Food and everyday life
Pizza, 30 cm diameter
Practically irrelevant.
Follow-up · the π laboratory
22/7 in practice – what happens when we calculate with 22/7 instead of π?
From pizza to the universe: eight experiments showing what 22/7 means in practice. Change size, time and curvature – and let the results decide when a small numerical difference matters.
When does a small numerical difference matter – and how do we test which calculation is right?
π
22/7
Relative difference – always the same+0,04025 %
The starting point: 22/7 = 3.142857142857… and π = 3.141592653589… So 22/7 is about 0.04025 % larger than π. We swap only the constant and keep everything else the same.
Calculated
01 · From the kitchen to the universe
The same percentage. Completely different consequences.
The deviation is always 0.04025 %. But 0.04 % of a pizza is something entirely different from 0.04 % of a solar system. Scroll outward in scale.
Car and bicycle
Distance from wheel turns
Less than ordinary tyre wear and pressure.
Water and industry
Cylinder tank, r = 1 m, h = 1 m
The physical tank is just as large – only the arithmetic changes.
Music and signals
The tone 440 Hz
Small phase errors add up quickly.
Time and clocks
A model with 1 oscillation per second
Timing errors keep growing – which is why clocks never use approximations.
The Earth
Equator, diameter 12,742 km
More than the width of a large city.
Spaceflight
Circle with a radius of 32 billion km
Here precision decides whether the probe arrives.
0,04025 % · 10⁻¹ m → 10¹³ m
Calculated
02 · The rolling wheel
Two wheels, the same number of turns.
Both wheels have the same diameter and roll the same number of times. One calculates distance with π, the other with 22/7. Watch the odometers part ways.
With π
With 22/7
Difference
Calculated
03 · The filling tank
The same tank – two different numbers.
The volume of a cylinder is π·r²·h. Swap π for 22/7 and the calculated volume grows, yet the tank holds exactly as much water as before.
With π
With 22/7
Difference
The tank keeps the same physical capacity; only the calculation changes. The golden strip at the top shows the “water” that exists only on paper.
Calculated
04 · Waves and sound
A small difference you can hear.
A tone is described by sin(2π·f·t). Swap π for 22/7 in the model and the wave oscillates slightly faster. At first they overlap – then they drift apart.
sin(2π·f·t)sin(2·(22/7)·f·t)
Phase difference
Fully out of step after
We change the frequency in the model when we swap the constant. A new wave pattern alone therefore does not show that we have found a more correct constant of nature.
Calculated
05 · Time and clocks
Errors that never stop growing.
Let a simulated clock count waves at a nominal one oscillation per second. With 22/7 in the model it runs slightly fast.
extra oscillations
The clock runs ahead by
The clock experiment changes the model's oscillation rate; it does not show that time itself runs differently.
Measured
06 · The circle under the magnifier
Geometry without a ready-made π.
Archimedes' method needs no value of π: start with hexagons inside and outside the circle and double the sides using simple means. The bounds close in – and reveal which value fits.
Lower bound
22/73.142857142857
Upper bound
Outer perimeter: a′ = 2ab/(a+b), inner: b′ = √(a′·b), starting from a = 2√3, b = 3. No π is entered in advance.
Calculated
07 · Earth and spaceflight
Drag the circle out into space.
Choose a diameter from a coin to the observable universe. The difference between π and 22/7 grows with size.
Difference in circumference
NASA/JPL uses π with 15 decimals in its most precise navigation calculations. For a circle with a radius of 32 billion km, that gives an error of about 1.5 cm.
Measured
08 · Could this explain the expansion of the universe?
The Hubble tension is 200 times larger.
Different methods give different values for the expansion rate of the universe: about 67.4 km/s/Mpc from the cosmic microwave background and about 73 km/s/Mpc from stars and supernovae. That is a difference of roughly 8 %.
In a formula whose result is directly proportional to π, the change is far smaller than the cosmological discrepancy. 22/7 therefore does not solve the problem. A full assessment would require examining all relevant equations and observations together.
Measured
09 · Curved space
Where the circumference really departs from 2πr.
On a curved surface, measured along the surface, the circumference of a circle is no longer 2πr. This is an established property of geometry and links directly to relativity. The constant π keeps its value – it is space that has a shape.
Circumference ÷ diameter
π3.141592653590
22/73.142857142857
10 · The answer
When does a small numerical difference matter?
When precision must be high
In spaceflight, surveying and manufacturing, 0.04 % becomes metres, kilometres and millions of kilometres.
When the error has time to grow
Phase, rhythm and time add up small deviations. A tone drifts out of step within seconds; a clock drifts every day.
When we test against independent measurements
Archimedes' polygons exclude 22/7 at 96 sides – without any value of π entered beforehand.
When geometry itself changes
In curved space the circumference departs from 2πr for entirely different reasons than a numerical approximation.
Interpretation
Åse's 22/7 – the key and the tool
In Åse's numerological reading, 22/7 is a symbolic key: master number 22 meets the searching 7. That meaning stands on its own. The laboratory shows something different and just as interesting: in everyday life 22/7 is an almost perfect tool, but as precision, time and distance grow, measurements require π. Both layers can be true – as long as we do not mix them.