ゼロと無限大のいい関係

円に内接する正ゼロ角形とは、その円そのものである。ゼロと無限大のいい関係を述べている： \section{$n=2,1,0$ regular polygons inscribed in a disc} We consider $n$ regular polygons inscribed in a fixed disc with radius $a$. Then we note that their area $S_n$ and the lengths $L_n$ of the sum of the sides are given by \begin{equation} S_n= \frac{n a^2}{2} \sin \frac{2\pi}{n} \end{equation} and \begin{equation} L_n= 2n a \sin \frac{\pi}{n}, \end{equation} respectively. For $n \ge 3$, the above results are clear. For $n =2$, we will consider two diameters that are the same. We can consider it as a generalized regular polygon inscribed in the disc as a degenerate case. Then, $S_2 =0$ and $L_2 =4a$, and the general formulas are valid. Next, we will consider the case $n=1$. Then the corresponding regular polygon is a just diameter of the disc. Then, $S_1 =0 $ and $L_1 = 0$ that will mean that any regular polygon inscribed in the disc may not be formed and so its area and length of the side are zero. Now we will consider the case $n=0$. Then, by the division by zero calculus, we obtain that $S_0= \pi a^2$ and $L_0 = 2\pi a$. Note that they are the area and the length of the disc. How to understand the results? Imagine contrary $n$ tending to infinity, then the corresponding regular polygons inscribed in the disc tend to the disc. Recall our new idea that the point at infinity is represented by $0$. Therefore, the results say that $n=0$ regular polygons are $n= \infty$ regular polygons inscribed in the disc in a sense and they are the disc. This is our interpretation of the theorem: \medskip {\bf Theorem.} {\it $n =0$ regular polygons inscribed in a disc are the whole disc.} \medskip The division by zero is uniquely and reasonably determined as 1/0=0/0=z/0=0 in the natural extensions of fractions. We have to change our basic ideas for our space and world: Division by Zero z/0 = 0 in Euclidean Spaces Hiroshi Michiwaki, Hiroshi Okumura and Saburou Saitoh International Journal of Mathematics and Computation Vol. 28(2017); Issue 1, 2017), 1-16.　 http://www.scirp.org/journal/alamt　 　http://dx.doi.org/10.4236/alamt.2016.62007 http://www.ijapm.org/show-63-504-1.html http://www.diogenes.bg/ijam/contents/2014-27-2/9/9.pdf http://okmr.yamatoblog.net/division%20by%20zero/announcement%20326-%20the%20divi Announcement 326: The division by zero z/0=0/0=0 - its impact to human beings through education and research