Jasper Gerald R. Cubias IV-Graviton

Euler’s Formula First and foremost, I want to clarify that the pronunciation of “Euler” in Euler’s

Formula is “Oiler” so it should be said as “Oiler’s” Formula.

The equation is called as such because one of the main variables in this formula is

e or Euler’s Number, which is named after the Swiss Mathematician Leohnard Euler.

This number e is an irrational number is approximated to be 2.718... This value of e is a

mathematical constant which is used as the base in natural logarithms instead of base ten,

which is commonly used in logarithms.

Another fundamental variable used in this equation is π, which is also an

irrational number. There are millions of known digits of π, which are presently calculated

using computers, but an example is 3.14159... Pi (π) is also a mathematical constant just

like e, and this constant represents the ratio of a circle’s circumference to its diameter. Pi

is one of the most important mathematical constants; its application is not only in math,

but it can also be used in science and engineering.

This equation also makes use of the mathematical constant i which is equal to the

square root of negative one. This constant i, is an imaginary number because square roots

of negative numbers do not exist. Since there are no values like that which exist, the

value is simply imagined as the square root of negative one and assigned the symbol i.

The last two constants that are involved with this equation are two symbols we are

all familiar with. These two are one and zero. One is an important mathematical constant

which is the identity factor for multiplication and division. Zero, on the other hand, is an

identity factor for addition and subtraction. These two numbers are very commonly used

and are very important for mathematics and other sciences.

Imagine the first three constants were mixed into one equation. These first three

constants which are all approximations, the first two being irrational, and the last one, i

being imaginary, were mixed into one equation. What would the expected outcome be?

Had I not known of this equation, I would have expected some complex value which

would give a person a nosebleed, but no. This formula, which raises e to the product of π

and i, states that this value is equal to negative one.

e(π*i) = -1 Rearranging this we get,

e(π*i) +1 = 0 which is also known to be Euler’s Formula.

The first thing that comes to your mind, I’m sure, is “why is this so?” The proof

for this is that there is also based on Euler’s Equation, proven by derivatives and other

complex mathematics, which is eix=cosx+isinx.

Substituting π for x, we get

e π*i =cos π +isin π

=(-1)+i(0)

e π*i =-1

This equation is special and mysterious not only because it contains five of the

most important mathematical constants, which are i, e, π, 1, and 0; but also because it

makes use of the three fundamental mathematical operations which are addition,

multiplication, and exponentiation. Another thing that is special about this equation is

that it raises an irrational constant, to a product of another irrational constant and an

imaginary constant, and it produces a whole number, and a simple one, which is -1.

This equation, Euler’s Formula, still holds many mysteries and amazes many

mathematics students and professors worldwide; but what is proven to be true holds

true—no matter how outrageous it may seem.

Sources:

http://www.math.toronto.edu/mathnet/questionCorner/epii.html

http://en.wikipedia.org/wiki/Euler's_identity

http://mathforum.org/library/drmath/view/51428.html

http://mathforum.org/library/drmath/view/51921.html

http://www.eveandersson.com/pi/digits/1000000.txt?

http://www.zyra.org.uk/log-e.htm