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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
The square root of 2 is irrational. In general, the square root of a positive integer is either an integer (if you take the square root of a perfect square), or it is irrational.
The website I linked below has pi up to a million decimal places.
Pi can usually be approximated to 3.14159265.
Nobody has solved the value of pi completely, since it is an irrational number that has an infinite number of decimal places.
What are the fourth roots of an imaginary number?
For an imaginary number R*i, where R is a real number. It helps to know about complex numbers, and how they can be rewritten using polar coordinates.
A complex number can be considered a vector in the real-imaginary plane, starting at the origin, and ending at the coordinates of the complex number.
For a complex number a + bi, the magnitude of this vector is sqrt(a2 + b2) and the angle that it makes in a counterclockwise direction from the real axis is tan-1(b/a). The number then can be written (using Euler's Identity) as Magnitude*e(i*angle), with i being the imaginary number: sqrt(-1).
So if you want to take the fourth root of a number, then this is the same as raising it to the (1/4) power, so you'd take the (1/4) power of the real magnitude, then multiply by e(i*angle/4). Note that angles are in radians in this relationship, but for simplicity, I'll use degrees.
So in this real-imaginary plane, pure imaginary numbers lie on the vertical axis (angle = 90° for positive imaginary or 270° for negative imaginary). So for 'positive' imaginaries, just divide 90° by 4 = 22.5°.
But we want 4 roots, so note that once we go 360°, then we are at the same place as 0°, so if we add or subtract 360° to an angle, we get an angle pointing in the same direction.
- 90° + 360° = 450°; 450° / 4 = 112.5°
- 450° + 360° = 810°; 810° / 4 = 202.5°
- 810° + 360° = 1170°; 1170° / 4 = 292.5°
The corresponding radians are: 22.5° = pi/8; 112.5° = 5*pi/8; 202.5° = 9*pi/8; and 292.5° = 13*pi/8.
If you want the complex number root back in the format a + b*i, a = magnitude* cos(angle), and b = magnitude* sin(angle)
You can find all of the roots for any order root (square, cube, etc) by using this same method. It works for real numbers, too. Just take angle = 0°, 360°, etc. for positive numbers, and angle = 180°, 540°, etc. for negative numbers. Example square root of 1: 0° / 2 = 0° (positive 1), 360° / 2 = 180° (negative 1)
See the PDF in the related links: Using the Shannon Sampling Theorem to Design Compact Discs - page 2 for a brief explanation on Euler's Identity and how it was derived. There are many other references available.
Do isotopes have the same atomic mass?
Nope, their chemical make up changes, changing the total atomic mass.
How does the average speed of light glass compare with its speed in a vacuum?
About 2/3 its speed in a vacuum.
What is the ratio of the mass proton to the mass of an ELECTRON?
Dunno, but the ratio of the mass of a proton to the mass of what prople think of as being an electron is approx 1980. I'd check that if I were you though. Probably OK to +- 5%.
What is the ratio of speed of light in a vacuum to the speed of sound in air?
In a rough, round figure? 930,000 to 1.
Sound travels roughly 1/5 of a mile per second in air.
Light travels 186,000 miles per second in a vacuum.
In five seconds sound travels one mile.
In five seconds, light travels 930,000 miles in a vacuum.
What is the first 1000000 numbers of pi?
You can also use formulas to calculate pi. they are best used when plugged into a program, but they are still very slow. James Gregory's formula is:
pi = 4*(1-1/3+1/5-1/7...)
A simple program to calculate pi using his formula is this (python programming language):
def pi(accuracy):
<tab>pi = 0.0
<tab>minus = 1.0
<tab>for i in xrange(1,accuracy):
<tab><tab>minus = -minus
<tab><tab>pi += minus/(i*2-1)
<tab>return pi*4
replace the <tab> with an actual tab (the editor doesn't support tabs)
Run it, than type in pi(accuracy) in the console, but replace accuracy with how accurate you want it to be.
But unfortunately it doesn't get very far, and it's not built to be quick or get vary far, it's just an example. if you want to, you can multithread it and make it capable of using larger number, like writing to a file as it calculates.
the actual digits of pi are these:
3.141592653589792324683846443746375843658475673548356786758346584564856643756655685764747473832883744765657473828911010102029939393838484848474774755656567488382991910101020202939393384848477575666757575848484939393929928293828337u8473565867467575647563853364973947248923343710308321038130183487329743758436573486543785635873538629423984328742748297289332932193182321301823217493887840328480284023843270705720520084703324623598746873467835834563856985634785358346537856829348329481037u120308702137103713139019309`0237121023130813943827647834584358538482382348678236284673284564757736478367284637468366565647347382828374765
The atomic mass refers to the number of what?
The atomic mass is approximately the sum of the number of protons and neutrons.
How do you differentiate between reaction rate and specific rate constant?
The reaction rate is the rate at which the moles of substance change that varies with both temperature and concentration of the reactants. The specific rate constant is a proportionality constant that will vary only with temperature.
How can you remember all the numbers in pi?
This might help...
My classmate remembered pi(3.14) by sitting in different positions
Ex. Remember 10 of the numbers sitting up, 10 more sitting down, 10 more with one eye closed, 10 more with hands on her head.
How many digits does Google have?
A googol [the number] is equal to 10 raised to the 100 power, which is 1 followed by 100 zeros. So it has 101 digits. Note the spelling of googol [the number] which is different from Google [the website search engine company].
What is a googol times a googol written as a power?
As a power: 10200
Googolplexian:10,000,000,000,000,000,000,000,000,000,000,000,000,000,
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000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
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000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
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000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
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000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
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000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
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000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,etc
So as to work out mathematical problems in the correct order of operations
Does the weight of the body remains constant everywhere in the universe?
no it does not remain contant.
What is the number of the most Pi didgits recited?
The record for memorizing digits of pi, certified by Guinness World Records, is 67,890 digits, recited in China by Lu Chao in 24 hours and 4 minutes on 20 November 2005.
pi is a letter of the Greek alphabet and predates its use in mathematics.
pi is a letter of the Greek alphabet and predates its use in mathematics.
pi is a letter of the Greek alphabet and predates its use in mathematics.
pi is a letter of the Greek alphabet and predates its use in mathematics.
What is the average atomic mass of tungsten?
If you look on a periodic table under the element tungsten which is represented as W, you will find the atomic mass on the top right side.
It's average weight is 183.84 and the atomic number of 74
