| INTRODUCTION | | | | units, tenths, hundredths or thousandth place, indicate |
| The philosophy of education is to acquire right | | | | their respective values and magnitude. |
| knowledge of different aspects and dimensions of the | | | | In arithmetic operations one finds use of complimentary |
| world around us and to disseminate the same for the | | | | numbers very effectively and finds 10 different |
| benefit of the individual, society, nation and world. | | | | varieties of multiplication based on the Vedic |
| The present day's education, though has undergone a | | | | mathematical Sutras propounded by H. H. |
| radical change, with the development of modern | | | | Bharatikrishna Teertha (1880-1964). He being a brilliant |
| science and technology, especially the computers, | | | | scholar and Saint discovered 16 aphorisms and 16 |
| much needs to be done on the holistic approach to | | | | corollaries after 8 years of intense penance, covering |
| education, which can evolve personality. One might get | | | | variegated topics (both elementary and advanced) in |
| tremendous amounts of information by logging on to | | | | mathematics. Consider the following examples: |
| the Internet, and the glut of information will lead to | | | | (i) Complimentary numbers Here the objective is to |
| information garbage. In spite of all these we are lagging | | | | convert all the numerals greater than 5 to less than 5 |
| in imparting right education to right people thereby, | | | | in order to facilitate speedy calculation and reduce |
| creating disharmony. Therefore, one needs to have | | | | carry over. For ex. 9,8,7,6 are expressed as 1,2,3 |
| proper guidance and an evolved system which will | | | | & 4 respectively with base as 10. |
| lead to evolution of personality. This system should | | | | (ii) Using complimentary notation known as 'Vinculum' |
| have a positive impact on the thinking process, beliefs, | | | | following examples will make clear, about the usage |
| attitudes with its holistic approach to concepts, | | | | and benefits of this: |
| methods and techniques; thus creating harmony and | | | | (a) 28 -> 32 [eq. to 30-2] |
| ushering in peace. | | | | (b) 19 -> 21 [eq. to 20-1] |
| Today, in majority of the cases, mathematics is | | | | (c) 278 -> 322 [eq. 300-22] |
| considered to be a dry subject and still notion exists | | | | (d) 289621 -> 310421 |
| that it is only for the intelligent. Many dread | | | | Note: whenever complimentary notations are used, the |
| mathematics, because the teachers themselves teach | | | | digit preceding, gets augmented by 1 and while |
| in an unimpressive way and the joy of making learning | | | | normalising it gets reduced by 1. In the example (d) we |
| of mathematics a pleasurable experience is almost | | | | see how only the digits greater than 5 are converted |
| lacking. This is found right from the school to the | | | | and the others remain as they are. |
| college level. | | | | Before we take up other topics in Mathematics we |
| In this regard, Vedic/Ancient Indian Mathematics (VM | | | | cannot help but quote some examples on the |
| AIM) with its wonderful concepts, methods and | | | | philosophical aspect of numbers, which the ancient |
| techniques, which have stood the test of time comes | | | | seers very effectively utilised. |
| in handy for imparting a holistic, creative education in | | | | Now let us consider this very interesting example. The |
| mathematics. | | | | idea of counting nine numbers and zero which is an |
| The Vedic Seers and Ancient Indian Scientists and | | | | Indian system is closely connected with nine months of |
| Mathematicians perceived mathematics in Nature, in | | | | development of human embryo. Man develops in nine |
| the form of primordial concepts, the different shapes | | | | months through nine successive stages, like the nine |
| and patterns symbolising the cosmic truths in the Micro | | | | number and completes his birth in the 10th and this is |
| and Macro aspects. | | | | the 10th Avatara of 'MAN' to put it figuratively. Similarly |
| Mathematics was developed right from the | | | | the body has nine openings (Navadvara) and the 10th |
| fundamental concepts of Numerals, Place value, Zero | | | | being the Brahmadvara which can be located in the |
| and Infinity to the advanced concepts finding their | | | | soft region in the head in a new born infant. This small |
| applications in the Artificial Intelligence, computer based | | | | micro-opening called the Brahmarandhra. At the top of |
| numerical methods, philosophy, science, arts, etc. In fact, | | | | the head through which a yogi leaves the body. Thus |
| one will be baffled by the fertile imagination of the | | | | the 10th opening is the gate to the highest stage of |
| ancient seers and scholars, who perceived | | | | development, similar to his birth from the womb in the |
| mathematics in nature in all its glory and expressed the | | | | 10th month. In the former he is delivered downwards |
| great mathematical truths and concepts through | | | | and in the lateral upwards! This is the essence of story |
| hymns, theorems and postulates which are lyrically | | | | of deliverance of man from the imprisoning restrictions |
| beautiful, yet mathematically precise which speak | | | | of matter which has been beautifully delineated in |
| volumes about them. It goes without saying that these | | | | many philosophical Tantric and musical texts. |
| methods, concepts and techniques of Mathematics in | | | | Similarly the concept of Sets and cardinal numbers are |
| the form of Slokas and Sutras (Aphorisms) were | | | | conceived by the Seers and scholars. For example |
| conceived by the Ancient Indian Seers and scholars, | | | | we have deep significance for numbers like seven as |
| centuries before their modern counterparts. | | | | Saptaswara (seven basic notes in Music), Sapta Rsis |
| OBJECTIVE | | | | (seven great sages), Saptavarna (seven colours), nine |
| (a) The present objective is to create an awareness | | | | planets (Navagrahas), Navanidhi (nine treasures), |
| about the vast potential of the Vedic/Ancient Indian | | | | Dasadik (ten directions), Ekadasa Rudra (eleven |
| Mathematics (V.M./A.I.M.) for the curriculum | | | | Rudras), Dvadasamasa (twelve months), Saptavimsat |
| development and R & D works. | | | | Nakshatrah (27 stars) etc. |
| (b) To demonstrate with practical examples chosen | | | | Similarly we can quote many examples from different |
| from different levels of mathematics education; the | | | | branches of mathematics, even in geometry: the Sulva |
| benefits of learning V.M./A.I.N. like faster computing | | | | Sutras (which are the origin of geometry) make use of |
| time, alternative and creative approach to problem | | | | this branch of mathematics to construct varieties of |
| solving, etc. This is substantiated by the results of | | | | altars for the purposes of sacrifices. The magnificent |
| number of workshops and case studies conducted. | | | | temples which stand testimony to the skills and designs |
| (c) To motivate scientists scholars, teachers, | | | | of the workers are the living examples of applied |
| philosophers and others to take up an in-depth study | | | | mathematics. |
| of VM/AIM in proper perspective and adopt it to the | | | | Mathematics was also brought into worship by use of |
| modern times, so that a great amount of this | | | | Mantrabandhas which are nothing but mystical |
| wonderful traditional knowledge is revived and | | | | geometric diagrams inscribed with digits or cosmic |
| developed which would be a true homage to the | | | | energy capsules (beejaksharas). These diagrams are |
| Seers and Scientists of yore. | | | | of various sizes, shapes and colours. The word of |
| (d) Last but not the least, to pave way for the | | | | Mantra and Tantra is indeed a network of energies, |
| adoption of time tested VM/AIM in the school/college | | | | forces and vectors and are very dynamic. These |
| curriculum and establish dedicated RBD centres. | | | | geometric forms indicate outward manifestation of the |
| APPROACH | | | | spirit so as to exert its influence in the desired manner. |
| An Integrated approach for the study and learning VM | | | | The power possessed by the Yantra (graphical |
| AIM is made: | | | | representation) is sought to be stepped up by their |
| (i) Mathematical concepts embodied in the Vedas, | | | | inscription and infusion of the appropriate Mantra. In |
| Upanishads. | | | | short these can be termed in the modern context as |
| (ii) 'Vedic Mathematics' as expounded by H. H. | | | | the printed circuit boards which vibrate into light through |
| Bharatikrishna Teerthaji consisting of 16 Aphorisms and | | | | the electrical energy passed and performs the desired |
| 16 Corollaries, covering different topics in Mathematics, | | | | functions independently and collectively. The Yantra is |
| right from the fundamental Arithmetic operations to the | | | | the basic hardware and the Mantra is the software. |
| higher level of Mathematics. | | | | CONCLUSIONS |
| (iii) Ancient Indian Mathematics - contribution by various | | | | 1. Vedic/Ancient Indian Mathematics (VM/AIM) with |
| mathematicians of yore up to the celebrated genius | | | | their novel methods, techniques and approach help the |
| Ramanuja. This integrated approach is unique of its | | | | learners to develop their aptitude and creative rational |
| kind. Various methods techniques are culled out, | | | | thinking. |
| analysed and are expressed in modern mathematical | | | | 2. The VM/AIM which have stood the test of time for |
| notations, making it easily adaptable. | | | | centuries with their novel creative approach and |
| SELECTION CRITERIA | | | | techniques help the students to develop their intuitive |
| The methods and techniques are selected based on | | | | capacity, which in turn has a positive impact on the |
| the following criteria. If the VM/AIM methods are better | | | | right half of the brain, paving way for the holistic |
| than the conventional ones in terms of step size, length, | | | | development. |
| computation time, elegance and novelty, either | | | | 3. Many workshops and courses conducted for |
| individually or collectively, then these are selected in | | | | students of different classes, be it urban or rural, have |
| place of the conventional ones. | | | | proved the efficacy of these and the results are very |
| TECHNIQUE | | | | encouraging. |
| The teaching of VM/AIM is done following the usual | | | | 4. It has been found from practical trials that one year |
| techniques like lecturing, using Audio-visual equipments | | | | portion of school curriculum in mathematics can be |
| like OHP, slide projector, computer aided learning, etc. | | | | completed in about 60% of the time, thus making |
| Before we go into the subject of VM/AIM in terms of | | | | learning faster and enjoyable. In fact VM/AIM has |
| examples, it is imperative to know at least some | | | | been popularly known as 'Maths with Smiles'. |
| fundamental facts about the Vedas, their nature, | | | | 5. This will prove to be a boon for all the competitive |
| structure, etc., which would facilitate in understanding | | | | exams, with its much faster and accurate results and |
| and appreciating the mathematical concepts embodied | | | | can be adopted globally. |
| in the Vedas. | | | | 6. Learning of VM/AIM leads to education in different |
| Vedas are the earliest systematic literature in the | | | | dimensions and appreciate philosophy, religion in better |
| entire world existing since thousands of years, which | | | | perspective which in turn has a positive impact on the |
| have stood the test of time and continue to challenge | | | | personality development, leading to harmony and |
| the mankind with renewed freshness and vitality. | | | | peace. |
| Vedas, which are the fountain head of knowledge and | | | | 7. VM/AIM open up new vistas for R&D, |
| wisdom, are built upon sound structure which are | | | | especially on computer based numerical methods, |
| definite, clear, unambiguous, generative and complete, | | | | development of new algorithms apart from opening up |
| thus satisfying the properties of an algorithm! This | | | | of frontier areas of interdisciplinary research. Example: |
| amply proves the fact that the Vedas are the highest | | | | Nyayasastra (one of the six Darshanas has wonderful |
| revelations to the Rsis (Seers) of Yore and are not a | | | | scope in Artificial Intelligence). The author has already |
| mere compendium and collection of literature from | | | | culled out and developed about 15 computer based |
| different parts of the world, and no second version of | | | | numerical methods based on VM/AIM which are |
| Vedas exists anywhere. Hence, the Vedas have to | | | | unique of their kind. |
| be studied and analysed in proper perspective, in order | | | | 8. The Ancient Indian Mathematics not only kept up the |
| to bring out the truths hidden in them. Now let us take | | | | curriculum development, but also made mathematics |
| some stock illustrations from Vedas and other ancient | | | | interesting to house wives, common people and people |
| Indian sources in Mathematics at different levels i.e. | | | | from non-mathematical areas of study. They |
| right from the fundamental level of Arithmetic to | | | | composed aphorisms, slokas and hymns, which were |
| Algebra, Calculus, Quadratics, Polynomials, Astronomy, | | | | lyrically beautiful yet mathematically precise, thus |
| Geometry, etc. which will give a glimpse of the vast | | | | contributing to the holistic development of the subject. |
| scope of the same. | | | | 9. Last but not the least, study and practice of VM/AIM |
| Now coming to the Vedas, the most outstanding, | | | | with their creative and novel approach can aid in |
| fundamental contribution for which the entire world is | | | | holistic development of personality. This will not only |
| beholden to ancient India is the invention of decimal | | | | revive the ancient treasure of knowledge and wisdom, |
| numerals (with place values), zero and infinity, for | | | | but also will be a true homage to the great Seers and |
| example: 576, 685, 1998, etc. Can there be a more | | | | Scholars of Yore. |
| elegant, better method where the digits placed in the | | | | |