With the BBP formular, we can find the 10th billion digit of Pi without calculting all the digits before it.
The French Mathematician and Physicist Joseph Fourier proved
e is irrational,
Another French mathematician Charles Hermite went further: e belongs to another mathematical world:
e is transcendental.
Hermite’s German student Lindermann followed the same method, proved:
pi is also transcendental.
1706 John Machin developed a formula for calculating Pi to an arbitrary number of decimal places:
Transcendental numbers: e, Π, L…
What about ?
Aleksander (Alexis) Osipovich Gelfond (1906-68):
a is algebraic, not 0 or 1
b irrational algebraic number
Hilbert Number: (Hilbert Problem proven by Gelfond}
Is log 2 transcendental ?
[log = logarithm Base 10]
1) Sufficient to prove log 2 irrational
Assume log 2 rational
log 2= p/q, p and q integers
raise power q
Case 1: p>q
Case 2: q>p
Left is even :
Right is odd:
Therefore p,q do not exist,
=> log 2 irrational
Reference: Top 15 Transcendental Numbers: http://sprott.physics.wisc.edu/pickover/trans.html
King Solomon – The Temple’s Furnishing:
“He made the Sea of cast metal, circular in shape,
measuring 10 cubits from rim to rim and 5 cubits
high. It took a line of 30 cubits to measure around
it.” – 1King 7: 23
[10 cubits = 15 feet, 30 cubits = 45 feet]
So mathematically by today’s primary school geometry:
Circumference = 30 = 2 *π *r
Diameter = 10 = 2 * r
π = 30/10 = 3
Note: Solomon’s period is equivalent to China’s Zhou 周 dynasty of the famous Prince “Zhou Gong” 周公
Google = Googol means ‘1 followed by 100 zeroes‘
Google raised Capital at IPO = $2.718281828 Billion = e Billion
Google’s 3 building names: e, pi, ø (Golden ratio)