EdTech 537: List Entry

Posted on July 4, 2014 by kimberlyhefty

al·ge·bra

ˈaljəbrə/ noun

noun: algebra

the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.   a system of algebra based on given axioms.

1. • Some numbers, such as your phone number or your Social Security number, are decidedly more important than others.  One of the cornerstones of Algebra, frankly all of mathematics, is numbers!  Here is my list of some of the most important numbers in Algebra:

     1)  Of course the first number must be:  1!!

     

     The number one is far more special than a prime!  It is the unit (the building block) of the positive integers, hence the only integer which merits its own existence axiom in Peano’s axioms.  It is the only multiplicative identity (1^.a = a^.1 = a for all numbers a).  It is the only perfect nth power for all positive integers n.  It is the only positive integer with exactly one positive divisor.  But it is not a prime.

     source:  Primes FAQ

     2)  Archimedes’ Constant (Pi): 3.1415…

     

     Wikimedia

     Pi

     Archimedes’ constant, or “Pi,” is the name given to the ratio of the circumference of a circle to the diameter, but it’s actually so much more than that.

     Greek mathematician Archimedes is credited with the first theoretical calculation of Pi, which he estimated was between 3 10/71 and 3 1/7 — or 223/71.

     Pi is now defined as 3.1415926535… etc

     Application: Pi is the key constant in any equation that involves circular or harmonic motion. It’s one of the most essential relationships in mathematics.

     Source: Math.com

     3)  Euler’s Number (e): 2.7182…

     

     Wikimedia

     Euler’s Constant

     Euler’s number is also known as the exponential growth constant. It is the base for natural logarithms and is found in many areas of mathematics.

     Application: In finance, Euler’s number is used to determine compound interest, which is extremely vital in understanding the time value of money — the backbone of finance.

     Moreover, Euler’s number is crucial when describing any decaying relationship – think Carbon 14 dating.

     Source: Math Is Fun

     4)  The Golden Ratio: 1.6180…

     

     The golden ratio is a number often encountered when taking the ratios of distances in geometric figures.

     Application: The golden ratio is often used in financial technical analysis to attempt to determine when a market will continue its path or reverse.

     It’s also observed very frequently in nature, especially in the way that some naturally occurring spirals expand outward.

     Source: Forexoma

     5)

     Imaginary Unit: i

     

     KhanAcademy

     “i” equals the square root of -1, which means that i squared is equal to -1.

     Application: Negative numbers don’t have square roots. Math had advanced to the point where saying “there is no square root of negative numbers” was holding back a lot of progress.

     Solutions of some polynomials have both real solutions that we could use in real life as well as solutions that involved the square root of a negative number, which can be discarded.

     Source: Wolfram

     6)  The “perfect squares”

     

     The important feature of the “perfect square” numbers is that they are the squares of Whole Numbers!  They are “perfect” because there are no fractions or decimals.  They literally describe the area of a square.  Taking the square root of a perfect square will give you the length of one side of your square.

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