Seventy Constructions in Geometry- Exploring into the Constructional Possibilities in Geometry (Bharatiya Sasthracinta Book X)

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About the Author Born at Chekrakkal illom of Chelannur Village, Kozhikode District. Degrees in Chemistry with Physics & Mathematics as subsidiaries from Madras University and in Teaching from Madras University. Certificate Courses of State Institute of Education in Guidance, Evaluation, Environmental Studies.

Health Education of Health Dept., Community Development Course of Sree Mouni Vidya Peeth, Gargotti, Maharashtra. State Resource Person in Science and Mathematics. Member of Syllabus and Text Book Committees in Mathematics.

Services as High School Assistant, Assistant Educational Officer, Headmaster of Govt. High School, Teacher Educator & Part Time Lecturer of Govt. Polytechnic.

Preface There are easy as well as difficult constructions in geometry. To divide a line segment into three equal parts is an easy construction but to divide an angle into three equal parts is a difficult one. It is even considered as an impossibility and is taught as such in P.G. classes in mathematics. In this context the author gladly submits his own invention of more than one method for trisection of a given angle. An example is given in these pages for the kind judgement of higher mathematicians. More than this the author proposes hitherto unproposed problems like pentasection of a given angle and also heptasection of a given angle. And solutions by way of construction followed by proof, can also be seen in these pages. The correctness or otherwise of these are to be examined and confirmed by experts.

For each construction, the statement of the problem, the actual steps of constructions, the figure representing this and also the proof for the correctness of the construction are given. Thus the book may be of interest to geometricians, artists, tantric artists researchers. Anyhow as an experienced academic teacher, as a teacher educator, as a member of mathematics syllabus committee and also of textbook committee, the writer feels it necessary to give greater importance to geometry in predegree education. It is also noteworthy that we Indians have a high heritage in the field of geometry. Sreechakra which is considered even as a divine figure representing the principles of creation, is indicated in Upanishads like Arunopanishad. Tripuratapinyupanishad etc. Though the guiding rules for construction have been given by different sources, the perfect figure is beyond them. The Russian Scientist Alexi Pavlovich Kulaichaiv, after his continued research with his latest type computer, opines that it is almost impossible to construct Sreechakra observing all the specifications given about it.

Introduction It is an honour to write a preface for this book on Seventy Constructions in Geometry, the 10 book in the Scientific Thought Series. Dr. C. Krishnan Nambudiri, the author of this compilation is more like a teacher to me. When I was engaged in my post doctoral research in Vastuvidya, trying to fathom into the traditional wisdom in architectural engineering Dr. Krishnan Nambudiri gave me an insight into technical Sanskrit for interpreting ancient treatises. Now reading through this concise book on geometrical construction I was delighted to revise the basics of many interesting application of geometry in the area of Vastuvidya.

The geometrical construction shown in fig. 50 for example is the basis of construction of ceiling of square shaped temples by stacking granite slabs successively from corners. Firstly the four corners of the cella are covered with thick slabs creating a smaller square opening. Secondly the corners of this smaller square are covered by slabs. This process is continued till the pyramidal ceiling is completed. This interesting pattern can be seen in temples of Tamilnadu, where one can go right inside the garbhagriha of a temple.

In the temples of Kerala, this method is modified as a corbelling process called kadalikarana. Here the square cella is first made octagonal in shape at the ceiling level of the wall. The basis of this construction is given in figure 53. The corbelling starts at mid height of the wall in the four corners and reaches the top of the wall. This construction continues till the octagonal pyramidal dome covers the cella with brick or stone.

The granite pillar of square section is called Brahma Sila. It can be made octagonal in section by method indicated in fig. 53. It becomes Vishnu khanda. This can be made 16 sided in section by method shown in fig. 55. This process can be used for conversion of the section to 32 sided and 64 sided polygonal shape. Lastly the section is smoothened into a circular section.

**Contents and Sample Pages**