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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
Root of 2 is rational or irrational?
Let's try a proof by contradiction (because it isn't rational). Try and follow along the best you can.
√2 = p/q
2 = p2/q2
2q2 = p2
This means that 2q2 (an even number) is equal to another number squared. But this means that p is even, because p2 is even, and only an even number sqaured is an even number. Lets replace p with 2b (because its twice a number because it's even).
IMMA DO THE THINGS THAT I WANNA DO, I AIN'T GOTTA THING TO PROVE TO YOU. I EAT MY CANDY WITH THE PORK AND BEANS!
TO BE CONTINUED
Where did takahasi do the calculations of the number pi?
Dr. Daisuke Takahashi and Yasumasa Kanada did their analysis of PI
at the University of Tokyo, in 1997.
Computer Centre, University of Tokyo
Bunkyo-ku Yayoi 2-11-16
Tokyo 113 Japan
http://www.cecm.sfu.ca/~jborwein/Kanada_50b.htmlh
How do you write Graham's number?
This number is too big for writing in scientific notation, or even power towers; it can be defined recursively (see the definition in the Wikipedia, for example), or approximated with special systems, more appropriate for very large numbers, such as the Conway Arrow Notation.
What two numbers are divided by each other to get pi?
No such numbers exist. PI is irrational, which by definition means that it cannot be expressed as the ratio of 2 integers. The more accurate approximations of pi are achieved by means more complicated than the simple division of 2 numbers.
As for its origin, I imagine it would have been derived by empirical observation. In ancient times, it was noticed that one could draw any circle, no matter the size, and its circumference divided by its diameter would always equal somewhere around 3.14159...
What is the imaginary number i to the 0 power equal to?
This is equal to 1. On the Wikipedia page for imaginary numbers, they have a table, but here is a summary for in:
n value of i^n
-- ------
-4, 1
-3, i
-2, -1
-1, -i
0, 1
1, i
2, -1
3, -i
4, 1
Notice there is a repeating pattern.
Is zero divided by ten equals zero?
Yes, zero divided by ten does equal zero. When zero is divided by any number, the result is zero.
What are the 2.5 trillion numbers of pi so far calculated?
Here are the first thousand
π = 3.
1415926535897932384626433832795028841971693993751058209749445923 0781640628620899862803482534211706798214808651328230664709384460 9550582231725359408128481117450284102701938521105559644622948954 9303819644288109756659334461284756482337867831652712019091456485 6692346034861045432664821339360726024914127372458700660631558817 4881520920962829254091715364367892590360011330530548820466521384 1469519415116094330572703657595919530921861173819326117931051185 4807446237996274956735188575272489122793818301194912983367336244 0656643086021394946395224737190702179860943702770539217176293176 7523846748184676694051320005681271452635608277857713427577896091 7363717872146844090122495343014654958537105079227968925892354201 9956112129021960864034418159813629774771309960518707211349999998 3729780499510597317328160963185950244594553469083026425223082533 4468503526193118817101000313783875288658753320838142061717766914 7303598253490428755468731159562863882353787593751957781857780532 171226806613001927876611195909216420198
Notice the number of angles when you write/display the numbers (1-9) with straight lines.
For example:
Two (2) has two angles when written/displayed as (Z).
Three (3) has three angles when written like the Greek letter "Sigma".
Six (6) has six angles and Eight (8) has eight angles (please see the display in digital watches or calculators)
Only Zero (0) is circular- or ellipse- shaped which has no angle.
What is seven divided by zero?
truthfully if your stupid the answer is 0 7 times what equal o and its zero dummy.
+++
You can't divide anything by 0.
What are the first thousand numbers of pi?
π = 3.
1415926535897932384626433832795028841971693993751058209749445923 0781640628620899862803482534211706798214808651328230664709384460 9550582231725359408128481117450284102701938521105559644622948954 9303819644288109756659334461284756482337867831652712019091456485 6692346034861045432664821339360726024914127372458700660631558817 4881520920962829254091715364367892590360011330530548820466521384 1469519415116094330572703657595919530921861173819326117931051185 4807446237996274956735188575272489122793818301194912983367336244 0656643086021394946395224737190702179860943702770539217176293176 7523846748184676694051320005681271452635608277857713427577896091 7363717872146844090122495343014654958537105079227968925892354201 9956112129021960864034418159813629774771309960518707211349999998 3729780499510597317328160963185950244594553469083026425223082533 4468503526193118817101000313783875288658753320838142061717766914 7303598253490428755468731159562863882353787593751957781857780532 171226806613001927876611195909216420198
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 is a leprecon is he real or imaginary?
Leprecon's only exist after generous portions of Irish stout. How do you know if it's a "he"?
What are the first 23 digits of pi?
Not including the initial digit, the first 23 decimal digits of pi are 3.14159265358979323846264.
Who invented the the golden ratio?
There are several who discovered the significance of this ratio (see related link post). Euclid (around 300 BC) noted the ratio, but it looks like it was referred to as 'Golden' by Martin Ohm in 1835.
Who is the first Physicist to measure the gravitational constant G?
In 1789 Henry
Cavendish measured G
Pi is defined as the ratio of the circumference of a circle to its diameter (pi = circumference / diameter). So that explains why it's in the circumference formula. For the area, a little knowledge of calculus is helpful. Here's a 'simple' explanation.
Suppose you have a polygon with many sides, which is inscribed into a circle. The area of the polygon can be found by adding up the areas of isosceles triangles formed by a polygon side and line segments extending to the center. If you have enough sides, then the base of each small triangle will approximately be equal to the corresponding arc of the circle. For sufficiently small triangles (a very large number of sides for the polygon), a 'long leg' of the isosceles triangle will be approximately equal to its altitude.
Say that we have a 100 sided polygon, with radius R and diameter = 2*R. So lets find the approximate area of the polygon. Each base (polygon side) will be approximately equal to Circumference/100, and each altitude will be approximately equal to R. So the area of one triangle is equal to Base*Altitude/2, which is approximately (Circumference/100)*R/2. Substitute Circumference = pi*Diameter = pi*2*R.
Each triangle area is approx (pi*2*R/100)*R/2 = (pi/100)*R2. Since there are 100 triangles, the polygon area is approximately pi*R2 (which is the area of the circle). Note the word approximate, because there is slight space between the polygon and the circle, but [here's the calculus part], as the number of polygon sides approaches infinity, the space between the polygon and the circle approaches zero, and the errors in approximation approach zero, so that the area of the circle and the infinite sided polygonare the same.
Why is pi an inrational number?
An irrational number has no end and pi is infinite and has no end, therefore pi is irrational.
Note: There are computers that have been computing the number pi for a long time and there has been no end yet. The numbers just keep going on and on and there is no rhyme reason or pattern to it.
What is the names of the numbers in a division problem?
example 32/4=8
32 is the dividend
/ is the division symbol
4 is the divisor
8 is the answer or the quotient
