The Quadrea of a Projective Quadrangle Theorem in Universal Hyperbolic Geometry: Using Archimedes' Function and Deriving Projective Pythagoras in Degenerate Quadrangles.
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2025
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| _version_ | 1866901859271180288 |
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| author | Coady, John David |
| author_facet | Coady, John David |
| contents | <div><span><span>This preprint presents a new theorem in Universal Hyperbolic Geometry (UHG). We introduce the metrical quatity the Quadrea of a General Projective Quadrangle and its dual in UHG, validated through algebraic proofs and exact numerical examples which demonstrate computational feasibility, verified by SymPy, Maple, and Mathematica implementations. This deposit includes two files: (1) UHG_Quadrea_of_a_Projective_Quadrangle</span></span><span><span>.pdf</span></span><span><span>, the full preprint, and (2) UHG_Quadrea_of_a_Projective_Quadrangle</span></span><span><span>.zip</span></span><span><span>, containing the Overleaf LaTeX source files (main.tex, refr.bib, Abstract.tex, Introduction.tex, Examples.tex, Preliminaries.tex, Details.tex, maple.tex, Proof3_1Eqns.tex, Supplemental.tex) for reproducibility. </span></span></div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17081214 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Quadrea of a Projective Quadrangle Theorem in Universal Hyperbolic Geometry: Using Archimedes' Function and Deriving Projective Pythagoras in Degenerate Quadrangles. Coady, John David <div><span><span>This preprint presents a new theorem in Universal Hyperbolic Geometry (UHG). We introduce the metrical quatity the Quadrea of a General Projective Quadrangle and its dual in UHG, validated through algebraic proofs and exact numerical examples which demonstrate computational feasibility, verified by SymPy, Maple, and Mathematica implementations. This deposit includes two files: (1) UHG_Quadrea_of_a_Projective_Quadrangle</span></span><span><span>.pdf</span></span><span><span>, the full preprint, and (2) UHG_Quadrea_of_a_Projective_Quadrangle</span></span><span><span>.zip</span></span><span><span>, containing the Overleaf LaTeX source files (main.tex, refr.bib, Abstract.tex, Introduction.tex, Examples.tex, Preliminaries.tex, Details.tex, maple.tex, Proof3_1Eqns.tex, Supplemental.tex) for reproducibility. </span></span></div> |
| title | The Quadrea of a Projective Quadrangle Theorem in Universal Hyperbolic Geometry: Using Archimedes' Function and Deriving Projective Pythagoras in Degenerate Quadrangles. |
| url | https://doi.org/10.5281/zenodo.17081214 |