If you are studying maths at school, then you are on your way to becoming a mathematician. Congratulations you are on your way to becoming fluent in the language of numbers in the style of trigonometry (trig.), algebra, geometry Pythagorean theorem, Linear equations, the long number Pi, the unusual Euler’s e, Equivalent fractions, the specific number i, also the golden ratio, probability and other mathematical concepts in your grade level math curriculum.
It may seem like a long time ago that you were learning about the maths basics that this knowledge is built upon. Since kindergarten you have been learning about maths, addition and subtraction, multiplication and division all laid the path for understanding your current mathematics education.
That is because math is everywhere,
The list goes on because mathematics is the common core standard of our society. From basic math to more complex equations, we use them every day, which makes all of us mathematicians even if very bad ones. But our ability to grasp math questions and solve problems gives us the opportunity to gain mastery in it.
If your maths practice is important to you, then you would have already spent time learning all about fractions and algebraic math concepts. But what about sequences? By now you know maths is not just a number system made up of whole numbers and clever counting. How about scientific notation, algebraic symbols, special numbers and sequences like perfect numbers. Perfect numbers are the mysterious number patterns, that have an interesting mathematical model. Let explore perfect numbers today and see what we can find out!
It may seem like a long time ago that you were learning about the maths basics. Photo Source: Unsplash
A perfect number is a rare number, to date on only 51 of them have been discovered. There are only three perfect numbers less than 1000: 6, 28, and 496. In fact there is 1 perfect number under 10, 1 under 100, 1 under 1000 and I expect that the pattern continues in this way to infinity.
When all factors of a number, excluding the number itself, add up to that number, it is known as a perfect number. Factors are the numbers lower than that number which can divide into it evenly. For example:
Is 8 a perfect number? Let’s see
The First Eight Perfect Numbers Are:
To see the next 43, you can go to Wikipedia
There still remain may unproven concepts and rules in relation to perfect numbers.
Here are a few:
Perfect numbers are related to prime numbers. Book IX of the Elements of Euclid states that if the Mersenne number 2n – 1 is prime, then 2n-1 (2n – 1) is a perfect number (Wikipedia). The combination of the results of Euclid and Euler (Swiss mathematician Leonhard Euler is also known for the Euler number e) gives a complete characterization of even perfect numbers.
Since then the research has accelerated rapidly thanks to more and more sophisticated techniques and computer use.
If you are studying maths at school, then you are on your way to becoming a mathematician. Photo Source: Unsplash
If prime numbers are recognized as being the very foundation of arithmetic by many mathematicians, then perfect numbers are easy to understand and have no particular use. They are not used to solve Trigonometric functions, Systems of equations, Multivariable calculus, Stochastic processes, Computational functions or Exponential function.
They are not useful for solving basic math problems like Calculus or Multiplication problems of general math problems. Perfect numbers are a purely mathematical concept, they are not useful to the fields of Economics, science and engineering for example.
However, perfect numbers were previously considered superior to all other numbers, and some saw a mystical role in them. They are one of the mysteries of mathematics, and the search for new perfect numbers still fascinates many mathematicians today. I think that perfect numbers can make a cool math game like Sudoku, “find the perfect number”. Maybe their purpose can be to make free math addition games ap. Now that would be mystical!
Discrete Spoiler! Maybe I am biased but knowing the tri-perfect, multi-perfect, and hyperperfect numbers will not help you much in your math classroom. Not with high school math, a college equation, a university degree or life in general.
As a serious learner concentrate the majority of your study time to reinforce your math skills and knowledge on more useful and interactive math. Like fractions, complex numbers, logarithms or reasoning in geometry.
If you are one of the people who never understood math, or who the math teacher always gave a low homework score. Then the thought of maths might put you off, but mathematics can be fun.
Learn math with fun tools like jigsaw puzzles, quizzes, math videos and perhaps worksheets. Will keep you engaged and also help you to relax which will make learning math easier.
The thought of maths might put you off, but mathematics can be fun. Photo Source: Unsplash
Have fun with your curriculum, be experimental, master your homework, erase the decimal places, find the symmetry, challenge the square roots, place value on the negative numbers, find new solutions and think above of your grade level, rise above the common core standard logic, don’t limit your mind.