The Prime Helix - A Geometric and Kinematic Translation of Prime Distribution Theory

We embed the real number line onto the helix (cos t, sin t, t) derived from Euler's formula and place the prime numbers as distinguished points on this curve. Consecutive primes are connected by straight-line chords through three-dimensional space, defining a two-particle thought experiment: a helix walker travelling the continuous curve and a chord hopper jumping only between primes, both at constant speed. The cumulative path ratio converges numerically to 1/√2 = cos(45°), a value determined by the helix pitch angle and driven by the prime number theorem. Tentative analogies are drawn to the Euler product formula, the pole of the Riemann zeta function at s = 1, and the oscillatory corrections from non-trivial zeta zeros. Three novel visualizations are presented: caustic rings on the phasor circle encoding prime gap frequencies, a phase function spectrogram with diagonal striations, and a convergence dashboard tracking the two-particle ratio. This is an exploratory work proposing a complementary geometric perspective on prime distribution, accompanied by interactive tools and open-source code.