Version 3.7 Collapse of the Hypotenuse

The paper shows that 1² + 1² = 0 is geometrically real (both legs genuinely positive) via two mechanisms—Minkowski null vectors from orthogonal timelike/spacelike pairs, and curved/topological manifolds (sphere reconvergence, torus short-circuits)—unlike the cheating complex foil i² + 1² = 0; it is a pedagogical contrast to Euclidean Pythagoras.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-03-27
DOI
https://doi.org/10.5281/zenodo.17151255
Primary Topic
Geochemistry and Geologic Mapping
Type
article
Field-Weighted Citation Impact
0.00
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article

Version 3.7 Collapse of the Hypotenuse

Zenodo (CERN European Organization for Nuclear Research)
Geochemistry and Geologic Mapping
article

Version 3.7 Collapse of the Hypotenuse

article en

Abstract

The paper shows that 1² + 1² = 0 is geometrically real (both legs genuinely positive) via two mechanisms—Minkowski null vectors from orthogonal timelike/spacelike pairs, and curved/topological manifolds (sphere reconvergence, torus short-circuits)—unlike the cheating complex foil i² + 1² = 0; it is a pedagogical contrast to Euclidean Pythagoras.

Zenodo (CERN European Organization for Nuclear Research)
Climate action
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Geochemistry and Geologic Mapping
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Version 3.7 Collapse of the Hypotenuse · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS