PAS Constant has Value for Zero

[Samrat261085]

Author:
Mr. Sandeep Ashokrao Patil, currently known as “Samrat”,
Independent Researcher | Mathematician | Copyright No. L-28659/2007, India

PAS Constant:
This article introduces the PAS Constant, a novel mathematical constant valued at 0.717, developed to rationalize and simplify the outcomes of limit and derivative problems in calculus. Traditionally, limits evaluated as x→0 tend to produce irrational or indeterminate results. The PAS Constant substitutes the classical approach by shifting the lower bound from 0 to 0.717, enabling the derivation of rational outputs. Registered under the Indian Literary Works Act (L-28659/2007), this constant holds theoretical and pedagogical significance, especially in rational approximation and symbolic computation. Drawing upon the philosophical and historical evolution of zero—from ancient Indian scholars like Brahmagupta to its modern abstraction—the PAS Constant reframes how near-zero behaviours are interpreted. Worked examples and graphical representations validate the rationalizing power of PAS, making it a new tool in analytical mathematics and AI-assisted symbolic reasoning.

Purpose
The PAS Constant aims to address challenges in evaluating limits and derivatives where irrational or indeterminate results typically arise when approaching zero. By using 0.717 instead of zero, results often resolve into rational values.
Mathematical Significance

• A rational alternative that may be applied in symbolic AI, rational modeling, and educational settings.

In a groundbreaking development that may shift how students and researchers tackle calculus problems, a new constant has emerged from the academic underground: the PAS Constant, valued at 0.717. Discovered by an independent researcher in India and registered in 2007 (L-28659/2007), the constant provides a rational alternative to zero in limit and derivative calculations.
Where traditional calculus leads to messy irrational numbers, PAS offers clarity. The secret lies in substituting zero with 0.717—and the results speak for themselves. Once indeterminate or irrational expressions can now be rationalized easily.
“This is not just a trick; it’s a philosophical evolution of the concept of zero,” says the inventor. PAS builds on the legacy of ancient Indian mathematicians like Brahmagupta, who gave us rules for operating with zero over 1,400 years ago.
Educators and theorists alike are taking note. Visual data and examples show clear rationalization when PAS is applied to limit problems—potentially making PAS the next big innovation in applied mathematics.

Applications
• Rational approximation in calculus
• Derivative evaluations
• Symbolic mathematical computation
Pedagogical tool for students learning calculus

6.0 More reading and publications:

1. Medium
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6.1 References

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2. Spivak, M. Calculus.
3. Penrose, R. The Road to Reality.
4. Russell, B. The Principles of Mathematics.
5. Nagel, E. The Structure of Science.
6. Turing, A. On Computable Numbers.
7. Feynman, R. QED: The Strange Theory of Light and Matter.
8. Gödel, K. On Formally Undecidable Propositions.
9. Whitehead, A.N. & Russell, B. Principia Mathematica.
10. Bhāskara II, Siddhānta Śiromaṇi.

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