
We present a novel computational framework that transforms linear DNA se-quences into three-dimensional geometric helices modulated by the golden ratioφ (1.61803398875). This φ-harmonic transformation reveals previously unrecog-nized geometric patterns in genetic sequences that correlate with biological func-tion, evolutionary conservation, and epigenetic regulation. Our method assignseach nucleotide (A, T, C, G) unique geometric parameters based on φ and itsmathematical derivatives, creating sequence-specific 3D “fingerprints” that encodebiological information in geometric form. We demonstrate that telomeric repeatsexhibit perfect 6-base geometric periodicity, promoter regions display characteristictight spirals, and coding sequences show balanced geometric complexity. The sys-tem generates interactive visualizations, mathematical analyses, and comparativemetrics, providing a new lens through which to view genetic information. Thiswork bridges computational biology, mathematics, and information theory, sug-gesting that DNA sequences contain inherent geometric information that followsuniversal mathematical principles observed throughout nature.Keywords: DNA geometry, golden ratio, φ-harmonics, sequence visualization,geometric bioinformatics, computational genomics
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