Question
वैदिक बीजगणित में गुणन एवं भाग की विभिन्न विधियों का उदाहरण सहित विवेचन कीजिए।
Answer :
Word Count : 1150
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Skip in 10
वैदिक बीजगणित भारतीय गणितीय परंपरा की एक विशिष्ट और सरल पद्धति है, जिसका आधार महर्षि भारती कृष्ण तीर्थजी द्वारा प्रतिपादित 16 सूत्र तथा 13 उपसूत्र हैं। इन सूत्रों के माध्यम से जटिल गणनाओं को अत्यंत सरल, शीघ्र और मानसिक रूप से हल किया जा सकता है। वैदिक बीजगणित में गुणा तथा भाग की अनेक ऐसी विधियाँ हैं जो पारंपरिक विधियों की तुलना में कम समय लेती हैं और गणना को अधिक सहज बनाती हैं। इन विधियों का प्रयोग संख्याओं के प्रकार, उनके परस्पर संबंध तथा गणना की आवश्यकता के अनुसार किया जाता है। प्रत्येक विधि का अपना विशेष महत्व है और उपयुक्त परिस्थितियों में उसका प्रयोग अत्यंत प्रभावशाली सिद्ध होता है। गुणन की सबसे प्रसिद्ध विधियों में "ऊर्ध्वतिर्यग्भ्याम्" सूत्र का विशेष स्थान है। इस सूत्र का अर्थ है – "ऊर्ध्व अर्थात् सीधा तथा तिर्यक् अर्थात् आड़ा।" इस विधि में संख्याओं का गुणन क्रमशः ऊर्ध्व तथा तिर्यक् रूप से किया जाता है और प्राप्त परिणामों को जोड़कर अंतिम उत्तर प्राप्त किया जाता है। उदाहरण के लिए 23 × 14 का गुणन करें। सबसे पहले इकाई के अंक का गुणन: 3 × 4 = 12, 2 लिखेंगे और 1 आगे ले जाएंगे। अब तिरछा गुणन: (2 × 4) + (3 × 1) = 8 + 3 = 11, इसमें पहले का 1 जोड़ने पर 12 प्राप्त होगा। 2 लिखेंगे और 1 आगे ले जाएंगे। अब दहाई के अंकों का गुणन: 2 ×
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