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Cultural & Aesthetic Values of Mathematics

The document discusses the integral role of mathematics in culture, education, and various aspects of life, emphasizing its values such as practical, intellectual, social, and aesthetic. It highlights connections between mathematics and art, architecture, music, and the concept of mathematical beauty, exemplified by the golden ratio and Fibonacci sequence. Additionally, it argues that mathematics is essential for understanding civilization and promotes cultural heritage across generations.

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Submitted by : Sreelekshmi V First Semester Mathematics (Optional)
 Introduction  Values of learning mathematics  What is culture?  Linking mathematics to culture  Cultural values  Mathematical beauty(Beauty in method, results, nature )  Golden ratio  Fibonacci sequence  Mathematics and architecture, music  Aesthetic values  Conclusion
 Mathematics is the abstract science of numbers, quantity and space  Mathematics is derived from the greek word “ mathema” meaning that “which is learnt”, “what one gets to know” hence also “study”  There are so many values of learning mathematics.
 Values are the outcomes or results achieved after teaching according to certain aims. They are the actual results of our teaching effort.  Practical/ Utilitarian values  Intellectual and international values  Social and moral values  Cultural and aesthetic values  Vocational and psychological values  Disciplinary values
 Culture can be defined as beliefs,values,attitudes, customs, social relationships, art and literature that define an ethnic group.  Culture is music, literature, visual arts, architecture and language.  Culture is what we do, what we think and how we feel.
 Mathematics is an integral part of all cultures which in turn influences how a person perceives and interprets mathematical knowledge.  Mathematics is a language that has its own symbols, syntax, grammar and representations (A symbol is an object that represent a visual image, an idea, a belief or an action. Symbols are cultural representations.  Mathematics is not a culture free discipline. It has close relationship with life. All cultures are rich in artifacts that exhibits mathematical concepts.  In the livelihood of certain race of people, we can see the “signs” of mathematics in basket weaving, bead work etc
 Helps in promoting cultural heritage and transmitting it to the future generation.  The welfare of our civilization depends upon scientific and mathematical developments.  Helped in the development of various subjects and occupation.  Understanding of the world,civilisation and culture requires mathematical concepts.  Progress of different occupations build up culture and mathematics is its backbone.
 Mathematical beauty is the aesthetic pleasure typically derived from the abstractness, purity, simplicity, depth of mathematics.  Beauty of mathematics can be seen in art forms, nature, results, architecture, music etc.
 Mathematicians describe an especially pleasing method of proof as elegant.  A proof that uses a minimum of additional assumptions or previous results.  A proof that derives a result in a surprising way (eg from an apparently unrelated theorem or a collection of theorems)  A proof that is based on new and original insights.
 Patterns occur in different contexts can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, waves, foams etc
 In mathematics two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities i. e. for a,b>0 and a>b (a+b/a) = (a/b) . This is equal to an irrational number phi that is a solution to the quadratic equation x^2-x-1=0, with a value of : φ=(1+√5)/2=1.6180339887
 Mathematics and architecture are related  Mathematics needed when engineering buildings, architects use geometry to define spatial form of a building.
 Elements of music such as form, rhythm, pitches of its notes and the tempo of its pulse can be related to the measurement of time and frequency, offering ready analogies in geometry  The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory , abstract algebra and number theory.
 One gets pleasure in solving mathematical problems especially when he get correct answers to his problems  Different symmetric designs by Ramanujan are a source of great pleasure.  Mathematics is closely related with arts, like drawing , paintings, music etc.  All musical instruments like harmonium, drum, flute, guitar, violin etc are played with the rules of mathematics.
 Mathematics have wide range of applications among all subjects.  Mathematics have relation with life, other subjects and different branches of mathematics and different topics of same subject.  Mathematics is a main part of our daily life.