0
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 is a number of the form a plus bi where a is the real part and b is the imaginary part?
a complex number
It is approximately Euler's constant.
The "true" value can be obtained from the infinite sum:
e = 1 + 1/1! + 1/2! + 1/3! + 1/4! + ...
where n! denotes 1*2*3*...*n.
After what digit does googol come into play?
A googol is the large number 10100, or 1 followed by 100 zeroes.
Note: The spelling is googol, not google.
How many zeros does 1 million centimaters have?
There will be 6 zeros - whatever centimaters might be.
How do you count up to 10 in portuguese?
1 um
2 dois
3 três
4 quatro
5 cinco
6 seis
7 sete
8 oito
9 nove
10 dez
If a number is an integer then the last digit (to the right) is the units' (or ones') place. In the case of a decimal fraction is it the digit to the immediate left of the decimal point. Note that 1 = 100.
The place value of the digit to its left is the tens' place, which is also 101.
The place value of the digit to its left is the hundreds' place, which is also 102.
and so on.
The the right of the decimal, the places are:
First after the decimal point is the tenths (= 10-1).
Next is the hundredths (= 10-2)
Then the thousandths (= 10-3).
Why is the krypton atomic mass not determined?
The relative atomic mass is 83.798. So where did you get that it is not determined.
What is the atomic mass of an element and how is it determined?
The atomic mass of a radioactively stable element is defined as the mass, usually measured in grams, of Avogadro's Number of atoms of the element as obtained from natural sources on Earth. For most elements, this atomic mass will be an average, weighted by natural isotope percentages, of the individual isotopes of the atom that naturally occur, but some elements have only one naturally occurring non radioactive isotope.
The scale of atomic masses is now established by defining the mass of a carbon-12 isotope to be exactly 12. The atomic masses of other elements are defined by their mass ratios to a carbon-12 isotope.
Yes, (greek letter 'tau') is used to represent the mathmatical constant exactly equal to 2π (2pi). is also a time constant sometimes referred to as the 'RC time constant'.
How is the Loschimidt's number related to the Avogadro's number?
The Loschmidt constant, NL is related to Avogadro's number, NA by the relationship:
NL = p0*NA/(R*T0) where
p0 is the pressure
T0 is the thermodynamic temperature and
R is the gas constant.
Is boltzman constant same as gas constant?
They are not the same, but related. From Wikipedia (article "gas constant"): " [The gas constant] is equivalent to the Boltzmann constant, but expressed in units of energy (i.e. the pressure-volume product) per temperature increment per mole (rather than energy per temperature increment per particle)".
What is Graham's number minus one?
There is no sensible way to write it other than as Graham's number - 1
Does the Golden Ratio appear in music?
Clearly, the Golden Ratio is used in music. Note the following quote:
Professor Sever Tipei sent this in response to a student who asked about the Golden Ratio in music:
The golden mean ratio can be found in many compositions mainly because it is a "natural" way of dealing with divisions of time. One can find it in a lot of works by Mozart, Beethoven, Chopin, etc., etc. It is a question if it was used in a deliberate way or just intuitively (probably intuitively). On the other hand, composers like Debussy and Bartok have made a conscious attempt to use this ratio and the Fibonacci series of numbers which produces a similar effect (adjacent members of the series give ratios getting closer and closer to the golden mean ratio). Bartok intentionally writes melodies which contain only intervals whose sizes can be expressed in Fibonacci numbers of semitones. He also divides the formal sections of some of his pieces in ratios corresponding to the golden mean. Without going into much detail, Debussy also does this in some of his music and so does Xenakis (a composer who writes exclusively by using stochastic distributions, set theory, game theory, random walks, etc.) in his first major work, "Metastasis". The idea is not new, already in the Renaissance composers used it and built melodic lines around the Fibonacci sequence -just like Bartok's "Music for strings, percussion and celesta".
THE GOLDEN RATIO AND SEMITONESA semitone is the smallest change of pitch (frequency) used in conventional music and musical notation. Semitones correspond with the individual keys of a tuned piano. A semitone is defined as the "12th root of 2" (1.05946...).
The Golden Ratio (1.61803...) when cubed, almost exactly equals 25 semitones. Therefore the 25th root of a cubed golden ratio (1.05945...) equals 0.99998... semitones. This difference, when accumulated over the entire range of human hearing (about 120 semitones) is less than 3.5/100 of one semitone, and is undetectable by the human ear.
What is the formula for atomic mass of carbon?
You don't need a formula for that. It's on the periodic table.
What is the characteristics of constant of proprotionality?
It is a numerical coefficient whose does not change as the variables change.
