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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
Prove thatsquare root of 2 is irrational?
You can find several such proofs in the Wikipedia article "Square root of 2". Many of these proofs (or perhaps all, but I didn't check carefully) apply to the square root of ANY positive integer, assuming the integer is not a perfect square.
What are the first 23 digits of pi?
Not including the initial digit, the first 23 decimal digits of pi are 3.14159265358979323846264.
How do you enter an imaginary number in a scientific calculator?
Some scientific calculators can't handle complex or imaginary numbers. If you happen to have a special calculator that does, probably the manual will tell you how to enter them.
The HP 48 and up series does. It depends on if your calculator is in Polar Coordinate mode or X-Y coordinate mode, but a quick way to get the imaginary number i (regardless of which mode the calculator is currently in), is to press -1, then 'square root' button.
What is avogadro number equal to?
6.0221367 × 1023
Or (less sensibly) 602 213 670 000 000 000 000 000
Why is anything divided by zero equal to infinity?
Division by zero is undefined. Even dividing zero by zero is undefined. That's because there are no unique results. This derives from the identity function of zero, such that any value multiplied by zero is zero.
While the division of any number by a diminishing fraction has a limit of infinity, there is no reverse operation possible. I.e. for any nonzero number n:
If n/0 = ∞ it implies ∞ x 0 = n but any number times 0 = 0
and
If 0/0 = n then n could be any real number, not just 1, because n x 0 = 0
Place value.
100 000 000 000 000
Trillions|billions|millions|thousands|units
1,000,000,000,000
12 zeroes, and a one.
Why represented the integers by the symbol Z?
It's short for Zahlen, which is German for "numbers". Why German? Why not?
Are imaginary numbers real numbers?
When people started classifying numbers in different ways Some numbers were grouped together and called Real numbers. Solutions that would create Imaginary numbers were simply explained away as impossible, later the rules for working with these numbers, but, even though they are not considered Real numbers some math operations will create Real number answers.
Mod is essentially the remainder when a given number is divided by the base (of the modulus).
So
10/3 has a remainder of 1 and so 10(mod 3) = 1
11/3 has a remainder of 2 and so 11(mod 3) = 2
Why do you say that pi is an imaginary number?
If I ask Answers™ "what is pi squared?" I find "It is approximately equal to 3.14 but in reality pi is an imaginary number that has no end." The answer also goes on to tell me that imaginary numbers cannot be multiplied by themselves. Now i must see what y'all have to say about imaginary numbers...
What is the speed of light through the liquid whose refractive index you have determined?
If the refractive index is k then the speed of light is c/k metres per second where c is the speed of light in vacuum (approx 299,792,458 m/s).
What is the equilibrium constant for the reaction h2g plus co2g h2og plus cog?
Keq = [H2O][CO]
[H2][CO2]
How do you find constant of proportionality?
You need to know the basic relationship between the variables: whether they are directly of inversely proportional to each other - or to a power of the other. Also, you need one scenario for which you know the values of both variables.
So suppose you have 2 variables A and B and that A is directly proportional to the xth power of B where x is a known non-zero number. [If the relationship is inverse, then x will be negative.]
Then A varies as B^x or A = k*B^x
The nature of the relationship gives you the value of x, and the given scenario gives you A and B. Therefore, in the equation A = k*B^x, the only unknown is k and so you can determine its value.
Why you use k as constant in proportional values?
Any letter of the alphabet - or indeed other alphabets - can be used. The letters c and k are the more common symbols because they represent the phonetic start of "constant".
Variables are often represented by the initial letter of the variable: v for velocity, t for time, m for mass and so on, or by letters at either end of the alphabet: a, b, c or x, y, z. Clearly, it can be confusing to use any of these as the constant of proportionality. So, through convention, k was selected as the default symbol.
Why universal force is called universal?
Because according to our current understanding of the universe, the force is believed to behave the same everywhere in the universe.
It means that the force of electrical attraction (or repulsion) between two particles with units charges will be greater than the gravitational attraction between two particles with unit mass which are the same distance apart.
What are pure imaginary numbers?
complex numbers with no real part
if any complex number z can be written a + i b
then pure imaginary numbers have a=0 and b not equal to 0
What is the meaning of equivalent fraction?
Equivalent fractio
n mea
ns that the fractio
ns have the same value.
Example: 1/2 is equivalent to 2/4
