Rey.BEng 18th September 2026
Which pi to choose, and how many significant figures?
- Position
E = m c^2 is not conversion. It is conservation of the stroke in one rotation.
Write it:
E = c^2 m
Tick before the square. The 2 is a count of the firing stroke, not a length-power. Nothing leaves the Real object in one rotation.
Name the leftover:
sigma_R = 2- = 1.999…
Infinity is a count, not a destination. Filament occupies piN. Write (f) if the hold of the angle must be visible. Otherwise f = practice.
Stroke map:
1^ –f–> ^2 4 : 2 : 1(-1)
- The three pis at 19 significant figures
Exact definitions
piN = 4 / sqrt(phi)
phi = (1 + sqrt(5)) / 2
piR = 22/7 piE = ordinary circle-ratio pi (Chudnovsky limit)
19 sig-fig print, for the eye only
piN = 3.144605511029693144
piR = 3.142857142857142857
piE = 3.141592653589793238
- What the eye is meant to see
piN 19-figure line, two 3144 posts, 11-figure span
3.144 60551102969 3144
Left post: 3144
Solid middle: 60551102969 (11 figures, the straight line)
Right post: 3144
Whole print: 19 significant figures 3.144 to 3144 is the same block twice.
piR 19-figure line, closed rational repeat
3.142857 142857 142857
Block: 142857 Period: 6
The pattern does not wander. It is a locked gear. 22/7 is exact. The 19 figures are only a print of that lock.
piE 19-figure line, no repeating block
3.141592653589793238
No 3144 posts. No 142857 gear. No 11-figure straight span. That is the trend: digits continue without a visual seal. Use this only when the question is the infinite census of the equatorial working circle.
Gaps at a glance (already split by the 3rd decimal)
piN – piR ~ 0.001748368 piR – piE ~ 0.001264489 piN – piE ~ 0.003012857
19 figures are a visual aid. They are far more than needed to tell the three apart.
- Recommended number by discipline
Particle physics
Choose an irrational. Preferred Ace lock: piN = 4 / sqrt(phi) Print: 3.144605511029693144 Or keep the exact form 4 / sqrt(phi) and do not expand. Alternative only if the question is the open equatorial census: piE to 19 figures, 3.141592653589793238
Do not use 22/7 as a particle constant.
Engineers
Always use rational piR = 22/7 Print if needed: 3.142857142857142857 Keep the fraction 22/7 in the calculation.
This is hoop, slab, tank, ring-tension, Rest Mass Physics, shell stroke.
Name leftover sigma_R = 2- = 1.999… Do not convert mass into energy.
Rest Mass Physics
Same as engineers. Always 22/7. Mass is polar height from stored twist. The working closure is rational. Print 19 figures only for the page. Compute with 22/7.
Mathematics
Standard mathematics chooses piE, the unique transcendental circle-ratio. Print for this page: 3.141592653589793238 Keep the series open if the question is proof or census.
Ace Mathsets may still choose by arena:
- M1 filament / hold of angle: piN exact, print 19 figures
- M2 stroke / shell: 22/7 exact
- M3 triad comparison: all three at 19 figures
- M4 digit hunt: piE only, any length Maths is allowed to keep piE infinite. That is a legitimate choice. It is not the only Ace choice.
Chemistry / Observational continuous second
Stay in the arena. Use piE to 3 or 4 decimals, or omit pi. Do not rewrite spacetime to close a dimer well.
- Mathset cut table
M0 Observational piE to 3 or 4 decimals, or none.
M1 Filament / Mef (f) piN = 4 / sqrt(phi) Print 3.144605511029693144 No Chudnovsky on piN.
M2 Shell / Meg stroke / engineering / Rest Mass piR = 22/7 Print 3.142857142857142857 Leftover sigma_R = 1.999…
M3 ERN comparison Show all three at 19 figures. Chudnovsky N = 0 separates them. N = 1 is the safety term, infinity-minus-one.
M4 Census of piE only Then extend the series. Extra piE digits do not cross piR or piN.
- Chudnovsky B, only for M3 / M4
piE(N) = 426880 * sqrt(10005) / Sum
Sum runs k = 0 to N Term = (6k)! * (13591409 + 545140134 k) / [ (3k)! * (k!)^3 * (-640320)^(3k) ]
N = 0 triad already split N = 1 engineering overkill N > 1 census only
- Copy block for WordPress
E = c^2 m tick before the square sigma_R = 2- = 1.999… filament occupies piN
phi = (1 + sqrt(5)) / 2
piN = 4 / sqrt(phi) = 3.144605511029693144
piR = 22/7 = 3.142857,142857,142857
piE = 3.141592653589793238 no repeating block
Particle physics : piN = 4 / sqrt(phi) or piE if census
Engineers : 22/7 Rest Mass : 22/7 Maths : piE by default; Ace Mathset may pick piN or 22/7
Observational : 3 or 4 decimals of piE, or omit
4 : 2 : 1(-1) One rotation. Nothing leaves. Do not convert. Conserve.
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