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Mathematical Constants
Intriguing, ubiquitous, and at times mysterious, numerical constants set the allowable limits for all universal phenomena. Whether your questions involves π, Avogadro's number, Planck's constant, the atomic mass unit, or any of the other multitudes of immutable numbers used in science, this is the category where they should be asked.
2,332 Questions
What are the cube roots of an imaginary number in trigonometric form?
z = y i where y is a real number
1: z^(1/3) = y^(1/3) (cos(30 deg) + i sin(30 deg))
2: z^(1/3) = y^(1/3) (-sin(60 deg) + i cos(60 deg))
3: z^(1/3) = y^(1/3) (- i)
What is the twenty seventh power of an imaginary number?
See the Wikipedia article on Imaginary Numbers. i^n = i^(n mod 4). With n = 27, 27 mod 4 = 3, and i^3 = -i. This is easier to visualize when you consider the graphical representation of complex numbers, and use polar coordinates. Writing i as exp(i*pi/2), (from Euler's formula), then i^27 = {using exp() to mean the natural base e, raised to a power} exp(i*pi/2)^27 = exp(27*i*pi/2) = exp(13.5*i*pi) = exp((12 + 1.5)*(i*pi)) = exp(12*i*pi)*exp(3*i*pi/2).
Since the coefficient of i in the exponent is an angle (in radians), then even multiples of pi are the same angle as 0 {exp(0) = 1} so we are back to the same as exp(3*i*pi/2), which is pointing straight down [-i]. Note that 3*pi/2 radians is the same as 270°.
Since the question asked about 27th power of an imaginary number, that could mean a multiple of i, such as bi, where b is any real number. In this case, you would have (bi)^27 = (b^27)(i^27) = (b^27)(-i). So if b = 1.5 for example, then you would have (-i)(1.5^27) ≅ -56815i.
Is graham number beyond all finite transfinite and transinfinite numbers?
Graham's number is a large but finite number. Therefore it is less than every transfinite cardinal number. "Transinfinite" doesn't make sense.
What numbers are in pi and how many are there?
Pi is the ratio of the circumference of a circle to its diameter. Pi is 3.1415926535897932384626433832795 but some just use 3.14
The canonical example is the square root of -1.
Mathematicians use the symbol i to represent it, electrical engineers use j because i is already busy.
Can Planck's constant is zero?
No. It is a very small number (approximately 6.626 × 10-34 joule-second) but that is NOT zero
Who is responsible for finding out that the numbers in Pi were trascedental?
Ferdinand von Lindemann proved, in 1882, that pi was transcendental.
Why you call zero by the name zero?
The derivation is from the early 17th cent.: from French zéro or Italian zero, via Old Spanish from Arabic ṣifr 'cipher.'
What is the solution to 30X to 29Y?
"30X to 29Y" is not an equation nor an inequality. There is, therefore, not a mathematical solution to the question.
Do ANY number series in pi repeat themselves?
There are short strings of digits which will repeat, but there is no sequence which will repeat forever.
The Boltzman's constant is the physical constant relating to temperature to energy.
How many decillions are in 1 googol?
In researching the answer, we found the following definitions on the www :
1 decillion = 1033
1 googol = 10100
So the number of decillion in 1 googol is
10100 / 1033 = 10(100-33) = 1067
We couldn't find a name for 1067. Apparently it doesn't come up very often.
They may be. But as far as pi has been carried out until now ... 2.5 trillion decimal places
claimed in 2009 by a team in Japan ... no repeating digits have been found yet.
