There is no perfect mathematical circle.

Any engineer needs accurate computer and physical modeling, especially if the company wants to create the most wear-resistant and durable bearing, its circle properties and parameters must be known, almost to the atom level.



Imagine, you give the task to the programmer to find the exact percentage and model of contact of the bearing, and it turns out that it is impossible, since it is impossible to simulate the exact circumference. As well as it is impossible to simulate the exact contact area.



The concept of a circle is one of the universal mathematical concepts, literally generalized to the case of arbitrary metric spaces. But in the informatics section, this topic is very rarely raised because it is impossible to be impossible.

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So what is a circle? And why is his exact mathematical model impossible.







In scientific understanding, a circle is a regular 65537 square (a sixty-five-thousand-five-three-third-seven-angle) is a regular polygon with 65,537 corners and 65,537 sides.



So for a programmer, a circle is a polygon with 65,537 corners - and these corners will touch a flat surface or the same circle, and changing the balance of the whole mathematical circle with 65,537 corners. Agree that the model is already outdated?



Gauss in 1796, it was proved that a regular n-gon can be constructed with a compass and a ruler, if the odd prime divisors n are different Fermat numbers. In 1836, P. Vanzel proved that there are no other regular polygons that can be constructed with a compass and a ruler. Now this statement is known as the Gauss – Vanzel theorem.



I can even discover a secret so narrow in the bearing industry that most road, rail and plane crashes occur precisely because of poor-quality bearings, since it is sometimes impossible to check the quality and circumference because science works mostly not with numbers but with “ranges” bearing industry due to the problem of creating a perfectly smooth bearing the highest.



We see this problem in games





And this accuracy is very low.



A 65 thousand corners of the circle is less than a million.







But even this is not the limit. The ideal circle is generally infinite (it has an infinite number of angles). How then to express it in programming, if any number will be its inaccurate model? Or will such high accuracy be unnecessary? Indeed, in any mass simulation of the smallest detail, cascade avalanche-like effects are formed which give different results.



Thanks for attention.