STORY OF NUMBERS

संख्याओं की कहानी

चतुर्भुज मंदिर, ग्वालियर का किला � काल 875 AD��शिलालेख में दर्ज है की मंदिर प्रांगण में 187 हाथ x 270 हाथ का बगीचा लगाया गया था जिसमें से मंदिर के लिए प्रतिदिन 50 मालाएं तैयार की जाती थीं। ��The inscription states that the community planted a garden of 187 hasta x 270 hasta(1 hasta = 1.5 feet) that the garden yielded 50 garlands for the temple everyday.

Numbers corresponding to fingers 1 to 10�11 Eleven derives from ein lifon means ‘one left over’�12 Twelve derives from twe lif means ‘two over ten’�13 Thirteen ‘three and ten’�14 Fourteen ‘four and ten’�…�19 Nineteen ‘nine and ten’�20 Twenty twe tig or ‘two tens’�and so on…

Babylonians ( 3000 to 2000 BC) used wedge shaped ‘cuneiforms’ on clay tablets such as � �1 ��10 ��e.g. 25 = 2(10) + 5 �

Greek Numbers (300 BC)��I for 1, for 5, for 10, H for 100, X for 1000, M for 10000���

Mayan numeral system(origin unknown)� vigesimal number system(base 20)�

Chinese and Japanese �Recorded their writing on bamboo slips.Characters written on them were arranged in vertical order from top to bottom.�Their numeral system is a multiplicative grouping to base 10.��

ROMAN NUMERAL SYSTEM�

Advantages of these numeral system�� Characters were of picture form, so remembering� it were easy . � Disadvaantages of these numeral system� Expressing large numbers was very tedious.�� Addition and multiplication was a very difficult task.�� It required a university degree in addition and� multiplication separately.��

Examples of addition and multiplication in Roman numeral system� � XIV + VIII = X + (IV + I) + V + II � = X + (V + V)+ II� = X + X + II� = XXII�III x VII = III + III + III + III + III + III + III� = (III + II)+(I+III+I)+(II+III)+(III+II)+I� = (V+V)+(V+V)+I� = X + X + I� = XXI

HINDU NUMERAL SYSTEM�1 11 21 31 41 51 61 71 81 91�2 12 22 32 42 52 62 72 82 92�3 13 23 33 43 53 63 73 83 93�4 14 24 34 44 54 64 74 84 94�5 15 25 35 45 55 65 75 85 95�6 16 26 36 46 56 66 76 86 96�7 17 27 37 47 57 67 77 87 97�8 18 28 38 48 58 68 78 88 98�9 19 29 39 49 59 69 79 89 99�10 20 30 40 50 60 70 80 90 100

Characterstics of HINDU NUMERAL SYSTEM�It has ZERO.�Any number greater than basic digits 0 to 9 can be formed with place value system�Every digit has its own unique place value�Digit placed second from left is at tens, so its place value is 10 times and so on.�E.g. 25 = 20 + 5� 225= 200+20+5� 9876=9000+800+70+6�Addition and multiplication is very simple because of place value system � 7806 539�+2945 x 36�10751 3234 � 1617x � 19404

A numeral system with any base can be formed�e.g. Binary numeral system with only digits 0 and 1�0 10 100 1000 10000�1 11 101 1001 and so on…� 110 1010� 111 1011� 1100� 1101� 1110� 1111

Mathematicians from Europe developed geometry and astronomy up to 2^nd century, but they could not develop arithmetic for two important reasons.�1.Europe suffered 1000 years of dark era because of the onslaught of sematic religion on its own population.�2.Europe lacked concept of zero because it means nothingness. They could not grasp this subtle idea because of cultural reasons.

Arab merchants learnt it from Mogul Darbar in India and spread it to Europe. That is why the HINDU NUMERAL SYSTEM is also called HINDU ARABIC NUMERAL SYSTEM by European scholars. �Now it is called International numeral system.�We must have deep pride because of its origin and development in India. �Its written record available at Gwalior adds special flavour to us.

Place value system can not be conceived without ZERO. �ZERO means nothingness which contains everything.�It is Indian Philosophy�ZERO and INFINITY are the integral part of our DHARMA

नासदीय सूक्त (ऋग्वेद 10 वाँ मण्डल 129 वाँ सूक्त)��नासदासीनो सदासीत तदानीम नासीद रजो नो व्योमापरो यत।�किमावरीव: कुह कस्य शरमन्नम्भ: किमासीद गहनं गभीरम्॥

​

वहाँ पर ‘कुछ नहीं’ भी नहीं था, अस्तित्व भी नहीं था। न वहाँ वायु थी, न आकाश था और न आकाश के परे अंतरिक्ष। इस सबको कौन ढके हुए था? यह सब कहाँ था ? अतल गहराइयों में व्याप्त ब्रम्हाण्ड के जल को कौन धारण किए हुए था?

�Then even nothingness was not , nor existence. There was no air, nor the heavens beyond it. What covered it? Where was it? In whose keeping was there then cosmic water , in depth unfathomed?�