Perfect Ratios: A Blueprint of Harmony
Nature and numbers intertwine in remarkable ways. Consider the Bluefin Tuna, its torpedo shape a
testament to perfect ratios, or the elegant spiral of a propeller. This page unveils a design where
geometry and mathematics converge, revealing patterns as precise as they are beautiful—echoes of pi,
repeating sequences, and a harmony that feels almost alive.
The Design Unveiled
Picture a small blue diamond perched atop a red line, pinpointing pi (3.14159...) with uncanny accuracy.
Below, a central disk flanked by circles forms a propeller-like shape, its proportions humming with
symmetry. Every horizontal and vertical measurement in this layout ends with the repeating remainder
142857—a fraction born from 1/7 (0.142857...).
These ratios rival the elegance of 22/7 (3.142857), a classic stand-in for pi, off by just a whisper.
Circles and Their Dance
Two key circles drive the design. Their diameters split the space in a 64.28% to 35.71% ratio, yielding 1.8
when divided—a clean, resonant figure. Zoom in: the disk’s diameter (53.428 mm) over 17 (the seventh
prime) lands at 3.142857, another nod to pi’s shadow. The circles themselves shrink toward the center by
a factor of 3.5, a rhythm that ties them to the whole.
The Power of Seven
Seven weaves through this tapestry like a thread. Take the propeller’s height (100 mm) and divide it by
half the disk’s thickness (14.285714 mm)—the result is exactly 7. This isn’t chance; it’s a signature.
From the recurring 142857 to the prime 17, seven signals a deeper order, linking this design to the cosmos.
Think of the Sun and planets, where ratios also sing.
Beyond the Flat Page
Flat drawings deceive; this is a three-dimensional marvel. The central disk, football-shaped in truer
renderings, hints at a sphere within a cube. Eight right triangles frame it, their 3-4-5 Pythagorean roots
grounding the structure. Three such units could curve into a sphere, a nod to nature’s preference for
roundness over edges.
A Universal Echo
Perfect ratios aren’t confined to this design—they ripple through reality. The Bluefin Tuna’s sleek form
mirrors these proportions, a living echo of the propeller’s balance. Here, math becomes art: pi’s infinite
dance, captured in finite lines, points to a universe built on precision. What begins as a sketch ends as a
window into creation’s hidden pulse.
While working on drawings for pi is by design, I noticed a propeller like shape.
Perhaps indicating optimum air/water flow possibilities for aircraft, ships, etc.
This design has many interesting features, such as:
The small blue diamond sitting on top of the red line contains the location for π 3.14159...,
All horizontal and vertical measurements end with the repeating remainder 142857
The proportions/ratios of this design are as perfect as 22/7 (3.142857...)
The two circle diameters 64.28...% / 35.71...% = 1.8
The number seven recurs frequently, for example, the height of the 100mm propeller (or %),
divided by one-half the thickness of the central disk (14.285714...mm) is 7.
The disk diameter 53.428... / 17 = 3.142857..., and 17 is the 7th number in the list of primes.
The circle diameters decrease toward the center by 3.5 x. There is also a Sun and Planets link.
Right triangles.
The central disk correctly depicted as football shaped in these next images.
Perfect ratios and patterns are a universal phenomenon,
and the torpedo shaped Bluefin Tuna is one such example.