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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
Where did the word googol come from?
One time a man showed his son the huge number and the boy was so surprised that he said "googol!".
The boy was Milton Sirotta, aged 9, in 1938. It was popularized by Edward Kasner. See the related links for more information.
Do not confuse this with google, which is a web site and search engine.
I will explain a method of constructing an illustration:
- Construct a square with the length of a side = 1 (one unit).
- Add another square of the same size to the first so they have one common edge (1 * 2).
- Add a square to the long edge of the exisiting squares (2 * 2 units).
- Add another square to the long edge ( that square should be 3 * 3)
- Contionue adding squres to the ling edge of the construction.
This is considered a plesing shape by many and many artists and architects use these proportions in their compositions.
Does the square 'root of 2 repeat?
No. It is an irrational number and so cannot have a repeating decimal representation (or in any other rational base).
What is the Difference between gravitational constant and acceleration due to gravity?
The acceleration due to gravity in the neighborhood of some mass is:
A = G m/R2
A = the acceleration of gravity
m = the mass of the mass
R = your distance from its center
==> G is the "gravitational constant".
Without it, you would know that the acceleration is 'proportional' to the mass of the mass, and 'inversely proportional' to the square of your distance from it. But you couldn't calculate an actual number without a 'proportionality constant'. That's what 'G' is.
The gravitational constant is a universal number that applies equally in all places, at all times, and upon all objects. It is expressed as:
6.67300 × 10-11 m3 kg-1 s-2
Acceleration due to gravity is the phenomenom in which all masses are attracted to all other masses. The force due to gravity is expressed as:
- Fg = Gm1m2/R2
where:
- Fg is the force due to gravity;
- G is the universal gravitational constant, above;
- m1 is the mass of the first object;
- m2 is the mass of the second object; and
- R is the distance from the centers of the two objects.
Acceleration is expressed as
- Ag = Fg/m1
where:
- Ag is the acceleration due to gravity;
- Fg is the Force due to gravity, from the equation above; and
- m1 is the mass of the object being accelerated.
Subsituting the equation for the force due to gravity (Fg) in the above equation for acceleration due to gravity (Ag), we get:
- Ag = Gm2/R2
Remember that m2 is the mass of the other object (say, planet Earth). Notice, too, that m1 (your mass) cancels out completely. So the acceleration of your body due to gravity depends on the mass of planet Earth, but does not at all depend upon you own mass, or weight. That means that all things, regardless of how heavy or light, experience the same acceleration due to gravity at sea level on planet Earth.
What is the mass of a .5 in diameter glass marble?
I don't believe there is a way to find the mass of an object knowing only the diameter of the object. If you had the volume, or some other measurements sure. the best bet would be just to weigh it, or find the volume using the principles of displacement.
How does the magnetic field of the moon and Jupiter compare to Earth's?
The Moon doesn't have one. At least if it does have one, then it's very faint. Jupiter's magnetic field works the same as Earth's. It has a molten metallic hydrogen core that flows and creates the the dynamo effect. Earth has an outer core that is liquid iron that rotates and generated this field. Jupiter's magnetic field is 14 times stronger than Earth's. In fact, it's so strong that if, you tune your car radio to dead radio station with static during(it was either) a certain part of the year or part of the night when driving on a deserted & or quiet country road, that you can sometimes hear a beeping/chirping/etc sound. It's the sound of Jupiter's magnetic field.
The speed of light and the speed of sound?
The speed of air at 20 degrees Celsius is 343 meters per second. The speed of light is 299 792 458 meters per second.
What is the function if the first derivative of a function is a constant?
A linear function, for example y(x) = ax + b has the first derivative a.
What is the most viewed video on YouTube Gangnam style PSY With nearly 2 000 000 000 views?
Yes, Gangnam Style by PSY is currently the most viewed video on YouTube.
Make a sentence with constant?
The constant pounding of the rain against the window kept everyone awake that night.
A googol is 10 to the hundred power, which is 1 followed by 100 zeros.
The square root of googol is 10 to the 50 power, or 1 followed by 50 zeros
Your engine is not running or your "RPM gauge" is broken.
Boyles Law problem and answer?
The Boyle (or Boyle-Mariotte) law is: the pressure and the volume in a closed system, at a constant temperature, is a constant. They are so inversely proportional.
How do you find out coupling constant?
Here is how you calculate a coupling constant J: For the simple case of a doublet, the coupling constant is the difference between two peaks. The trick is that J is measured in Hz, not ppm.
The first thing to do is convert the peaks from ppm into Hz. Suppose we have one peak at 4.260 ppm and another at 4.247 ppm. To get Hz, just multiply these values by the field strength in mHz. If we used a 500 mHz NMR machine, our peaks are at 2130 Hz and 2123.5 respectively. The J value is just the difference. In this case it is 2130 - 2123.5 = 6.5 Hz This can get more difficult if a proton is split by more than one other proton, especially if the protons are not identical.
What has the golden ratio in it?
A great many things have the golden ratio in them varying from things fabricated by humans such as architecture, the proportions of the sides of a book also fall into the golden ratio. The golden ratio also occurs naturally for example the spiral in the snail's shell falls into the golden ratio. Generally most man made things have the golden ratio in them as it has been found quite simply, to look good.
I presume mean the "fine structure constant," which is abbreviated as alpha.
It is the ratio of the square of the electric charge, divided by Planck's Constant and the speed of light. It has no units, and thus does not depend on which system of units you are using. More importantly, it involves all three of the most fundamental numbers of our Universe.
Whether this number has any special meaning in our Universe is still a matter of discussion. It may be nothing more than a unit-less ratio of three fundamental numbers, with no meaning beyond that fact.
How were imaginary numbers discovered?
Imaginary numbers were discovered when mathematicians tried to solve equations of the form x^2 + 2 = 0
How does the golden ratio relate to platonic solids?
The golden ratio, phi occurs many places in the platonic solids. The dihedral angle on the dodecahedron is 2*atan(phi), and the dihedral angle on the icosahedron is 2*atan(phi2) or 2*atan(phi + 1). The mid radius of the dodecahedron is similarly phi2/2 or (phi + 1)/2, and the mid radius on the icosahedron is phi/2. There are several other measures within Platonic solids which involve phi.
