In this paper we show that all known types of numbers — natural, integer, rational, irrational, real, complex, and even transcendental — are not independent abstractions but are generated from a single geometric object: the infinium ℑ = △₁ₓ₁ (an isosceles right triangle with legs 1 and hypotenuse √2). Each type of number arises as a definite projection or deformation of this fundamental quantum. We give rigorous definitions and formulas for each transition and discuss how such a geometrization of arithmetic resolves the fundamental contradictions associated with the traditional set-theoretic foundation (ZFC). In particular, we show that ZFC with its paradoxes and the axiom of infinity proves to be redundant: numbers arise as a geometric necessity rather than as formal-logical constructions. This removes centuries-old contradictions between the discrete and the continuous, between arithmetic and geometry, and also eliminates singularities and "heat death" in physics. Replacing the structureless point with the infinium turns arithmetic into a branch of geometry.
Alexey (KAMAZ) Petrov (Tue,) studied this question.