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Rabindra Bharati Patrika Vol. XII, No. 2 (2009)

FOLK MATHEMATICS : CONCEPT & DEFINITION - AN OUT LINE

N. C. GHOSH

Department of Mathematics

Rabindra Bharati University

Email : ghoshnc@rediffmail.com

ABSTRACT

Culture is the man-made part of environment and behaviour is cumulative

  product of one’s continuous movement along with hereditary knowledge

achieved from family and society. Knowledge and culture is part of continuous

cumulative effect developed, processed and refined culture is mathematical 

culture and or mathematical knowledge. Folk life is full of folk culture and 

behaviour. Mathematical culture of folk life is folk mathematics. These culturehave been discussed by mathematicians and educators in different term and 

 form. Giving an out line of previous investigations folk mathematics has been

discussed here citing some of its manifestation in folk-life.

MEANING OF THE TERM FOLK The term Folk usually mean, the great proportion of the members of a people residing in any particular 

region who share at least one common factor viz. common occupation, religion or ethnicity etc.Folklore means folk learning. It comprehends all knowledge that is transmitted by word of mouth and

crafts and techniques that are learned by imitation or example, as well as the products of these crafts.

In non-literate societies folklore is virtually identical with culture.

Folklore includes folk art, folk crafts, folk tools, folk costume, folk custom, folk belief, folk 

medicine, folk recipes, folk music, folk dance, folk games, folk gestures and folk speech, as well asthose verbal forms of expression called folk literature but which are better described as verbal art.

Verbal art includes folktale, legends, myth, proverbs, riddles and poetry are the primary concern of 

folklorists from both the humanities and the social sciences since the beginning of folklore as a field

study.

MEANING OF THE TERM MATHEMATICS

Mathematics is a science that deals with the relationship and symbolism of numbers andmagnitudes and that includes quantitative operations and the solution of quantitative problems.

Though foundation of Mathematics is real world due to development of mankind it has reached inhigher form for which it seems an entirely free activity, unconditioned by the external world. It is more

 just to call an art than a science. It is as independent as music of the external world; and although,

unlike music, it can be used to illuminate natural phenomena, it is just as ‘subjective’ just as much of a product of the free creative imagination.

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The literature of mathematics is full of æsthetic terms. But art is not something which existsmerely to satisfy an ‘æsthetic emotion’. Art is worthy of the name reveals some aspect of reality. The

real function of art is to increase self-consciousness to make a man more aware of what he is and

therefore what the universe in which man live really is. Mathematics, in its own way, also performsthis function, it is not only æsthetically charming but profoundly significant. It is an art, and a great

art.

MATHEMATICS IN FOLK-LIFE 

Ethnomathematics is the mathematics of ethnic people. Better way to say all the mathematical

concepts that ethnic people uses in their daily life, not knowing it as mathematics; but part of their life.These knowledge ethnic persons acquired from their predecessor and they can transfer acquired

knowledge to their next generation with no hurdle.

In the way of naming mathematics of people’s life it was termed as

i. Indigenous Mathematics, ii. Socio-mathematics, iii. Informal Mathematics, iv.Mathematics in

the socio-cultural Environment, v. Spontaneous Mathematics, vi. Oral Mathematics, vii. Oppressed

Mathematics, viii. Non-standard Mathematics, ix. Hidden or Frozen Mathematics, x. Mathematicscodtified in know-hows, xi. Anthropological Mathematics, xii. Sociology of Mathematics, xiii. Self-

generated Mathematics, xiv.Practical Mathematics

Ethnomathematics is the study of the relationship between mathematics and culture. It refers to a

 broad cluster of ideas ranging from distinct numerical and mathematical systems to multicultural

mathematics education. The goal of ethnomathematics is to contribute both to the understanding of 

culture and the understanding of mathematics, but mainly to appreciating the connections between thetwo.

The Development and Meaning of 'Ethnomathematics'

The term 'ethnomathematics' was introduced by the Brazilian educator and mathematician UbiratanD'Ambrosio in 1977 during a presentation for the American Association for the Advancement of 

Science. Since D'Ambrosio put forth the term, people - D'Ambrosio included - have struggled with its

meaning. Below is a sampling of some of the definitions of ethnomathematics proposed between 1985and 1998:

"The mathematics which is practiced among identifiable cultural groups such as national-tribe

societies, labour groups, children of certain age brackets and professional classes" (D‘Ambrosio,1985).

"The mathematics implicit in each practice" (Gerdes, 1986).

"The study of mathematical ideas of a non-literate culture" (Ascher, 1986).

"The codification which allows a cultural group to describe, manage and understand reality"(D‘Ambrosio, 1987).

"Mathematics…is conceived as a cultural product which has developed as a result of various

activities" (Bishop, 1988).

"The study and presentation of mathematical ideas of traditional peoples" (Ascher, 1991)."Any form of cultural knowledge or social activity characteristic of a social group and/or cultural

group that can be recognized by other groups such as Western anthropologists, but not necessarily bythe group of origin, as mathematical knowledge or mathematical activity" (Pompeu, 1994).

"The mathematics of cultural practice" (Presmeg, 1996).

"The investigation of the traditions, practices and mathematical concepts of a subordinated social

group" (Knijnik, 1998)."What is the difference between ethnomathematics and the general practice of creating a mathematical

model of a cultural phenomenon (e.g., the “mathematical anthropology” of Paul Kay [1971] and

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others)? The essential issue is the relation between intentionality and epistemological status. A singledrop of water issuing from a watering can, for example, can be modeled mathematically, but we would

not attribute knowledge of that mathematics to the average gardener. Estimating the increase in seeds

required for an increased garden plot, on the other hand, would qualify." (Eglash et al 2006).

  Mathematics in folk art

One way mathematics appears in art is through symmetries. Woven designs in cloth or carpets (toname two) commonly have some kind of symmetrical arrangement. A rectangular carpet often has

rectangular symmetry in the overall pattern. A woven cloth may exhibit one of the seventeen kinds of 

 plane symmetry groups [Crowe (1973)] for an illustrated mathematical study of African weaving  patterns]. Several types of patterns discovered by ethnomathematical communities are related to

technologies [Berczi (2000)] about illustrated mathematical study of patterns and symmetry in

Eurasia].

FOLK MATHEMATICSMathematics, Folk body of traditional MATHEMATICS , was originally transmitted orally. Folk 

mathematics may be regarded as an undercurrent to the main stream of mathematics; it nourishes the

mainstream, and at the same time, is nurtured by it. Being extremely practical in nature it serves thedaily need of the people of every walks of life. Common people with elementary education can applyit at ease to the solution of various problems arising out of everyday life, seek recreation in it, and are

encouraged to devise new problems or puzzles orally. Several problems of folk mathematics had

 been current in ancient India is evident from traces that can still be found in the Bakhshali manuscript(300 AD), the Patana manuscript (775 AD), Mahavira's Ganita-sara-sanggraha (850 AD) and in other 

works of mathematics. Even though Bangalis in general did not show much interest in the study of 

mathematics, a sort of mathematics contained in the Shubhangkar were most probably cultivated by

the Bangalis since 300 BC. Shubhangkar literally means a book on arithmetic, beneficial for masseducation. Though there is dibet whether the arithmetical system was introduced by Shubhangkar 

during the reign of the Mallas in the first half of the 17th century, but there was certainly a

mathematician, Shubhangkar by name, in medieval Bengal, who had written several rules (aryas) pertaining to mathematics in the form of folk rhymes. The language in which the rules were composed

is mainly the Bengali prevalent in medieval Bengal with lots of words taken from Prakrit,

Apabhrangsha, Abahatta and from Austro-Asiatic languages. In medieval time there were many aryaauthors in Bengal and Assam whose names were mentioned at the end of several aryas.

Following aryas is to find the area of a plot of land in bighas:

Kurba kurba kurba lijje

kathay kurba kathay lijjekathay kathay dhul pariman

 bish ganda hay kathar praman

ganda baki thake yadi katha nile par 

sholo diye pure tare sara ganda dhar Translation: kurba multiplied by kurba, take it, as (square) kurba, katha by kurba as (square) katha;

katha by katha as dhul, it being divided by 20 yields (square) katha; the remainder (if there be) whenmultiplied by 16 gives forth (square) ganda.

Interestingly, ganda and pana are Austro-Asiatic words and had been in use since 300 BC as is evident

from the excavation at MAHASTHANGARH in the district of BAGORA in Bangladesh.Folk mathematics or  mathematical folklore means theorems, definitions, proofs, or mathematical

facts or techniques that circulate among mathematicians by word-of-mouth but do not appear in print,

either in books or in scholarly journals.

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Folk mathematics can also mean informal mathematical practices, as used in everyday life or byaboriginal or ancient people. While modern mathematics emphasizes formal and strict  proofs of all

statements from given axioms, practices in folk mathematics are usually understood intuitively and

 justified with examples -- there are no axioms.Quite important at times for researchers are folk theorems, which are results known, at least to experts

in a field, and considered to have established status, but not published in complete form. Sometimes

these are only alluded to in the public literature. For example, in tidying up loose ends of theclassification of finite simple groups around 2004 (a result which had been claimed, somewhat

 prematurely, to be proved around 1980), Michael Aschbacher  devoted an entire volume to proving

various infrastructural results, some of which had not previously been proved in print.

Folk-mathematics some times is called as Ethnomathematics.

FOLK SONGS ABOUT MATHEMATICS AND PIPi day is March 14th, like in 3.14. Festivities peak at 1:59pm (3.14159).

The Pi Song (sung to the tune of "Oh Christmas Tree")Oh Number pi, oh number pi,Your digits are unending.Oh number pi, oh number pi,

No pattern are you sending.You're three point one four one five nine And even more if we had time.Tom Lehrer\ New MathTom Lehrer\ That's Mathematics

Hard 'N Phirm\ Pi\ Horses and Grasses

Women singing the digits of pi

MATHEMATICS IN EVERYDAY LIFEIt is sometimes it is difficult for students to appreciate the importance of Mathematics. They often

find the subject boring and hard to understand. But if any one can realize them mathematics as a part

everyday life then hopefully it will help students to be enthused to understand that Mathematics isnot just a subject on their time-table but a tool they use in their everyday life! So before theoretising

the subject let us see some examples where and how people are using mathematics in their daily life

with out any hurdle.

Areas

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PercentagesMathematics is everywhere and yet, one may not recognize it because it doesn't look like the math done in

school. Mathematics in the world around the people sometimes seems invisible. But mathematics is present inthe world all the time--in the workplace, in residence, and in life in general. When one buy a car, follow a

recipe, or decorate home using mathematical principles.

Percentages are used in everyday life and one may not even realize it !!This presentation was prepared by the Class of Form 3A and by the Class 1 Ga

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Car LogosMost manufacturers use symmetry of some kind in designing their logos. For example, Audi uses four 

intersecting circles in a line. This pattern has one line of reflection symmetry.

 

Polish folk art - Paper Cutout

Wycinanki - Polish folk  art paper cutouts are known through out the world as a beautiful craft.

These beautiful paper cut-outs have been used to decorate the interior of Polish homes since the

early 19th century! They were used to decorate the walls of ceiling beams in countryside cottagesand given as gifts to family members and friends. The complexity of the designs is been created by

repeating symmetrical patterns and folk motifs inspired by nature and geometric shapes.

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Wycinanki - paper cutouts which was made by polish students.

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Mathematical concepts in Old Architecture

Tajmahal

Jorbangla Temple at Bisnopur (W.B.) Palace of Mursidabad (W.B.)

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 Library Celsus (Turkey) Gondola and buildings besides the sea in Vanish

(Italy)

Indian Embroidery

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Indian Jewllary

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Polish Folk Embroidery

Traditional Polish outfit are very brightly colored, with embroidery and beadwork highlighting the outfit.

Embroidery from Podhale.

 

Embroidery from Kujawy

 

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The Kashubian Costume is all about embroidery which is very pronounced.

Patterns

Maltese Architecture

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 Unakoti (Tripura)

 

Ajanta (Maharastra)

 Ajanta (Maharastra)

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  Buddhist Vihara at Paharpur (Bangladesh)

 

 Nalanda University

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 Painting in Ajanta Cave (Maharastra) Ajanta Cave (Maharastra)

 Ajanta Cave (Maharastra) Ellora Cave (Maharastra)

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Carpets & Rugs

A long tradition of the use of symmetry in rug patterns spans a variety of cultures. American

 Navajo Indians used bold diagonals and rectangular motifs. Many Oriental rugs have intricatereflected centers and borders that translate a pattern. Not surprisingly most rugs use quadrilateral

symmetry -- a motif reflected across both the horizontal and vertical axes.Conclusion : In the November  1976 issue of The Math Learning Center Report the term ‘Folk Mathematics’ was first appeared. The report was published and distributed with the support of a

 National Science Foundation Dissemination grant. It was reprinted in the February 1977 issue of 

Instructor magazine and in the December 1980 issue of Mathematics. Since then the term Folk Mathematics has drawn attraction of Educators, researchers and social scientists. To develop

mathematics teaching methodology folk mathematical ideas, particularly way of transmission of 

mathematical concepts among the folk people are drawing attraction. In India, though posses’

glorious past, practically no significant work on folk-mathematics study and its impact has beendone till date. Author will be delighted if this article can motivate people to work in this line.

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