Where did the imaginary number symbol i come from?
"i" stands for imaginary. It represents the square root of -1.
phi, the Golden ratio is [1 + sqrt(5)]/2 = approx 1.6180...
The Fibonacci sequence is defined as follows:
U1 = 1, U2 = 1 and Un =Un-1 + Un-2 for n = 3, 4, 5, ...
that is, the first two terms are 1 and after that, each term is the sum of the previous two terms.
Now consider the sequence Un+1/Un for n = 1, 2, 3, ... that is, the sequence of each Fibonacci number divided by the one before it. This goes
U2/U1 = 1/1 = 1
U3/U2 = 2/1 = 2
and so on.
Then
U7/U6 = 13/8 = 1.6250 which is less than 1% away from phi.
U9/U8 = 34/21 = 1.6190 which is less than 0.1% away.
U16/U15 = 987/610 = 1.6180 which is less than 1 in a million away.
Thus, after the first few, terms of the Fibonacci sequence increase in approximately the Golden ratio.
Does 1.0 mole of carbon contain Avogadro's number of particles?
Yes. 1 mole of all elements (including carbon) or compounds contain Avogadro number of particles (6.023 x 1023 particles)
What is the derivation of Coulomb's constant?
Coulomb's constant 'k' in the equation F=kQQ/r2 is derived from Gauss's law. Gauss's law stated that the charge enclosed by a theoretical surface is equal to the permittivity constant, represented by the Greek letter epsilon (because I can't use an epsilon, I will use an X) times the electric flux through the surface. Flux is equal to the closed integral of electric field vector dot the vector dA (infinitesimal change in surface area) of the surface. Becasue the surface surrounding one point charge is a perfect sphere, the dot product can be ignored (The surface is uniform and every change in area is normal to the electric field), and the Electric field is constant so it can be brought out of the integral leaving integral dA. When the integral is solved, the resulting equation is XEA=Q. A equals the surface area of the sphere so XE(4*pi*r2)=Q and E=Q/(4*pi*X*r2) and because F=EQ, F=QQ/(4*pi*X*r2). This is probably looking pretty familiar. All we have to do is make k=1/(4*pi*X) to make this equation equal to good old Coulomb's law. X, the permittivity constant equals 8.854*10-12 Farads per meter, or coulombs squared seconds squared per kilograms meters cubed. If you substitute this constant into the equation k=1/(4*pi*X), you obtain Coulmb's constant.
How do you show a number divided by zero is undefined?
Programming language?
For example:
For A ÷ B
If B = 0
Then
Answer = "Undefined"
Else
Answer = A ÷ B
End If
By the way, in Calculus, you often find out that 'passing the limit' you will get a rational value when dividing by zero. It depends on the equation.
Yes, the smallest value bank note in the Lebanon is for 1000 pounds.
How do you keep contra virus from constant pestering you?
Contra Virus is the latest rogue (fake) antivirus (antispyware) software.
Run the anti spyware removal programs spybot and Superantispyware
How do you change the gravitational constant of the universe?
The universe has a detachable plastic cover at the back. Remove this cover using a Philips screwdriver. You will see small thumb wheels labeled, Gravitational Constant, Plank's Constant, Boltzman's Constant, Speed of Light, mass of electron, etc. These can be changed by turning the thumb wheel either towards the "+" or "-" signs.
Caution! Unless you know exactly what you're up to, don't play around with these dials. If you change these constants even ever so slightly, the results can be quite dramatic and you may not be able to turn them back. For example, if your new settings don't allow the existance of calcium, carbon or iron, then you're goosed!
What is the ratio of the speed of light in a vacuum to the speed of light in a different medium?
This is called the index of refraction. When light crosses the boundary between mediums (media) with different indices, it is bent (refracted).
It's usually defined the other way around ... the ratio of the speed of light in vacuum to its speed in the medium. Since the speed of light is greater in vacuum than in any medium, the number is always greater than 1. It's referred to as the "refractive index" of the medium.
How do you determine avogadro's number?
The easiest way is to look it up in a book! But if you mean how can you measure it directly, it really depends what you tools and information you give yourself to start with. How hard to you want to make it for yourself? Since it is a known number that is easily determined from other known quantities, it is a kind of artificial problem... which means that how you find it depends on what information you have. As I said, you can just look it up... in a book or on this site!
How many zeros in a Google com?
None. Google com is an internet search engine and other facilities. It is not a number and so has no zeros.
Will constant light kill microoganisms?
The best chance would be with ultraviolet (UV) light. One of the best ways to keep something like bed lines clean is to put them out in the sunlight to kill off all the 'bed bugs.'
UV light is especially harmful to DNA, it's wavelength range hits right on the distance between adjacent nucleotides in DNA, creating whats known as a thymine-dimer. It disrupts the bacterias ability to code for proteins, and if a necessary protein is halted, the bacterium dies. UV light can also disrupt proteins, leading to the demise of the bacteria. Simple exposure to visible, or white light, will not generally harm microorganisms.
You might tell your parents, though they may not believe you, that it is actually better not to make your bed, because doing that traps the microorganisms in a dark and moist environment that they love. So undo your bed and let fresh air, and maybe some sunlight 'clean' it for you. Please don't complain to me if you get grounded for following my suggestion. Just let your parents read this posting.
There are two main areas where the ratio is used and they are for different reasons.
One reason is that the human mind finds the Golden ratio aesthetically pleasing. It is, therefore, used in art and architecture.
The second reason is directly related to its mathematical properties (the ratio of the whole to the larger part is the same as the ratio of the larger to the smaller parts). This is used in designing paper sizes like the A and B series. Divide an A3 sheet in half and you will get two A4 sheets which have the same aspect ratio as the A3. Repeat and you get two A5s with the same property and so on.
What is reciprocal of zero divided by one?
Swap the numerator and the denominator to obtain 1/0. Anything divided by zero is undefined.
How does the speed of light in glass compare to the speed of light in a vacuum?
It will depend on the type of glass, and something called its refractive index. All materials have a refractive index which will effect the speed of the light through it. The speed of light through a vacuum is 3.0x10^8 m/s, and a material such as glass will be lower than this.
Why does the electron cloud have a very small mass?
The electron cloud has such a small mass because that's where all the electrons are! Electrons are fundamental particles having a mass of only 9.109 X 10-31 kg. To put that into perspective, a proton has a mass of over 1,800 times that of the electron.