"What equation is considered to be remarkable for its ""mathematical beauty"", because 3 basic arithmetic operations occur exactly once each (addition, multiplication, and exponentiation), and it links five fundamental mathematical constants: (the numbers 0, 1, , e, and i)?"
Euler's identity Euler's identity In mathematics, Euler's identity (also known as Euler's equation) is the equality where Euler's identity is named after the Swiss mathematician Leonhard Euler. It is considered to be an exemplar of mathematical beauty, as it shows a profound connection between the most fundamental numbers in mathematics. Euler's identity is often cited as an example of deep mathematical beauty. Three of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants: Furthermore, the equation is given in the form of an expression set equal to zero, which is common
Multiplication and repeated addition Once 0 is brought in, it affects no significant change because which is 0, and the commutative property would lead us also to define Thus, repeated addition extends to the whole numbers (0, 1, 2, 3, 4, ...). The first challenge to the belief that multiplication is repeated addition appears when students start working with fractions. From the mathematical point of view, multiplication as repeated addition can be "extended" into fractions. For example, literally calls for “one and three-fourths of the five-sixths.” This is later significant because students are taught that, in word problems, the word “of” usually indicates a