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We also see that Jaina and Buddhist Acharyas contributed immensely to the development of mathematics since early times. The knowledge of Samkhyana, literally, the “science of numbers” meaning arithmetic and astronomy, was regarded as one of the principal accomplishments of a Jaina priest. Mahavira was regarded as one of the best mathematicians of his time. He had a great understanding of the subject. He composed the book called Ganitasarasangraha. The following shlokas show his appreciation and use of mathematics.

We also see that Jaina and Buddhist Acharyas contributed immensely to the development of mathematics since early times. The knowledge of Samkhyana, literally, the “science of numbers” meaning arithmetic and astronomy, was regarded as one of the principal accomplishments of a Jaina priest. Mahavira was regarded as one of the best mathematicians of his time. He had a great understanding of the subject. He composed the book called Ganitasarasangraha. The following shlokas show his appreciation and use of mathematics.

<span style="color:#ff7f50">लौकिके वैदिके वापि तथा सामायिकेऽपि यः । व्यापारस्तत्र सर्वत्र संख्यानमुपयुज्यते ।। 9

<span style="color:#ff7f50">'''लौकिके वैदिके वापि तथा सामायिकेऽपि यः । व्यापारस्तत्र सर्वत्र संख्यानमुपयुज्यते ।। 9'''

<span style="color:#ff7f50">कामतन्त्रेऽर्थशास्त्रे च गान्धर्वे नाटकेऽपि वा । सूपशास्त्रे तथा वैद्यो वास्तुविद्यादिवस्तुषु ।। 10

<span style="color:#ff7f50">'''कामतन्त्रेऽर्थशास्त्रे च गान्धर्वे नाटकेऽपि वा । सूपशास्त्रे तथा वैद्यो वास्तुविद्यादिवस्तुषु ।। 10'''

<span style="color:#ff7f50">छन्दोऽलङ्कारकाव्येषु तर्कव्याकरणादिषु । कलागुणेषु सर्वेषु प्रस्तुतं गणितं परम् ।। 11

<span style="color:#ff7f50">'''छन्दोऽलङ्कारकाव्येषु तर्कव्याकरणादिषु । कलागुणेषु सर्वेषु प्रस्तुतं गणितं परम् ।। 11'''

<span style="color:#ff7f50">सूर्यादिग्रहचारेषु ग्रहणे ग्रहसंयुतौ । त्रिप्रश्ने चन्द्रवृत्तौ च सर्वत्राङ्गीकृतं हि तत्।। 12

<span style="color:#ff7f50">'''सूर्यादिग्रहचारेषु ग्रहणे ग्रहसंयुतौ । त्रिप्रश्ने चन्द्रवृत्तौ च सर्वत्राङ्गीकृतं हि तत्।। 12'''

<span style="color:#ff7f50">द्वीपसागरशैलानां संङ्ख्याव्यासपरिक्षिपः । भवनव्यन्तरज्योतिर्लोककल्पाधिवासिनाम् ।। 13

<span style="color:#ff7f50">'''द्वीपसागरशैलानां संङ्ख्याव्यासपरिक्षिपः । भवनव्यन्तरज्योतिर्लोककल्पाधिवासिनाम् ।। 13'''

<span style="color:#ff7f50">नारकाणां च सर्वेषां श्रेणीबन्धेन्द्रकोत्कराः । प्रकीर्णकप्रमाणाद्या बुध्यन्ते गणितेन ते ।। 14

<span style="color:#ff7f50">'''नारकाणां च सर्वेषां श्रेणीबन्धेन्द्रकोत्कराः । प्रकीर्णकप्रमाणाद्या बुध्यन्ते गणितेन ते ।। 14'''

<span style="color:#ff7f50">प्राणिनां तत्र संस्थानमायुरष्टगुणादयः । यात्राद्यास्संहिताद्यश्च सर्वे ते गणिताश्रयाः।। 15

<span style="color:#ff7f50">'''प्राणिनां तत्र संस्थानमायुरष्टगुणादयः । यात्राद्यास्संहिताद्यश्च सर्वे ते गणिताश्रयाः।। 15'''

<span style="color:#ff7f50">बहुभिर्विप्रलापैः किं त्रैलोक्ये सचराचरे । यत्किञ्चिद्वस्तु तत्सर्वं गणितेन विना न हि ।। 16 (Ganita Sarasangraha 9-16<ref>Rangacharya, M. (1912) ''Ganitasarasangraha of Mahaviracharya with English translation and Notes.'' Madras: The Government Press ([https://archive.org/details/RangacaryaTheGanitaSaraSangrahaOfMahavira1912/page/n35/mode/2up Page 2-3])</ref>)</span>

<span style="color:#ff7f50">'''बहुभिर्विप्रलापैः किं त्रैलोक्ये सचराचरे । यत्किञ्चिद्वस्तु तत्सर्वं गणितेन विना न हि ।। 16''' (Ganita Sarasangraha 9-16<ref>Rangacharya, M. (1912) ''Ganitasarasangraha of Mahaviracharya with English translation and Notes.'' Madras: The Government Press ([https://archive.org/details/RangacaryaTheGanitaSaraSangrahaOfMahavira1912/page/n35/mode/2up Page 2-3])</ref>)</span>

Meaning: In all transactions which relate to worldly, Vedic or other similar religious affairs calculation is of use. In the science of love, in the science of wealth, in music and in drama, in the art of cooking, in medicine, in architecture, in prosody, in poetics and poetry, in logic and grammar and such other things, and in relation to all that constitutes the peculiar value of the arts, the science of calculation (ganita) is held in high esteem. In relation to the movements of the sun and other heavenly bodies, in connection with eclipses and conjunctions of planets, and in connection with the triprasna (direction, position and time) and the course of the moon—indeed in all these it is utilised. The number, the diameter and the perimeter of islands, oceans and mountains; the extensive dimensions of the rows of habitations and halls belonging to the inhabitants of the world, of the interspace between the worlds, of the world of light, of the world of the gods and of the dwellers in hell, and other miscellaneous measurements of all sorts—all these are made out by the help of ganita. The configuration of living beings therein, the length of their lives, their eight attributes, and other similar tilings; their progress and other such things, their staying together, etc.—all these are dependent upon ganita (for their due comprehension). What is the good of saying much? Whatever there is in all the three worlds, which are possessed of moving and non-moving beings, cannot exist as apart from ganita (measurement and calculation).

Meaning: In all transactions which relate to worldly, Vedic or other similar religious affairs calculation is of use. In the science of love, in the science of wealth, in music and in drama, in the art of cooking, in medicine, in architecture, in prosody, in poetics and poetry, in logic and grammar and such other things, and in relation to all that constitutes the peculiar value of the arts, the science of calculation (ganita) is held in high esteem. In relation to the movements of the sun and other heavenly bodies, in connection with eclipses and conjunctions of planets, and in connection with the triprasna (direction, position and time) and the course of the moon—indeed in all these it is utilised. The number, the diameter and the perimeter of islands, oceans and mountains; the extensive dimensions of the rows of habitations and halls belonging to the inhabitants of the world, of the interspace between the worlds, of the world of light, of the world of the gods and of the dwellers in hell, and other miscellaneous measurements of all sorts—all these are made out by the help of ganita. The configuration of living beings therein, the length of their lives, their eight attributes, and other similar tilings; their progress and other such things, their staying together, etc.—all these are dependent upon ganita (for their due comprehension). What is the good of saying much? Whatever there is in all the three worlds, which are possessed of moving and non-moving beings, cannot exist as apart from ganita (measurement and calculation).

<blockquote>“With the help of the accomplished holy sages, who arc worthy to be worshipped by the lords of the world, and of their disciples and disciples’ disciples, who constitute the well-known series of preceptors, I glean from the great ocean of the knowledge of numbers a little of its essence, in the manner in which gems are picked from the sea, gold is from the stony rock and pearl from the oyster shell; and give out according to the power of my intelligence, the Sara-samgraha a small work on ganita which is (however) not small in value.”</blockquote>Is it not amazing how Acharya Mahavira describes the role of mathematics in our daily lives?'''

<blockquote>“With the help of the accomplished holy sages, who arc worthy to be worshipped by the lords of the world, and of their disciples and disciples’ disciples, who constitute the well-known series of preceptors, I glean from the great ocean of the knowledge of numbers a little of its essence, in the manner in which gems are picked from the sea, gold is from the stony rock and pearl from the oyster shell; and give out according to the power of my intelligence, the Sara-samgraha a small work on ganita which is (however) not small in value.”</blockquote>

Is it not amazing how Acharya Mahavira describes the role of mathematics in our daily lives?

* Worldly affairs, Vedic and other religious activities

* Worldly affairs, Vedic and other religious activities

* Science of love

* Science of love

* Poetics and Prosody

* Poetics and Prosody

* Logic and Grammar

* Logic and Grammar

* Time  

* Time

* Planetary movements and distances

* Planetary movements and distances

* Number and dimensions of oceans, mountains and islands

* Number and dimensions of oceans, mountains and islands

== Mathematics as a Subject ==

== Mathematics as a Subject ==

Since ancient days the main subjects of mathematical study were lipi or lekha (alphabets, reading and writing), rupa (drawing and geometry) and ganana (arithmetic). In ancient Buddhist literature we find mention of three classes of ganita:  

Since ancient days the main subjects of mathematical study were lipi or lekha (alphabets, reading and writing), rupa (drawing and geometry) and ganana (arithmetic). In ancient Buddhist literature we find mention of three classes of ganita:  

 

* mudra (‘finger arithmetic’)

·       mudra (‘finger arithmetic’)

* ganana (‘mental arithmetic’)  

 

* samkhyayana (‘higher arithmetic in general’)

·       ganana (‘mental arithmetic’)  

 

Gradually, in subsequent times, ganita came to mean mathematics in general, while finger arithmetic as well as mental arithmetic were excluded from the scope of its meaning. Calculations were performed on a board (called paati) with a piece of chalk or on sand (dhuli) spread on the ground or in the paati. Thus higher mathematics came to be called Paatiganita or science of calculation on the board or dhuli-karma or dust work. Apart from boards and sand, a string of cord, a sanku (a stick) or gnomon whose shadow is cast using a mounted lamp source came to be used in many mathematical concepts such as that of length, distance. Shadows and calculation of time from them played vital role in astronomical calculations.

·       samkhyayana (‘higher arithmetic in general’)

 

Gradually, in subsequent times, ganita came to mean mathematics in general, while finger arithmetic as well as mental arithmetic were excluded from the scope of its meaning. Calculations were performed on a board (called paati) with a piece of chalk or on sand (dhuli) spread on the ground or in the paati. Thus higher mathematics came to be called Paatiganita or science of calculation on the board or dhuli-karma or dust work. Apart from boards and sand, a string of cord, a sanku (a stick) or gnomon whose shadow is cast using a mounted lamp source came to be used in many mathematical concepts such as that of length, distance. Shadows and calculation of time from them played vital role in astronomical calculations. '''(Illustrations of Paatiganita and Dhulikarma, Sanku, Drawing circle using a string)'''

 

 

 

== Classroom Activity ==

== Classroom Activity ==

 

Make a simple shadow using a sanku (take a stick or a pencil) placed in front a source of light (Sun, candle lamp). Compare the shadows formed with different things (small stick, big stick, pencil, crayon, book) with your classmates.

Make a simple shadow using a sanku (take a stick or a pencil) placed in front a source of light (Sun, candle lamp). Compare the shadows formed with different things (small stick, big stick, pencil, crayon, book) with your classmates.

CT = shadow formed

CT = shadow formed

== Classroom Activities ==

 

== Other Activities ==

1.  Name a five instances where think mathematics is used in your house?

1.  Name a five instances where think mathematics is used in your house?