figure and by usual practice.’ Practice makes a man perfect’. Step 5: With the help of the foot rule mark the mid points of these nine lines (2+2+2+3) (Fig.5) Step 6: The end points of the third line from top be joined to the bottom end point of the diameter. Similarly the end points of the third line from bottom be joined to the top end point of the diameter. Step :7  The end point of the second line from bottom be joined to the mid point of the third line from top. The end point of the first line from top be joined to the mid point of the forth line from bottom (Fig. ) Step : 8  The end point of the first line from bottom be joined to the mid point of the third line from top. The end point of the first line from top be joined to the mid point of the forth line from bottom (fig ) Step : 9  The end point of the forth line from top be joined to the mid point of the second

line from bottom. The end points of the forth line from bottom be joined to the mid point of the second line from top. The end point of the fifth line from top be               joined to the mid point of third line from bottom

In search of ‘SRIYANTRA’ GEOMETRICAL CONSTUCTONS

BY D.N. UKIDWE D-238 NEW SABNISWADA SAVANTWADI, SINDHUDURG MAHARASHTRA, INDIA 416510 TEL NO. 02363-273317

MOST HUMBELY DEDICATED TO THE BRAHMIBHUT P.P.SWAMI TAT- TAMANANDJI SARASWATI (ALISE TAMBE SWAMI) OF KASHI-VARANASHI

Author D.N. Ukidwe Birth Date 02-05-1928