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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
What is special about the number pi?
It's the ratio between the circumference of any circle to its diameter.
How can you use the pythagorean theorem to find out if a triangle is a right triangle?
The pythagorean theorem states that a2 + b2 = c2.
This means that in a right triangle, both legs squared will add up to the hypotenuse squared.
To see if a triangle is a right side, add up the two legs squared and see if it equals the hypotenuse.
What is the average constant speed of light in vacuum?
The speed of light in vacuum is 299,792,458 meters per second,
and that's not an average. That's what it always is.
Is speed of light all different speeds?
As long as it stays in one medium (substance), the speed of all wavelengths of
visible light is very close to the same number. It only changes when the light
crosses into a different substance, like going from air into water, or from glass
into jello.
What number does PI stand for?
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989
These are just the first 1000 numbers in pi. Pi has about 30,000,000 digits.
How many zero are there in infinite?
An infinite amount. Trying to place any numbers at all would require a finite number, to which you could always add one more 0 to.
If both speeds are measured in the same medium, whether it be
vacuum, water, or jello, then they are equal.
What number is the tenth number after the decimal point in pi?
The number 5. This would round up, however, if ten decimal places are used.
Pi to 10 decimal places is 3.1415926536 (5 rounded up to 6).
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What will happen if the universal gravitational constant reduced to one sixth of its original value?
Since there is no possibility of this actually happening, there is no harm in revealing that every sun in the Universe would suddenly go nova; consequently all life in the Universe would cease to exist. A Universal reduction of gravity by 83.333% would mean that there was now insufficient force to hold all the matter of the suns against the force of the constant chain of thermonuclear explosions within. They would erupt in unimaginable explosions, scattering all their matter in an expanding globe of destruction.
The 5/6ths decrease in gravity would do virtually nothing to solid bodies like our rocky planets Mercury, Venus, Earth and Mars. Their atmospheres would expand, dropping in pressure. Earth's, now barely held down by gravity would expand so breathing would become almost impossible, but at least you could watch all the bodies of water like lakes and oceans start to boil away into vapour as you suffocated. Although minutes to hours after the change, these planets would be melted in the expanding globe of the Sun. Gas giants like Jupiter and even Saturn could expand tremendously, engulfing their Moons long before the expanding cloud of destruction that was the former Sun could reach them travelling at a mere 186,282 miles or 299,793 kilometres per second. Of course that would only be the electromagnetic radiation; it would be followed days later by particulate matter that would shred and tear away the atmosphere laying bare the metallic hydrogen/helium core, which it would then erode away to nothing as well.
There would be no place imaginable where life as we know it could survive anywhere in the entire Universe. It would be the end of everything.
But, it'll never happen.
What whole number is closet to the value of pi?
3 is because pi is 3.14159265358979323846264338327950288419716939937510... so if you round it, it goes to 3.
Is 1234567890098765432112345678900987654321 a prime number?
No, it is not.
The number is divisible by 3 for instance (it is equal to 3 x 411522630032921810704115226300329218107).
What if you get constant erections?
Some boys have erections often as they begin Puberty. It is common and natural to happen. Try not to worry about it as it will get less often as you grow older and learn to control your thoughts. Some boys find it helps to masturbate regularly when in the privacy of their bedroom or bathroom. Try not to let it become a habit though as addiction is not good in anything.
Planck's constant describes the ratio between the energy of an electromagnetic wave and the frequency of that wave.
(This answer assumes you know how Graham's number is obtained - if you don't, check the Wikipedia page about it.)
Graham's number is inconceivably huge - in fact, 3↑↑↑3 is many orders of magnitude larger than a googolplex, let alone g64.Each step up from gito gi+1is so gigantic, that to divide one by the other - and this is two consecutive terms here - would have practically no effect on the outcome.
I can say with absolute certainty that if every number ever written down by mankind in the entire history of the universe was to be multiplied together, the amount of digits in Graham's number would still exceed the result by many orders of magnitude. No sarcasm, no exaggeration, nothing - this is absolutely certain.
Graham's number is a monster - a transfinite among transfinites - and is not to be trifled with.
When was the modern number system invented?
It was invented in prehistoric times and has evolved as our understanding and needs developed.
From natural (counting) numbers to the set of integers, to rational numbers (fractions) to real numbers (incorporate irrational numbers), to complex numbers and then quaternions. The last of these, which even many mathematicians will not have come across in their work, were formally introduced to the world of mathematics by Hamilton in 1843.
Can a real number be a pure imaginary number?
even if you can't see it.... the number is real. but question to that, what's the number?
* * * * *
Clearly, the above answer was provided by someone who had no knowledge of the complex field.
A real number cannot be a pure imaginary number, nor can it contain any part that is imaginary.
In the context of the coordinate plane, the real numbers can be seen as the x-axis, the pure imaginary numbers form the y-axis excluding the origin. Complex numbers are all the point in the four quadrants.
