A Research Project: “TAPARI KO GANIT” [TA KO GA] “Mathematics of Leaf Plates”

Authors: Lok Bahadur Gurung - [email protected] Amrit Bahadur Thapa - [email protected] Amrit Bahadur Poudel - [email protected]

Hypothesis: Use of mathematics/knowingly and unknowingly Measuring ideas, shapes, corners, directional sense, number sense…..

Introductory Poem in Nepali and English in PDF Format Background: Mathematical knowledge has been so universalized through science and technology that it has overruled the traditionally existing mathematical ideas and theories (knowingly or unknowingly) used by the people living in the remote parts of the world. Globalization and universalization of the technology has definitely made the human life easier in some extent but it will be a big mistake and a short term illusion if we totally depended on other’s culture and other’s knowledge by abandoning the knowledge which is invented by the ancestors in a long run of experience and practice. It is no doubt that everyone should learn and adopt better ideas from any part of the world or any one in the world to enhance the existing knowledge. But if

other’s knowledge is adopted without any idea of the treasure hiding in own culture and experience it becomes a great disaster for the future. Human being without culture is a man without heart and feeling. Another part of this scene is that when people blindly adopt other’s knowledge and tradition for a long time they slowly loose their own strength of knowledge and identity and become completely dependent on other’s knowledge and start considering self as passive, value less and second class human being. Low self-esteem develops inferiority and ultimately individual becomes unproductive and docile follower. Nepal is land locked country between two giant countries China and India. In the history both China and India were colonized by the British empires. Though Nepal was a country with low population and poor income resources, it was able to free its sovereignty from the occupying forces from both north and south. White commanders used to say that Nepal was not occupied by any of the foreign forces because “Nepal and Nepalese both are mountainous”. Thus Nepal had been able to save its treasure of knowledge in the form of traditional and cultural forms. It is no doubt that people living in hilly and other parts of the country used their own mathematical knowledge for food and survival. Since there was easy means of transportation due to geographical locations of the country there have been unique mathematical knowledge used by different people living in different corners of the country. Even very small communities living in different places invented unique knowledge in favor of their own living style and natural environment. Nepal being geographically in three divisions; Mountain, Hilly and Terai; especially in the high altitudes people lived in remote places in small communities. Since it was difficult to travel from one place to another, they had to develop their own knowledge for the survival and prosperity of the community. They used their knowledge for maintaining economic and social balance in the family and the community. They used horses for the trade and business. They dig out coal, metal and other mines on their own. The utensils they developed are still used in agriculture and other family purposes. If we research the mathematical knowledge which is used by so called illiterate people living economically poor places, we can find that the knowledge they use are much more complex than the knowledge what our school teach to the students. Thus

it is very necessary to explore and unearth the hidden treasure in our tradition and culture. If we incorporate the knowledge that already exists in our own minds to the modern science and technology, we can benefit from it to further police which can be better useful for the development of our country and the society than by the imported knowledge which we buy or receive in donation that are sent in pity of our poorness. It is doubtless that people in the ancient age when they had not developed metal utensils; they used leaf or other such organic materials for keeping their food or meat products. Even they had to use leaves of trees to cover their body. It is not difficult to assume that people used leaf plates for different purpose. Even in recent days people all over the world use leaf products for different purpose. Here in Nepal also, people use leaves of different trees to make different organic products which are very useful in day to day life. Here we are going to study about one of the leaf product which is traditionally very famous in nepali society from long time. We call this leaf plate as “TAPARI” which is used in different sizes and shapes and for different purposes in our culture. It has been widely used for having food in place of metal plates and also used in marriage or other traditional ceremonies.

Ganit (mathematics in Tapari): The shapes and sizes of these “Taparies” vary according to the purpose or the occasion. Even it is different from community to community. Though it has been slowly phased out from the cities but it has been much popular in the villages and specially for the religious purpose as these taparies are considered as pure and free from all sorts of impurities. Mostly female are involved in making such taparies. Tapariko Ganit and the lady inventor: A young girl approximately an age of fifteen or sixteen regularly comes to a corner of Ason(a busy place in Kathmandu for trade and business). She sits for about three or four hour in the evening sells the few Taparies she brings with her. With this she manages to collect money

for her brother who is younger and studies in a government school. She belongs to a poor family, her father works as a labor in the market carrying loads from place to place. It is difficult for them when her father is sick or becomes unable to carry heavy loads. His income is very low and so it is difficult for them to survive in the city like Kathmandu. Her mother sells vegetables in the market which she buys from a wholesale market in the mornings and evenings from which she makes some money. Though it seems that the whole family is involved in business, they have a very small amount of money which does not produce good profit. She helps her mother for doing household works and her mother helps her to make leaf plates out of the leaves they buy from a wholesale market. She and her mother sit together when they are free from their household work. Specially after her brother goes for his school she and her mother sit together for making different types of leaf plates. They need to know what type of Tapari is used for what purpose. The shapes of the Tapary vary according to the purpose of use. People come to her for different kinds of Taparies. She needs to update about the shape and size of the Taparies and their use. Sometimes people come without the knowledge of the shape and size of the Taparies they needed. She needs to understand what kind of Taparies they need according to the purpose they state. She has different sized Taparies, some are rectangular, circular, polygonal and with many other shapes. She shows the Taparies with four corners (rectangular), five corners but she says that she never makes Taparies with eight and twelve corners because people say that eight and twelve corner Taparies are unlucky. She left her school after she passed her five class because of her poor family background. She does not know about geometrical figures and does not know about the sequence and any model in mathematics. However, she has learnt and developed her own skill of making Taparies for the purpose of herself and her family. She has learnt a lot about making Taparies at home. Her mother is her teacher. She learnt from her mother what shape and what kind of leaves she needs for making what kind of the Taparies. She needs to collect the leaves of different sizes in different groups, she also needs to decide what leaf to put in the bottom and what on the sides. She needs to know what part to cut off and what part to hide inside the other leaves while making the Taparies. She says that between the two faces of the Tapary one is smooth and another is rough. She says that she needs to put the smooth side towards the inside face of the

Tapary. First she makes the foundation for the plate which is flat and wider than the actual bottom of the Tapary. The margin she leaves in the foundation helps her to fold upward from the outside so that the Tapary does not leak. For the strength of the plate she prefers a special type of the leaves. After the foundation is made she needs to decide what should be the size of the bottom of the Tapari and how many leaves she requires on the sides. She decides the number of the leaves on sideways according to the circumference or the volume of the Tapary she wants to make. She uses bamboo needles to stitch the leaves with each other. It is very interesting to see that she bends the leaves so skillfully that her Taparies are very similar to each other. She does not know what geometrical shapes her brother draws in his copy but she uses these shapes for her work skillfully. Her brother never asks her about what geometrical shapes she is working with and she never bothers to know if her brother works with the same geometrical shapes with pencil and paper. How would it be if she was told that she uses geometrical structures on her work and her brother be shown that his sketches on the mathematics copy are same as what his sister works with?

Future Research Topics: 1. Bridging Mathematics from home to school 2. Study of Nepalese Rural Women in mathematical actions 3. Use of informal mathematics to improve girls achievement in school mathematics