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Singularity Projection in Three-Dimensional Space and the Discretization of a Continuous Interval

Primarily human-written textHuman understanding: all partsmath.AT — Algebraic Topologymath.GT — Geometric Topology

Contributed by zoushanzhong zou ↗

Version 1 / Nov 10, 2026 / CC BY 4.0

Abstract

We study the projection geometry induced by a singular point on the boundary of a three-dimensional fan-shaped cylinder. The cylinder is defined in the first quadrant of the real coordinate plane, with x and y both between zero and one, and a singular point located at x=1 on the boundary. Through an iterative projection process involving the angle bisector of the quadrant, we prove that the continuous interval [0,1] is precisely discretized to an infinite set of boundary points.

References

  1. Titchmarsh, E. C. (1986). The Theory of the Riemann Zeta Function . Oxford University Press. (For background on the elementary geometry of projections; no analytic number theory is used in this paper.)
  2. Coxeter, H. S. M. (1969). Introduction to Geometry . Wiley.
  3. Bohrium SciencePedia. Nontrivial Zeros: The Key to the Music of the Primes [EB/OL]. Beijing: Bohrium, n.d.

Version history

  1. v1 · 4 pagesSubmitted by zoushanzhong zouRevised after moderator-requested changesCurrentNov 09, 2026