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π
Mathematical Facts
The wonder of this infinite number
📚 Facts About π
π is transcendental - it cannot be the root of any polynomial with rational coefficients
The decimal expansion of π never repeats and never terminates
Archimedes approximated π using 96-sided polygons around 250 BCE
In 2024, π was computed to over 100 trillion digits
The symbol π was first used by William Jones in 1706
March 14 is Pi Day because 3/14 looks like 3.14
Einstein was born on Pi Day (March 14, 1879)
π appears in Euler's identity: e^(iπ) + 1 = 0
The probability that two random integers are coprime is 6/π²
π appears in the normal distribution: the bell curve
Buffon's needle experiment can calculate π with probability
The circumference of a circle with diameter 1 is exactly π
You can memorize π to thousands of digits using memory palaces
In the Star Trek episode 'Wolf in the Fold', Spock defeats an evil entity by forcing it to compute π to the last digit
π is approximately equal to 355/113 (accurate to 6 decimal places)
The 'feynman point' at position 762 is six consecutive 9s
22/7 is 'Pi Approximation Day' (July 22)
No pattern has ever been found in the digits of π
In the TV show 'Person of Interest', the machine's admin password is √π
The digits of π have been searched for in other numbers; √2 contains a million-digit run
🧮 Famous Formulas Containing π
Circle circumference:
C = 2πr
Circle area:
A = πr²
Sphere volume:
V = (4/3)πr³
Euler's identity:
e
iπ
+ 1 = 0
Gaussian integral:
∫e
-x²
dx = √π
Leibniz formula:
π/4 = 1 - 1/3 + 1/5 - 1/7 + ...
Basel problem:
π²/6 = 1 + 1/4 + 1/9 + 1/16 + ...
📅 History of Pi Calculation
~1900 BCE:
Babylonians used 25/8 ≈ 3.125
~1650 BCE:
Egyptians used (16/9)² ≈ 3.16
~250 BCE:
Archimedes: 3.1408 < π < 3.1429
~150 CE:
Ptolemy: 377/120 ≈ 3.1416
~500 CE:
Zu Chongzhi: 355/113 (accurate to 6 places)
1706:
John Machin: 100 digits
1949:
ENIAC: 2,037 digits (70 hours)
1973:
CDC 7600: 1 million digits
2024:
100+ trillion digits calculated
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