On square structures...

I am amazed at how many friends/family members are coming through on their interests in numbers, and favorite numbers. That makes me happy!! Thank you all and keep sending in those quirks...when i blog about a relevant number or topic, i will surely give you a shout out - discreetly of course! How many of you were able to work the color system into the numbers...did it help? Keep me posted. You can email me/call me or just post a comment - I love getting feedback. I have some other tricks and tips up my sleeve, but writing them out and thinking them through will depend upon the level of interest i find.

My initial thought today was to write about how the color-number theory works for basic mathematical functions - addition, subtraction, multiplication, and division. However, i decided that i am going to wait a few days before writing about them so that you have some time to get familiar with the color spectrum.

Today I want to explore the number 4 - why four you ask? Well, it comes right after 3 and is the first non-prime number in the series of natural numbers. It is also the first square (other than 1 of course), and it plays an important role in many aspects of our life, just like all other numbers. As a kid, I was very fond of the number 4 (you will find soon enough that at different times in my life, different numbers take the place of "second favorite number"). For a long time, i was obsessed with the number 4. Think of 4 as an exotic butterfly that is about to perch on a flower!  By the way, during the discussion of each number i will give some visual images to connect to the number. This is another good method of remembering number sequences.

If you see carefully, the butterfly pictured here starts with the base of number 4. I also would like to point out that for a standard keyboard, 4 key corresponds to $!! Anyways, back to the characteristics of number 4. In order to test divisibility by the number 4, one only needs to consider the last 2 digits any number. If the last 2 digits are divisible by 4, the entire number is divisible by 4. Check it out - let's assume a large number 265418. Here, as we can see 18 are the last two digits and 18 is NOT divisible by 4. Thus, 265418 is not divisible by 4. If you want, type it into your  calculator and you will find that 265418/4 = 66354.5. On the other hand 265416/4 = 66354 because 16 is perfectly divisible by 4.

A legitimate question here would be why is this the case. I will attempt to explain - any even number is divisible by 2, correct? Now, every alternate even number is divisible by 4 (check out numbers such as 4, 8, 12, 16, 20, 24, etc.) because 4 is 2 multiplied by 2. Just like the "evenness" of a number implies that 2 is a factor, the divisibility of the last two digits by 4 implies that the number has to be divisible by 4. Another quick note to make here is that if you are trying to divide an even number by 4, it will either result in a whole number or a number ending with 0.5. (See above example for illustration).

A unique feature of the number four is that it is a square of and the sum of the same numbers. There are no other real whole numbers that fulfill this criterion. That is to say that X + X = X^2 is true only of 4 (among the population of real whole numbers).

A quick look at literature in English, or other regional languages will indicate that not much special attention is given to the number 4. While 3 is sacrosanct and a staple in many children's books, historical and religious references, 4 often gets sidelined. This is partially due to the fact that 2 is a MAJOR factor of 4, and therefore carries its properties over to 4. Moreover, other than four-leaf clovers, which are considered to be special and lucky even, one does not often find 4 occurring in most natural events or creations.

However, mathematically 4 is quite powerful. Guess how many sides to a square or rectangle? That's right - 4!! It is important to note though, that in cases like this having the measures of the length and breadth (just 2 numbers) will usually suffice for all calculative purposes. A cool feature of 4 sided shapes (quadrilaterals) is that the sum of all the angles within the shape is always 360 degrees. Why the number 360 is awesome, will be dealt with in another blog some day... but for now, note that 360 degrees in a circle always implies a complete circle such that the beginning point and the ending point are the same. While this might have significant philosophical implications for those who are leaning towards the philosophy of 360 degrees... it is significant in trigonometry and calculus for a variety of reasons.

So what are the major four-sided shapes aka quadrilaterals? Square, rectangle, rhombus, parallelogram, trapezoid, and kite. While exploring the internet i found this Website that shows what each of these shapes looks like. If you look closely, you will find many many examples around your own room/residence that resonate the principles of four!! I think the Egyptians had it right when they placed a quadrilateral (perfect square) at the bottom of their pyramids!! More on that someday, i promise...

Till tomorrow, or later...ADIOS!!