Алексей Виноградов – Fermat's Last Theorem (Conditions and decisions) (страница 5)

The coordinates of the point Ф_n on the Pythagorean ray ƛ ₀ can be written as

Ф_n ( x₀/ⁿ√(x₀ⁿ+ y₀ⁿ), y₀/ⁿ√(x₀ⁿ+ y₀ⁿ)) or Ф_n ( x₀ h_n), ( y₀ h_n), where h_n = R_n/ z₀ = 1/ ⁿ√(x₀ⁿ+ y₀ⁿ) (14)

The coordinates of the Pythagorean point P₀ can be written as P₀(x₀ h₀, y₀ h₀), where h₀ = 1/ z₀ is the step of partitioning the unit square. (15)

Obviously, h_n > h₀,, since R_n > 1, (h_n = h₀ R_n)

If we construct a square with a side equal to the length of the radius vector of the point Ф_n and cover this square with a uniform mesh with a step of h_n = R_n/z₀, then the point Ф_n in this square will be a nodal (Pythagorean) point. At this point, as well as for the Pythagorean point P₀ ϵ S₂ = 1, the Pythagorean theorem is fulfilled integer over cells (Fig. 2).

It remains for us to consider the rays ƛ^* passing through the nodal (rational) points of various partitions of the unit square, which are not Pythagorean rays for any partitions. These rays intersect the unit circle at irrational points. For example, ƛ

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