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math.GM2025
Newton-Mandelbrot set and Murase-Mandelbrot set
Shunji Horiguchi
We obtain four extended Newton's methods and three extended Mandelbrot's recurrence formulas from the Wasan (Japanese mathematics in the Edo period (1603-1868)). Furthermore, two e…
math.GM2021
Binomial expansion of Newton's method
Shunji Horiguchi
We extend the Newton's method and show the extended Newton's method leads to the binomial expansion of Newton's method that the convergences become the quadratic and linearly. In c…
math.GM2009
An Elementary Proof by the Heegaard Splittings of the 3-Dimentional Poincare Conjecture
Shunji Horiguchi
v1: In this paper, we will give an elementary proof by the Heegaard splittings of the 3-dimentional Poincare conjecture in point of view of PL topology. This paper is of the same t…