Vedic Geometry

 

Vedic geometry

A salute to Indian Mathematics

 தாய் அவள் போல் ஒரு ஜீவனில்லை

அவள் காலடி போல் சொர்க்கம் வேறு இல்லை

தாய் மண்ணை போல் ஒரு பூமி இல்லை

பாரதம் எங்களின் சுவாசமே

               India stands as an epitome in contributing rich values, ethics, knowledge to the entire world all through the ages. Mathematics is a branch of wisdom which ancient Indian people practiced in a well-structured and developed manner. Indians gave the world ‘ZERO’. The mathematical achievements of ancient India remains hidden, but they are coming to the surface in recent times. Now – a – days many books have been written about the advanced mathematics practices in India, including trigonometry and calculus which reached Europe in the Middle Ages through the Arabs. 

1. Drawing East West line

·         A stick is fixed and a thin rope of length equal to the stick is fastened to it. A circle is drawn with the help of the rope with the stick as the centre.

·         The shadow of the central stick touches the circle twice in a day. Mark the points and two sticks are fixed at those points.

·         The line joining these sticks represents East – West line.

                                                                                        

·         After fixing East – West line, a rope of double the length is tied to the two sticks.

·         The midpoint of the rope is stretched on both the sides to locate a point on either side of East – West line.

·         Joining these two points provide a perpendicular to East – West line and represents the North – South line.

2. Construction of an exact square

·         Fix a rope of required angula (say 5 angula) and place it on East – West line and mark E and W such that EW = 5 angula.

·         Mark the midpoint P of EW. (Hold the two ends of rope together to fix the midpoint.

·         Draw a circle C with EW as diameter.

·         Draw circles with E and W as centers and EP as radius.

·         Now in North – south line C intersects at two points say Q and R.

·         Again draw circles with Q and R as centers and same radius.

·         These 4 circles intersect at four points A, B, C and D.

·         Join AB, BC,CD,DA.

·         Now ABCD is a perfect square of side 5 angula.

3. Construction of a circle of same area 

Now we construct a circle whose area is equal to the area of above constructed square S.

·         With O as center (midpoint P is taken to be O) and OA as radius draw a circle C1.

·         C1 meets East West line at F.

·         Measure the length between the meeting points of C1 and S with EW – line using a rope.

·         Fold the rope as such it forms 3 equal pieces.

·         Place the rope on EW – line such that its one end is at G and other end meets GF segment at H.

·         Now with O as center and OH as radius draw a circle shaded orange in Figure.

·         This circle has same area as that of square S.

Calculations behind:

Let us verify whether it is true or not.

The area of S = 25 sq. angula.

Area of the circle = 25.4 sq. angula.

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