SPECIAL NUMBERS (MATH) Pi,1,0,e,log,i?

Question

i need to write a report on special numbers for my math class and I was wondering if anyone knows anything about these numbers and where I could be able to find any information about how they are related and where they came from and what they are. thanks so much.

Answer 1

pi :the ratio of the circumference of a circle to its diameter
1: the multiplicative identity element(x*1=x)
0:the additive identity (x+0 = x)
e: base of natural log, 1+ 1/x + 1/x^2 + ..... to infinity
log:it is a function not a number
http://en.wikipedia.org/wiki/Transcendental_number

Answer 2

Consider this,
e^(iz) = cos z + i sin z
if z is a real angle and equal to pi, you get,
e^(i.pi) +1 = 0

This equation holds most of these special numbers in an intimate and intrinsic connection.
The first equation is known as Euler's identity/formula and is proven by using MacLaurin expansions or calculus.

I suggest you use mathworld.wolfam.com and en.wikipedia.org for your research, use the helpful search tools.
The simplest definitions are as follows,
pi is the ratio circumference : diameter of any circle.
unity is the identity element of the real and complex number systems.
e is the value exp 1, defined by the series identity
S [r=0 to infinity] 1/r! = exp 1
where exp z = S [r=0 to infinity] z^r / r!

The logarithmic function can be extended to any complex number and is multivalued for non real values of the variable.
It is defined by the following definite integral identity.
log z = integral [1 to z] 1/z dz
Note that this is the natural logarithm.
i is the square root of -1,(as you might recall it appears in Euler's identity), with i introduced we come to the complex number system in which every equation, say one of the n th degree has exactly n roots. i was considered from a long time ago but the first significant use of it can be attributed to Bombelli.

Visit mathworld and do a search for more.

Answer 3

Pi - discovered by Pythagoras (not sure about spelling) ratio of circumference to diameter of a circle. Turns up often when you start looking into geometry of circles. 2pi radians to a full circle.

1 - the number that started it all. Once you get your head around 1, you're a lot closer to understanding mathematics. 1 is whatever you want it to be, and everything else follows.

0 - huge debate as to whether it's a number or a concept, I don't see this as important. Used as a 'placeholder' for nothing, the void between positive and negative. Necessary for most modern mathematical operations.

e - a graph of y=e^x has the differential equal to the function. For natural growth functions e crops up regularly. Like population growth - where the rate of growth is proportional to the population.

log - function not number, originally used to avoid having to do long multiplications, by allowing them to be done as additions. with computers/calculators this isn't so neccessary, but logarithmic scales are still used to make things easier to understand.

i - square root of -1, which in itself is quite a funky number. doesn't exist in the real world, but you can represent numbers as imaginary to make calculations for things like electronic circuits easier.

Also - e^i(pi) + 1 = 0

Answer 4

Fractions are the device of the devil. If God had meant so which you would be able to divide issues by different issues then He might have made them neat multiples of the different. case in point, there is not probably such component as "a one million/2". in case you're taking a real component and shrink it into 2 products, then each and each remains an entire component in its very own perfect (in spite of the reality that it won't be able to be usable for the comparable purpose because of the fact the unique component). and there is no could have fractions of measuring instruments because of the fact there are smaller measuring instruments which could be used instead. "one million/2 a litre of milk" remains 500ml., and 500 is an entire variety. So there's no choose ever to apply fractions. in case you have been attempting to take a third of a litre you will possibly have slightly over 333 ml., yet in view that some milk constantly sticks to the interior the measuring jug then you definately would as properly call it 333 ml. and say God is protecting something for Himself.

Answer 5

its so simple
pi :the ratio of the circumference of a circle to its diameter
1: the multiplicative identity element(x*1=x)
0:the additive identity (x+0 = x)
e: base of natural log, 1+ 1/x + 1/x^2 + ..... to infinity
log:it is a function not a number
if your not satisfy then go for wikepedia

Answer 6

pie numbers are the numbers can only be devide by 1 and itself only. like 2,3,5,7,11,13,17,19,23,31.....
i know nothing about 1,
zero is a even number and nothing can devide zero. for example, you can 2 apples, you can give it to 2 friends or 1 friend but you cant give it to 0 friends...impossible..
e is a number come from this equation (1 + 1/n)^n, when n is a very big number like infinity... (1 + 1/n)^n will reach to e, and e = 2.71828... and it's a very useful number in calculus, they use e alot in the higher math. also nutural law(ln) come with e. nutural law and log almost the same idea but the only different is (ln) has a base as e, and log has a base as 10. for some example 10^6, if you take the log(10^6)=6. same as ln, ln(e^8) = 8. i have more to say about e, ln and log, but i think i write too much.

finally, i is a imagian number, it's not a real number and you will not find it in the real life or the number line. i is the idea for square root of a nagitive number. in math, you cant solve for square root of a nagitive number, so some stupid guys come up with i. i is square root of -1, so if you have i x i = i^2, also equal to -1.

Answer 7

log isn't a no., it is a function
the other special nos are
pi - 22/7 or 3.14
Phi (that was in the best seller "The Da Vinci Code") - 1.618
for pi surf http://www.wikipedia.com
for Phi surf http://www.goldennumber.net

Answer 8

just surf wiki
http://en.wikipedia.org/wiki/number