The Great Indian Ancient Knowledge forged the Global Knowledge Order
Ancient India’s integration of mathematics, astronomy, and philosophy shaped foundational concepts in global science, from the decimal system to celestial mechanics, cementing its role as the architect of humanity’s intellectual heritage
Inspiring and enlightening mathematical journey!
Arun
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Ancient Math Wisdom: The 16 Sutras of Mathematics
The 16 Vedic algorithms and ancient Indian mathematics knowledge for enhanced problem-solving skills. Discover the ancient wisdom of Vedic Mathematics - concise formulas derived from ancient Indian texts that simplify arithmetic, algebra, geometry, and calculus. These powerful sutras, attributed to scholar Sri Bharati Krishna Tirthaji, enable faster mental calculations and problem-solving across modern fields.
Modern Applications of Vedic Mathematics
Vedic Mathematics has found applications across modern fields: In AI/ML, Urdhva-Tiryagbhyam speeds up matrix operations in neural networks, while Nikhilam Sutra optimizes numerical computations in cryptography. In education, these sutras simplify mental math for competitive exams like SAT and GRE. In FinTech, they enhance rapid calculations in trading algorithms, bridging ancient wisdom with contemporary challenges.
Ekadhikena Purvena & Nikhilam Navatashcaramam Dashatah
Ekadhikena Purvena
"By one more than the previous one"
Used for squaring numbers ending in 5. For example, to calculate 25², multiply 2×3=6 and append 25, giving 625.
Modern Use: Simplifies exponentiation in algebraic computations.
Nikhilam Navatashcaramam Dashatah
"All from 9 and the last from 10"
Simplifies subtraction from bases like 10, 100, or 1000. For example, 1000−876=124.
Modern Use: Efficient base calculations in computer science and cryptography.
Urdhva-Tiryagbhyam & Paravartya Yojayet
Urdhva-Tiryagbhyam
"Vertically and Crosswise"
General multiplication method. For example, 12×13=(1×1),(1×3+2×1),(2×3)=156.
Modern Use: Optimizes matrix multiplication in AI/ML algorithms.
Paravartya Yojayet
"Transpose and Apply"
Solves linear equations by rearranging terms. For example, solving 3x+4=19.
Modern Use: Applied in optimization problems and linear algebra.
Urdhva-Tiryagbhyam & Paravartya Yojayet
Urdhva-Tiryagbhyam
"Vertically and Crosswise"
General multiplication method. For example, 12×13=(1×1),(1×3+2×1),(2×3)=156.
Modern Use: Optimizes matrix multiplication in AI/ML algorithms.
Paravartya Yojayet
"Transpose and Apply"
Solves linear equations by rearranging terms. For example, solving 3x+4=19.
Modern Use: Applied in optimization problems and linear algebra.
Shunyam Saamyasamuccaye & Anurupyena
Shunyam Saamyasamuccaye
"When the sum is the same, that sum is zero"
Solves equations where the sum of terms on both sides is equal (e.g., x+4=x+4).
Modern Use: Error detection in data validation.
Anurupyena
"Proportionately"
Adjusts proportions for easier calculations (e.g., scaling ratios).
Modern Use: Feature scaling in machine learning datasets.
Sankalana-Vyavakalanabhyam & Puranapuranabhyam
Sankalana-Vyavakalanabhyam
"By addition and subtraction"
Solves equations through simultaneous addition/subtraction (e.g., solving x+y=10, x−y=2).
Modern Use: Simplifies linear algebra operations.
Puranapuranabhyam
"By completion and non-completion"
Completes squares in quadratic equations (e.g., solving x²+6x+5=0).
Modern Use: Polynomial equation solving.
Chalana-Kalanabhyam & Yaavadunam
Chalana-Kalanabhyam
"Sequential motion"
Solves differential equations through incremental adjustments.
Modern Use: Calculus and dynamic system modeling.
Yaavadunam
"Whatever the extent of its deficiency"
Squares numbers near a base (e.g., 98²=(100−2)²=9604).
Modern Use: Rapid approximations in data science.
Vyashtisamanstih & Shesanyankena Charamena
Vyashtisamanstih
"Split into parts"
Breaks complex problems into simpler parts (e.g., partial fractions).
Modern Use: Modular arithmetic in cryptography.
Shesanyankena Charamena
"The remainders by the last digit"
Divisibility checks (e.g., checking if 169 is divisible by 13).
Modern Use: Number theory and encryption.
Sopaantyadvayamantyam
"The ultimate and twice the penultimate"
Financial Applications
Solves equations with recurring decimals.
Sopaantyadvayamantyam is particularly useful in financial calculations and interest rate models.
Ekanyunena Purvena
"By one less than the previous one"
Algorithmic Optimization
Used in multiples of 9 calculations
Ekanyunena Purvena simplifies calculations like 9×7=63, where 6=7−1 and 3=9−6, optimizing algorithmic loops in programming.