विश्व के प्राचीनतम ग्रन्थ वेद संहिताओं से गणित तथा ज्योतिष को अलग-अलग शास्त्रों के रूप में मान्यता प्राप्त हो चुकी थी शास्त्र के रूप में ‘गणित’ का प्राचीनतम प्रयोग लगध ऋषि द्वारा प्रोक्त वेदांग ज्योतिष नामक ग्रन्थ का एक श्लोक में माना जाता है।
- यथा शिखा मयूराणां नागानां मणयो यथा।
- तद्वद् वेदांगशास्त्राणां गणितं मूर्ध्नि संस्थितम्।। (वेदांग ज्योतिष - ५)
(जिस प्रकार मोरों के सिर पर शिखा और नागों के सिर में मणि सर्वोच्च स्थान में होते हैं उसी प्रकार वेदांगशास्त्रों में गणित का स्थान सबसे उपर (मूर्धन्य) है।
भारत में गणित के इतिहास को मुख्यता ५ कालखंडों में बांटा गया है-
- १. आदि काल (500 इस्वी पूर्व तक)
- (क) वैदिक काल (१००० इस्वी पूर्व तक)- शुन्य और दशमलव की खोज
- (ख) उत्तर वैदिक काल (१००० से ५०० इस्वी पूर्व तक) इस युग में गणित का भारत में अधिक विकास हुआ। इसी युग में बोधायन शुल्व सूत्र की खोज हुई जिसे हम आज पाइथागोरस प्रमेय के नाम से जानते है।
- २. पूर्व मध्य काल – sine, cosine की खोज हुई।
- ३. मध्य काल – ये भारतीय गणित का स्वर्ण काल है। आर्यभट्ट, श्रीधराचार्य, महावीराचार्य आदि श्रेष्ठ गणितज्ञ हुए।
- ४. उत्तर-मध्य काल (१२०० इस्वी से १८०० इस्वी तक) - नीलकंठ ने १५०० में sin r का मान निकालने का सूत्र दिया जिसे हम ग्रेगरी श्रेणी के नाम से जानते है।
- ५. वर्तमान काल - रामानुजम आदि महान गणितज्ञ हुए।
अब दिए गए कुछ ऐसे नाम है जिनके बारे मे आप सब स्वयं विचार कीजिये कि क्या इन संस्कृत आचार्यो के बिना गणित शास्त्र संभव था।।।।।।।।।।।
1.आर्यभट
2.ब्रह्मगुप्त
3.महावीर
4.नीलकंठ
5.स्वामी भारती कृष्ण तीर्थ (वैदिक गणित)
भारतीय परम्परा में गणेश दैवज्ञ ने अपने ग्रन्थ बुद्धिविलासिनी में गणित की परिभाषा निम्नवत की है-
ReplyDeleteगण्यते संख्यायते तद्गणितम्। तत्प्रतिपादकत्वेन तत्संज्ञं शास्त्रं उच्यते।
(जो परिकलन करता और गिनता है, वह गणित है तथा वह विज्ञान जो इसका आधार है वह भी गणित कहलाता है।)
वेदांग ज्योतिष में गणित का स्थान सर्वोपरि (मूधन्य) बताया गया है -
यथा शिखा मयूराणां नागानां मणयो यथा।
तद्वद् वेदांगशास्त्राणां गणितं मूर्ध्नि संस्थितम् ॥ -- (वेदांग ज्योतिष - ५)
(जिस प्रकार मोरों के सिर पर शिखा और नागों के सिर में मणि सर्वोच्च स्थान में होते हैं उसी प्रकार वेदांगशास्त्रों में गणित का स्थान सबसे उपर (मूर्धन्य) है।
इसी प्रकार,
बहुभिर्प्रलापैः किम्, त्रयलोके सचरारे।
यद् किंचिद् वस्तु तत्सर्वम्, गणितेन् बिना न हि ॥ — महावीराचार्य, गणितसारसंग्रह में
(बहुत प्रलाप करने से क्या लाभ है ? इस चराचर जगत में जो कोई भी वस्तु है वह गणित के बिना नहीं है / उसको गणित के बिना नहीं समझा जा सकता)
खगोल-विज्ञान के साथ तो गणित का अन्योन्य सम्बन्ध माना गया है। भास्कराचार्य का कहना है कि खगोल तथा गणित में एक दूसरे से अनभिज्ञ पुरुष उसी प्रकार महत्त्वहीन है, जैसे घृत के बिना व्यंजन, राजा के बिना राज्य तथा अच्छे वक्ता के बिना सभा होती है—
भोज्यं यता सर्वरसं विनाज्यं राज्यं यथा राजविवर्जितं च।
सभा न भातीव सुवक्तृहीना गोलानभिज्ञो गणकस्तथात्र ॥ -- (सिद्धान्तशिरोमणि, गोलाध्याय, श्लोक 4)
गणकों के गुण
गणितसारसंग्रह के संज्ञाधिकार के अन्त में महावीराचार्य ने गणकों (गणितज्ञों) के ८ गुण गिनाए हैं-
अथ गणकगुणनिरूपणम्
लघुकरणोहापोहानालस्यग्रहणधारणोपायैः।
व्यक्तिकराङ्कविशिष्टैर् गणकोऽष्टाभिर् गुणैर् ज्ञेयः॥
(लघुकरण, उह, अपोह, अनालस्य, ग्रहण, धारण, उपाय, व्यक्तिकरांकविशिष्ट - इन आठ गुणों से गणक को जाना जाता है।)
ब्राह्मस्फुटसिद्धान्त के अनुसार 'आचार्य' की योग्यताएँ
कुट्टक-ख-ऋण-धन-अव्यक्त-मध्य-हरण-एक-वर्ण-भावितकैस् ।
आचार्यस् तन्त्र-विदाम् ज्ञातैस् वर्ग-प्रकृत्या च ॥
By Ranita Das Class 8c 😄
Aryabhatta was the first person to find the correct value of pi
ReplyDeleteTributes to the great mathematician
Good👌
ReplyDeleteब्रह्मगुप्त
ReplyDeleteजिस्नुगुप्त के पुत्र ब्रह्मगुप्त का नाम भारत के उन प्राचीन गणितज्ञों और खगोल शास्त्रियों में शुमार हैं, जिन्होंने अपने आविष्कारों के दम पर मैथ्स की रूपरेखा को तैयार की, उसके थ्योरम्स को गढ़ा।
राजस्थान में जन्म
वर्तमान राजस्थान के भीनमाल से संबंध रखने वाले ब्रह्मगुप्त का जन्म 598 ईसवीं मंं हुआ था, इन्हें भीनमालाचार्य के नाम से भी जाना जाता था। आर्यभट्ट के पश्चात भारत में भास्कराचार्य प्रथम नाम के मशहूर गणितज्ञ हुए जिनके बाद ब्रह्मगुप्त का नाम आता है।
खगोलशास्त्री
महान गणितज्ञ और खगोलशास्त्री रहे ब्रह्मगुप्त ने शून्य के उपयोग के विभिन्न नियमों की खोज की थी। प्रसिद्ध ज्योतिषी भास्कराचार्य ने ब्रह्मगुप्त को ‘गणचक्र-चूड़ामणि’ का शीर्षक प्रदान किया और साथ ही उनके मूलांकों को ही अपने ‘सिद्धांत शिरोमणि’ का आधार बनाया।
अंतरिक्ष प्रयोगशाला
ब्रह्मगुप्त के विषय में माना जाता है कि ये तत्कालीन गुजरात प्रदेश की राजधानी तथा हर्षवर्धन साम्राज्य के तहत आने वाले राजा व्याघ्रमुख के समकालीन थे। ब्रह्मगुप्त प्राचीन भारत की पहली अंतरिक्ष वेशशाला, जोकि उज्जैन में स्थापित थी, के प्रमुख भी बनाए गए थे।
दो महान ग्रंथ
वेधशाला के प्रमुख के रूप में कार्य करते हुए ब्रह्मगुप्त ने 628 ईसवीं में ब्रह्मस्फुट सिद्धान्त और 665 ईसवीं में खंड-खाद्यक नामक दो ग्रंथों की रचना की थी।
ब्रह्मस्फुट सिद्धांत
ब्रह्मस्फुट सिद्धांत पहला ऐसा सिद्धांत है जिसमें शून्य का एक स्वतंत्र अंक के रूप में प्रयोग किया गया है। इतना ही नहीं बल्कि इस ग्रन्थ में ऋणात्मक अंकों और शून्य पर आधारित गणित के सभी नियमों का भी उल्लेख किया गया है।
ग्रहों का स्थान
ब्रह्मस्फुट सिद्धांत में उन्होंने यह लिखा है कि आर्यभट्ट, श्रीषेण, विष्णुचन्द्र आदि की गणना से ग्रहों का स्थान स्पष्ट रूप से उल्लिखित नहीं होता है, इसलिए उन्हें गणना का आधार नहीं बनाना चाहिए।
गणना की शुद्धि
ब्रह्मगुप्त के इस कथन से यह सिद्ध होता है कि उन्होंने 'ब्रह्मस्फुटिक सिद्धांत’ की रचना ग्रहों का प्रत्यक्ष वेध करने के बाद ही की थी। वे इस बात को अच्छी तरह समझते थे कि जब कभी गणना और वेध में अंतर आने लगे तो वेध के द्वारा गणना को शुद्ध कर लेना चाहिए।
विभिन्न अध्याय
ब्रह्मगुप्त पहले ऐसे आचार्य थे जिन्होंने गणित ज्योतिष की रचना को एक विशेष क्रम दिया और ज्योतिष और गणित के विभिन्न विषयों को अलग-अलग अध्यायों में बांटकर उल्लेखित किया।
पद्यात्मक रूप
ब्रह्मगुप्त की बहुत सी रचनाएं दीर्घवृत्तीय छंदों में गढ़ी गई थीं जिन्हें पद्यात्मक रूप दिया गया था। लेकिन अभी तक इस बात से जुड़ा ऐसा कोई प्रमाण उपलब्ध नहीं हो पाया है कि ब्रह्मगुप्त द्वारा रचित गणित के सिद्धांत की उत्पत्ति कहां से हुई थी।
सिंधहिन्द
बगदाद के इतिहासकार अल-बरूनी ने अपनी किताब तारीक-अल हिन्द में इस बात का उल्लेख किया है कि अबसिद खलीफा अल-ममून का भारत में एक दूतावास स्थित है। भारत से ही एक किताब को बगदाद लाया गया था जिसे अरबी भाषा में सिंधहिन्द के नास से अनुवादित किया गया गया। माना जाता है सिंधहिंद ब्रह्मगुप्त के ब्रह्मगुप्त सिद्धांत का ही रूप है।
इस्लामी देशों से संबंध
यह तथ्य इस बात को प्रमाणित करता है कि भारत के विज्ञान, खगोलविद्या, तकनीक और गणित का इस्लामी देशों में विज्ञान और गणित की दिशा में होने वाले उभार और विकास के साथ गहरा नाता रहा है।
रिद्धिमा नाथ
Mahavira was 8thcentury Indian mathematician (Jain) from Gulbarga who asserted that the square root of a negative number did not exist. He gave the sum of a series whose terms are squares of a arithmetical progression and empirical progression and empirical rules for area and perimeter of an iliipse. He was patronised by the great Rashtrakuta king Amoghavarsha Nrupatunga.
ReplyDeleteMahavira was the author of Ganit Sara Sangraha. He separated Astrology from Mathematics. He expanded on the same subjects Arybhata and Brahmagupta had worked on, but he expressed them more clearly.
He is highly respected among Indian mathematicians, because of his establishment of terminology for concepts such as equilateral and isosceles triangle, rhombus, circles and semicircle. Mahavira’s eminence spread all over south India and his books proved inspirational to other mathematicians in South India. It was translated into Telugu by Pavaluri Sanganna as Saara Sangraha Ganitam.
Mahavira also established equations for the sides and diagonals of cyclic quadrilateral.
~Annesha Biswas
Class VIII-A
Annesha👌
ReplyDeleteThank you ma'am
DeleteMam ye sab copy me likhna hai
ReplyDeleteSrinivasa Ramanujan (1887-1920) was an Indian mathematician who made great and original contributions to many mathematical fields, including complex analysis, number theory, infinite series, and continued fractions. He was "discovered" by G. H. Hardy and J. E. Littlewood, two world-class mathematicians at Cambridge, and enjoyed an extremely fruitful period of collaboration with them from 1914 to 1919. Unfortunately, his mathematical career was curtailed by health problems; he returned to India and died when he was only 32 years old.
ReplyDeleteThe most wonderful thing I like about Mr.Srinivasa Ramanujan is his discovery of infinite series or Ramanujan Summation.
For those of you who are unfamiliar with this series, which has come to be known as the Ramanujan Summation after a famous Indian mathematician named Srinivasa Ramanujan, it states that if you add all the natural numbers, that is 1, 2, 3, 4, and so on, all the way to infinity, you will find that it is equal to -1/12.
Name:Jahnab Dewri
Class:VIII
Sec:B
The remarkable, prolific mathematician and astronomer Brahmagupta lived in seventh century India and made many important contributions to mathematics and astronomy. He was the first to explain how to use the numeral zero and negative numbers in mathematical calculations.
ReplyDeleteBy Aayan Angkit Kashyap
Class:X-'D'
Very good aayan and jahnab 👌
ReplyDeleteBeta kisi ko bhi copy mai nhi krna hai ye
ReplyDeleteThe remarkable and great mathematician Aryabhatta has a good contribution to mathematics & astronomy
ReplyDeleteHe is known as the 'Father of mathematics'(IN INDIA)
Aryabhata was an acclaimed mathematician-astronomer. He was born in Kusumapura (present day Patna) in Bihar, India. His contribution to mathematics, science and astronomy is immense, and yet he has not been accorded the recognition in the world history of science. At the age of 24, he wrote his famed “Aryabhatiya”.
ReplyDelete- Tohsina Annam
Class 6 A
Very good harshita and tohsina 👌
ReplyDeleteSome of the famous Indian mathematians are -
ReplyDeleteAryabhata ,Varahamihira ,Brahmagupta ,Bhaskara ,Mahavira ,Madhava ,Nilakantha ,Srinivasa Iyengar Ramanujan ,Harish Chandra ,Mahalanobis ,C.R.Rao ,D.R.Kaprekar ,Satyendranath Bose ,Narendra Karmarkar .
Shristeerupa Chaudhury VI D.
Aryabhatta a great Indian mathematician and astronomer.He was born in Kusumpura(now known as Patna)in Bihar.At the age of 23,he started to teach mathematics and astronomy.His greatest contribution to the world is zero through which he becomes immortal throughout the world.
ReplyDeleteBy:-Nafisa Zahin
Class:-VI B
Sanskrit has a very important and significant contribution in the field of mathematics . Without the contribution of sanskrit in Mathematics it would not be the same as the mathematics of today.
ReplyDeleteOf the many personalities who have immense contributions in mathematics , Bramhagupta is someone who has made some very valuable contibutions in mathematics . Aryabhata was the one who discovered 'O' and Bramhagupt is the one explaines the use of O to the world. He also explained the use of negative numbers.
One dicovery of Bramhagupt which is of great importance among his other discoveries, is his discovery of a formula which calculates the area of a cylic quadrilateral.This formula was named after him as the 'Bramhagupt formula'
Sanskrit has a large influence on mathematics .there is hardly any subject which is not influened by Sanskrit.So we should study and learn this great language,in ordr to bring ot to its former glory.
Thank You.
-Aditya Mazumder
class X D ,Kendriya Vidyalaya Khanapara.
Agar iss prithvi main Aryabhatta, Brahmagupta, Mahavir aur Nilkantha jaisay vaydhik nahi hotay to ganith ka upchar kaisay hota.Aur humlog ganith ko kaisay krtay aur samajhtay.Issliye humay in sab vidyano ko dyannyabaad karna chahiye ginkay bja sa hamara desh bahut agay br raha hain.
ReplyDeleteName-Tisa Dutta
Class-Vl-B
Shrishtirupa mafisa👌
ReplyDeleteAaditya and tisa 👌👌👌👌👌
ReplyDeleteA.A krishnaswami Ayyangar was a mathematician from India. He got a M.A. in mathematics at the age of 18 from Pachaiyappa' s College and subsequently started teaching Mathematics there . He was born on 1December 1892, Chingleput district. In 1981 he joined the mathematics Department of University of Mysore and retired from there in 1947. He died in June 1953.
ReplyDeleteName- Arohi Mazumder VI B
Brahmagupta was a great Indian mathematician.He was born in 598 CE in Bhinmal. He is known for his contributions in mathematics and astronomy.He gave the solution of a general quadratic and linear equations.His other contributions in mathematics are-
ReplyDeleteHe was the first to explain how to use the numeral zero and negative numbers in mathematical calculation.
He was first to prove that the product of two negative numbers is a positive number.
We find many contributions of Brahmagupta in both mathematics and astronomy and he wiuwo always remain immortal among us.
Krittika Bhattacharya VIII C
Brahmagupta was a great Indian mathematician.He was born in 598 CE in Bhinmal. He is known for his contributions in mathematics and astronomy.He gave the solution of a general quadratic and linear equations.His other contributions in mathematics are-
ReplyDeleteHe was the first to explain how to use the numeral zero and negative numbers in mathematical calculation.
He was first to prove that the product of two negative numbers is a positive number.
We find many contributions of Brahmagupta in both mathematics and astronomy and he wiuwo always remain immortal among us.
Krittika Bhattacharya VIII C
Kritika and aarohi 👌👌👌
ReplyDeleteToday,all the things that we have in mathematics are because of the contribution of the Sanskrit Scholars. Today we are solving numerous problems using those formulas and techniques. The Sanskrit Scholars have played a very important role in mathematics. So I thank those Scholars who helped us so much.
ReplyDeleteThe ancient mathematical works were all composed in Sanskrit that consisted a section of Sutras.The Indian Mathematicians (like Aryabhata ,Brahmagupta , Bhaskara etc.) and their contribution in mathematics made them immortal for ever.
ARYABHATA-Aryabhata became famous as a mathematician and an astronomer. He was the first person who discovered the approximation of pi.He also believed that the planets and the moon shine by reflected sunlight.
BRAHMAGUPTA- Brahmagupta (the hindu astronomer and mathematician) discovered the symbol of zero(0) and its operation.
So these are the discoveries of Aryabhata and Brahagupta that I know.
Apart from these there is something else that has made all the children curious.This is nothing but VEDIC MATHS.Today, all children are very interested in learning Vedic Maths. This is because it help us to do calculations very quickly. There are some special sutras and techniques in Vedic Maths which help us to solve the arithmetic operations very easily.I also like to solve the arithmetic operations using Vedic Maths.
There is no subject and no thing in this world which is not in Sanskrit. Sanskrit has lightened my thoughts. I have learnt many good moral values from it. I am very lucky that l am learning it.
Bhargabi Sharma
Class -VIII (B)
*BRAHMAGUPTA
DeleteBrahmagupta was born on 598 CE in Ujjain. He was an Indian mathematician and astronomer. His book Brahmasphutasiddhanta is the first text that mentions zero as a number. Besides that, he also gave out many algebra and arithmetic related concepts and formulas.
ReplyDelete~Vaishnabi Devgan-Vlll C
Aryabhata was born on 476 CE in Pataliputra which is present day Patna, Bihar. He is famous for putting out concepts like lunar eclipse and solar eclipse, rotation of Earth on its axis, reflection of light by moon, value of pi correct to 4 decimal places, circumference of Earth to 99.8 per cent accuracy. His works include the famous Aryabhatiya which he wrote when he was just 23 years old. He influenced other future mathematicians and thinkers like Lalla, Bhaskara I, Brahmagupta, Varahamihira.
ReplyDelete~Vaishnabi Devgan-Vlll C
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ReplyDeleteBhargavi and vaishnavi 👌👌👌
ReplyDeleteThank you ma'am
DeleteAryabhata was the first of the major mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy.Aryabhata was born in 476 C.E. .Aryabhata is the author of several treatises on mathematics and astronomy,some of which are lost.
ReplyDeleteBramhagupta was an Indian mathematician and astronomer.Bramhagupta was born in 598C.E.in Bhillamala (modern Bhinmal). He is the author of two early works on mathematics and astronomy.Bramhagupta was the first to give rules to compute with zero.The text compused by Bramhagupta were in elliptic verse in Sanskrit, as was common practice in Indian mathematics.
Sanskrit has a very important and significant contribution in the field of mathematics. Without the contribution of Sanskrit in mathematics it would not be the same as the mathematics of today what we are study.I am very lucky that I am learning about this great person today.
Mrinmoy Haloi
Class 8-D
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ReplyDeleteAryabhata was the first of the major mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy.Aryabhata was born in 476 C.E. .Aryabhata is the author of several treatises on mathematics and astronomy,some of which are lost.
ReplyDeleteBramhagupta was an Indian mathematician and astronomer.Bramhagupta was born in 598C.E.in Bhillamala (modern Bhinmal). He is the author of two early works on mathematics and astronomy.Bramhagupta was the first to give rules to compute with zero.The text compused by Bramhagupta were in elliptic verse in Sanskrit, as was common practice in Indian mathematics.
Sanskrit has a very important and significant contribution in the field of mathematics. Without the contribution of Sanskrit in mathematics it would not be the same as the mathematics of today what we are study.I am very lucky that I am learning about this great person today.
Mrinmoy Haloi
Class 8-D
In my view the relationship between mathematics and sanskrit during vedic period stood from the sanskrit word sulba meaning a piece of cord or string and the sutra translate to formula. Hence, shulba -sutras stand for mathematics that grew out of the use lengths of cord for the purposes of construction of sites for sacrificial altars associated with the practice of vedic rituals.
ReplyDeleteDivyaanga gautam- class viii b
Aryabhata was the first mathemathician. He was born in Pataliputra in Bihar. Aryabhatta was the first person to find the correct value of pi
ReplyDeleteTributes to the great mathematician
Sorry ma'am sent mistakely
DeleteSanskrit has been a boon since early days as we are now changing our life economically and politically. Beginning from the past and now the present. Sanskrit has changed our lives a lot. It has been observed that most of the inventions that people now can't think anything besides that is the gift of the sanskrit gurus.
ReplyDeleteFirstly let us talk about one topic.....
A widely known and a popular sanskrit guru Aryabhatta who was born on 476 CE in the city Patna in Bihar had made many inventions including the value of PI, the circumference of the earth, lunar eclipse and solar eclipse, the rotation of the earth on its axis, reflection of light etc. Nowadays sanskrit has although not considered the mother language, but still there are some people who are trying to reveal that hidden treasure lies beneath the surface of the earth. Not only Aryabhatta but many other sanskrit gurus had preached our life to modernity and we are very thankful to them . Without the sanskrit gurus, mathematics would have probably not existed on our earth.
From Priya Basumatary
Class 8B
Aryabhata was the first mathemathician. He was born in Pataliputra in Bihar. He was born in 476 CE and died in 550 CE. Explanation of lunar eclipse and solar eclipse, rotation of Earth on its axis, reflection of light by moon, sinusoidal functions, solution of single variable quadratic equation, value of π correct to 4 decimal places, diameter of Earth, calculation of the length of sidereal year was the notable ideas of Aryabhata.
ReplyDeleteBy Swastika S Dutta
Class 6 A
All of your text are superb👌
ReplyDeleteSANSKRIT has a very important and as as a very significant contribution in the field of Mathematics... Without the contribution of this subject i.e Sanskrit in Mathematics it would not be the same as the Mathematics of today's generation !!!
ReplyDeleteSanskrit and Mathematics are tightly related with each other. Like for solving Maths problem we have some rules like Theorems, Identities, Assumptions, Easy Trick etc and in the same way Sanskrit has also some predefined rules like Dhatu Rup, Shabd Rup etc for making correct sentences...
As someone said that " PRACTICE MAKES A MAN PERFECT " so both Maths and Sanskrit needs practice to have good command over these subjects !
~ Regarda Nitika Sinha
From X-D