In the bible, it is mentioned that God created the Earth in 6 days and it takes 28 days to complete a full cycle, the first and second perfect numbers. The philosopher Saint Augustine put is as, "Six is a number perfect in itself, and not because God created all things in six days; rather the inverse is true; God created all things in six days because this number is perfect" (Hoffman).

        Like mentioned in early (in the history section), the perfect number 6 was associated with marriage, health and beauty in the time of the Pythagoreans. Because 6's proper divisors add up to neither to large or too small with regard to the number itself, Nicomachus acclaimed "that perfect numbers strike a harmony between the extremes of excess and deficiency" (Voight). Hrotsvit, one of the first female German poets, stated in her play Sapientia, "We should not leave unmentioned the principal numbers . . . those which are called "perfect numbers." These have parts which are neither larger nor smaller than the number itself, such as the number six, whose parts, three, two, and one, add up to exactly the same sum as the number itself. For the same reason twenty-eight, four hundred ninety-six, and eight thousand one hundred twenty- eight are called perfect numbers" (Voight).

        Throughout time, perfect number have had deep ties to the empirical world, but as Marin Gardner said, "One would be hard put to find a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery - and more totally useless - than the perfect numbers" (Garcia).

        Although there aren't really applications of perfect numbers, these numbers can be used pedagogically. One way perfect numbers can be useful in teaching is using them to teach students how to factor. Because all of the factors of perfect numbers add up to the number itself, they can be stacked nicely using physical manipulatives, as seen in the figure below and through this applet. An enjoyable way for students to participate in an activity in the classroom is by using Legos. Have Legos for your students that are the lengths of the divisors of the perfect number (like the image below) and have your students try to build rectangles out of the given pieces. For a worksheet for students who have been exposed to perfect numbers previously, click here.

                                                                                                                    (Wikipedia)

        All perfect numbers are triangular, among their other qualities, which means the numbers can be found through the formula n(n+1)·½, and perfect numbers have, yet again, another aesthetically pleasing way to physically represent themselves. There are many more numbers produced by this formula other than the perfect numbers, but on certain primes, the perfect numbers will be produced. See this applet for an example.

        "[An] application of triangle numbers that [the University of Cambridge] discovered was listing outcomes through sample space diagrams. If two independent but identical events were to occur, a sample space diagram would often be used to display all of the possible outcomes. If you were then to ask students to find the number of different outcomes there were to the problem and it was such that the order of events was not important, students would find that their answer was a triangle number. If the repeated events were dismissed in a systematic way, an obvious triangle in one of the corners would be seen, reinforcing this to students" (Moat). Even though this is not a direct application of perfect numbers, triangular numbers can be used to as an introduction to perfect numbers, as they are related to one another.

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