A symbol of concentric circles and 33 rays -Created by Charles R Henry. This is our symbol as sign of honoring a friend.

A key to unlock

The mystery on a

Geometrical Nazca Marking.

Part-2

T.L. Subash Chandira Bose and Jack Andrews.

With the modern technology of CAD design we begin our study by drawing in our home PC (computer).

“Orientation”(Marking the Cardinal and Ordinal Directions)

Chapter 6 – Orientation, Maya Mata describes the ancient geometrical method to find out the directions.

6.1-2a: Now I give the method of determining the cardinal points with the help of gnomon. (One should proceed) at sunrise during a month when the solar path is towards the north during a bright fortnight when sunrise is beautiful, when there are no spots in the solar disc and when the sun is in the asterism of the appropriate fortnight.

6.2b- 3a: First of all a piece of ground in the middle of the chosen site should be leveled by the water method; this must be square one square pole in the center in the center of which the gnomon should be set.

6.3b- 5: Herewith the dimensions of the gnomon (Sanku): the largest kind is one cubit long, its diameter at is one digit at the top and five at the bottom, it is perfectly circular and without irregularities; one of medium size (has a length of) eighteen digits and a small one a length of twelve or nine digits, their diameter at the top and bottom being (in all case) proportionate to their length.

6.6- 7a: The materials prescribed for the making the gnomon are as follows: Ivory, sandalwood, wood of khadira, kadara, sami, saka or tinduka or other hard wood; its tip should be perfectly circular.

6.7b- 8a: When the gnomon has been made it is set up in the chosen place at sunrise, then a circle is drawn of which the gnomon is the center and which the diameter is double the length of the gnomon.

6.8b-11a: The line which join the two points where the shadow (of gnomon) has touched the circle in morning (A) and in the evening (B), gives the east - west direction. The line which passes through the space between these two points and (which is like that which) connects the head and tail of a carp, is the north - south axis; the sage should draw these two lines, Then the circles which have their centers at the east and west points should be drawn.

Apacchaya

6.11b- 13: (When the sun) is in Taurus or Virgo there is apaccya; when it is in Aries, Gemini, Leo or Libra the (east-west axis) must be put back two digits; when it is in Cancer, Scorpio or Pisces it must be adjusted by four digits, when it is in Sagittarius or Aquarius (it must be adjusted) by six digits and when it is in Capricorn by eight digits. The east-west line is to be fixed after it has been moved to the right or to left of the shadow.

Apacchaya – Contd.

6.27: (The east=west line) should be established with adjustments of the following numbers of digits for each ten day period of each month: (Aries) two, one, zero, (Taurus) zero, one, two, (Gemini) two, three, four, (Cancer) four, three, two, (Leo) two, one, zero, (Virgo) zero, one, two, (Libra) two, three, four, (Scorpio) four, five, six, (Sagittarius) six, seven, eight, (Capricorn) eight, seven, six, (Aquarius) six, five, four, (Pisces) four, three, two.

6-28: When the course of the sun has been taken into consideration in relation to the constellations, the indicated adjustment should be made, when necessary; the correction once made, the line is drawn from the stake and the ground can be prepared.

With refer to “Mayamata: Chapter-6”, an ancient method of marking Cardinal direction and four cardinal (lines) four directions N-S and then E-W were marked. On the basis of ancient geometry “Bodhayana Sulpasutra: 1.22-23” a square was drawn and four ordinals directions (NE, SE, SW and NW) are marked.

Plus + (cross) mark or “KA”

In the above diagrams of marking the cardinal directions; the E, W, N and S directions forms a symbol of a Plus + (cross) mark.

When we studied various ancient manuscripts and we are surprised to know that “KA” is the first number. “The One” in ancient number system and also represents unity. Since it is part of all numbers it represents the ideal symbol of deity. It is the origin, the elementary.

Interestingly we find in Mayamata, Diagrams - Chapter: 7. 57, the word “Ka” represent “The Supreme”. In the ancient Puranas we find many names for Sun (Surya) one among those name is “Arka” (Ar + Ka) –“The Radiant One”. We also find the word “KA or CA” in Inca (In + ca).

The ancient numerical system were initially originated in India, and during the third Tamil Sangam period and also in post Indus (Brahmi) numerals; the number “one” was symbolized as a plus (cross) + mark. We have found many ancient inscriptions in Tamil Nadu, in which the Tamil Letter “KA” was used for, number “one”. The plus (cross) + mark or “KA” will further discussed in part 3.

A: Pre Second Tamil Sangam Period or early Indus Numerals. B: Pre-Third Tamil Sangam Period or mature Indus Numerals. C: Third Tamil Sangam or post Indus (Brahmi) numerals.

Thanks to: “Indus Scripts Among Dravidian Speakers”- Dr. R. Mathivanan.

Thanks to: S.Ganesan and R.Jayaraman –Jr. Epigrapher, Department of Archeology, Tamil Nadu, India.

For additional information regarding ancient numerals please visit the web site:

http://www.oocities.org/rmlyra/hindi.html http://www.oocities.org/rmlyra/Numbers.html.

Above Left: A marking of the Plus + mark with in the square, which also represents four directions.

Above right: The symbol at right with eight directions. Below: The symbols showing the Plus + mark (cross) found in Tamil Nadu, India.

Interested persons to use these pictures for reference with the exact location of the symbols in Tamil Nadu are requested to get the written permission from :(lscbose@eth.net)

Doubling the area of Square: The famous “Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.”

The above “Pythagorean theorem” is applicable to a right angled triangle but we find in Bodhayana Sulpasutra: 1.46-47(theorem of rectangle) the steps by set, we can go up to the square with area =na², which is also indicated in Katayana Sulpasutra.II.8-9.

The first area of the square is doubled and three circles are also drawn {refer the below diagram squares (red) and the circles (Green)}.

The area of square further doubled and nine circle all drawn as shown in the below diagrams. The square was divided into sixteen parts (squares) and finally into sixty-four parts (squares).

Sixteen Directions or rays: In the book “Hidden Treasure of Vastu Shilpa Shastra and Indian Traditions” - Derebail Muralidhar Rao, Page 23.) We find: It is a common knowledge that the direction where the sun rises is known as East - Poorva or Puurab, where it sets as west-Paschima, the North- Uttara and South- Dakshina. The corners where two directions meet obviously is more significant since it combines the forces emanating from both the directions. Northeast corner is called as Eeshanya, Southeast corner as Aagneya, Southwest corner as Nairuthrya and Northwest corner as Vaayavys. The every corner has been further divided into two sides each such as:

North –East 1. East North East - Eastern side of North-East.

2. North East - Northern side of North- East.

South-East 1. East South East - Eastern side of South –East.

2. South East- Southern side of South-East.

South-West 1. South West- Southern side of South=west.

2. West South West – Western side of South West.

North-west 1. West North West - Western side of North West.

2. North North West – Northern side of North-west.

Interestingly we observe in the diagrams of orientation of cardinals directions, only a circle “One”, circle with divided into with North and South cardinal line, which divide the circle into ”Two”, with four cardinal directions (E, W, N and S) divide the circle/square in to four and with eight directions divide the square into eight triangles. With the above sixteen directions, form a square with sixteen parts.

1,2, 4, 8 and 16 directions, It is amazing to know the “MU” symbol found in Peru have sixteen rays. Also we have observed there are sixteen rays in the center of the Geometrical Nazca Marking or GGF.

“The Surprise is the beginning of understanding the Mystery ”.

(Part – 3 shall continue.)

http://www.oocities.org/tlscbose/NazcaPart-3.htm