Simple Estimation of Mathematical Factorials

The year 2026 is a historic year. From that year onward, the formula developed by the British mathematician James Stirling, used for approximately 250 years to estimate mathematical factorials, will become largely obsolete. Stirling’s formula proves to be worthless, especially for factorials with an exponent greater than 3 in the base 10. According to Stirling’s formula, one would first have to divide the number n, from which the factorial is to be determined, by Euler’s number e, and then calculate the exponent n of the result. However, modern calculators can generally calculate factorials up to the range of numbers with an exponent of 3 in the base 10. Beyond that, they typically fail, just as Stirling’s formula fails when calculating the intermediate result, as described above. In other words, Stirling’s formula cannot be used precisely where it would be needed as an approximation. And where it’s needed, it tends to deliver rather imprecise results, where-as calculators provide precise results by calculating the exact factorial. With the formula described in this book, estimating factorials at least on the order of the exponent up to a number with 101 digits, i.e., a number with an exponent of 100 in the base 10, is easily possible. Theoretically, there’s no limit to the number’s height it’s simply a matter of diligence. The author has carried this out up to an exponent of 100 in the base 10, and the results can be found in a 10-page table in this book. Of course, it would be interesting to determine even higher exponents. But that will be the subject of a future book. In this book, the author explains the formula as simply and clearly as possible, even for people without any prior math-ematical knowledge. The great advantage of this formula is that, unlike Stirling’s formula, it doesn’t require constants like pi or Euler’s number. These are the simplest multiplications and additions, the kind even a schoolchild can manage.