Since I created the BLOG last October, there have been 5 articles on various topics issues. Number 5, the 3rd prime number that equals the sum of the preceding and succeeding prime numbers 2 and 3, was issued on January 24, 2014. Now, for number 6 which equals the product of the same two prime numbers I am proposing a pause in issuing articles with my topics. Instead, I am turning the tables around and suggesting that repliers submit constructive comments for everyone’s benefit on any topic of their choice.
Judging from the comments that have been submitted by repliers to date for all the articles, these have all been formulated in an intelligent, responsible and courteous fashion, and have been beneficial to most people. I hope this process will continue.
I am looking forward to receiving your constructive comments for the benefit of everyone.
***My Little Puzzle or Conundrum***
As site visitors and repliers will have probably observed by now I have a fascination and passion for math. For many years I have played with numbers and divided them with divisible and prime numbers. It’s not so much the whole number or integer portion of the quotient but the decimal portion that extends indefinitely that I am interested in. Quite often, the decimals will demonstrate a sequence or string of digits that repeat over and over. This is referred to as a rational number since the pattern can be identified. However, there are numbers such as pi 3.14159…., the golden ratio 1.618… and natural logarithm 2.7182818…. that are described as irrational numbers since the decimals sequence do not repeat or denote a set recurring pattern.
To demonstrate this let’s take a large number like 123456789 and divide it by, say a prime number like 77 = 1603334.9220779220779220779220779. Now divide the same number a divisible number like 124 = 1603334.9220779220779220779220779. In both instances, the recurring decimal sequence does appear or gets revealed through a close look.
Now for more fascination is when the numbers are divided by prime numbers 37 or its inverse 73. 123456789 divided by 37 = 1603334.9220779220779220779220779 and 123456789 divided by 73 = 1603334.9220779220779220779220779. Reversing the dividend we then obtain 987654321 and dividing by 37 = 26693360.027027027027027027027027 and dividing by 73 = 13529511.246575342465753424657534. These divisions demonstrate sequences of recurring decimals. Now, I invite readers that are interested to take the Windows calculator and divide any number they chose by either 37 or 73 and look closely at the sequence of repeating decimals, assuming of course there is a string of decimals and not something like 551/73 =7. As such, both 37 and its inverse 73 have some special characteristics.
I suspect a number of site visitors and repliers will think that this guy has lots of time on his hands. Yes, but the information I have indicated above was developed when I was in high school and was about 15 years old and completed in preparation for the special math contest I was chosen to participate in the following year. In those days there were no sophisticated calculators where divisions extended with many decimals like the one available in Windows today that I used to demonstrate the above in a few seconds.
Judging from the comments that have been submitted by repliers to date for all the articles, these have all been formulated in an intelligent, responsible and courteous fashion, and have been beneficial to most people. I hope this process will continue.
I am looking forward to receiving your constructive comments for the benefit of everyone.
***My Little Puzzle or Conundrum***
As site visitors and repliers will have probably observed by now I have a fascination and passion for math. For many years I have played with numbers and divided them with divisible and prime numbers. It’s not so much the whole number or integer portion of the quotient but the decimal portion that extends indefinitely that I am interested in. Quite often, the decimals will demonstrate a sequence or string of digits that repeat over and over. This is referred to as a rational number since the pattern can be identified. However, there are numbers such as pi 3.14159…., the golden ratio 1.618… and natural logarithm 2.7182818…. that are described as irrational numbers since the decimals sequence do not repeat or denote a set recurring pattern.
To demonstrate this let’s take a large number like 123456789 and divide it by, say a prime number like 77 = 1603334.9220779220779220779220779. Now divide the same number a divisible number like 124 = 1603334.9220779220779220779220779. In both instances, the recurring decimal sequence does appear or gets revealed through a close look.
Now for more fascination is when the numbers are divided by prime numbers 37 or its inverse 73. 123456789 divided by 37 = 1603334.9220779220779220779220779 and 123456789 divided by 73 = 1603334.9220779220779220779220779. Reversing the dividend we then obtain 987654321 and dividing by 37 = 26693360.027027027027027027027027 and dividing by 73 = 13529511.246575342465753424657534. These divisions demonstrate sequences of recurring decimals. Now, I invite readers that are interested to take the Windows calculator and divide any number they chose by either 37 or 73 and look closely at the sequence of repeating decimals, assuming of course there is a string of decimals and not something like 551/73 =7. As such, both 37 and its inverse 73 have some special characteristics.
I suspect a number of site visitors and repliers will think that this guy has lots of time on his hands. Yes, but the information I have indicated above was developed when I was in high school and was about 15 years old and completed in preparation for the special math contest I was chosen to participate in the following year. In those days there were no sophisticated calculators where divisions extended with many decimals like the one available in Windows today that I used to demonstrate the above in a few seconds.