EdTech 537: List Entry


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.

    • 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…

      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…

      Euler's Number (e): 2.7182...


      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: 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


      Imaginary Unit: i

      “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”
      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.

About kimberlyhefty

Hello. My name is Kimberly Hefty and I live in Sammamish, Washington. For the past 23 years I have taught high school and college level mathematics. 13 years ago I started a private tutoring business. I specialize in working with public high school students who are taking math courses "on-line". I work closely with both the students and the local school district. I typically work with 40-50 students per week. I also have 2 children ages 14 and 23. My daughter just graduated from Elon University in North Carolina. My son plays competitive golf and premiere soccer so most of my weekends are spent at either soccer or golf tournaments. I am excited to be completing the Master's In Educational Technology Program from BSU (M.E.T.) Spring 2015! Through this program I have gained a better understanding of educational technology and it’s applications. I believe that the knowledge that I have gained will be beneficial personally, as well as to my students. With these skills that I have learned in the Educational Technology program, I hope to help myself and my students be successful in future endeavors. The M.E.T. program has allowed me to create an environment for all of us, my students along with myself, to gain skills for education, employment, and existence.
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5 Responses to EdTech 537: List Entry

  1. Kim, this interesting stuff. I had hear about the golden ratio before on an episode of Criminal Minds, but much of this was new to me.

  2. I love math and so I found this very interesting. As someone who has taught Yearbook in the past and done a lot with photography I love teaching students about the golden ratio and its application in photography

  3. Pingback: EdTech 537: List Entry | Angie Kruzich: EdTech Learning Log

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