The number 5

Howdy y'all! I  know i have been a little slow in posting this note but i just haven't found the time to sit down and write! Today's short note is on the number 5. It is a number that looks like a half fruit!

5 is the fourth prime number and plays quite an important role in our lives. We have 5 fingers on each hand, and 5 toes on each foot. Turns out that the addition of the 5th finger (thumb) and big toe makes humans different from other mammals! The opposable thumb is responsible for the variety of tasks humans can do that monkeys can't!

I also like the number 5 because all numbers ending in 5 and 0 are perfectly divisible by 5. I remember as a kid that after learning the times tables for 1 and 2, the times tables for 5 were the easiest! Actually, i believe that once children "get" the times table for 5, it is easier to learn the others.
Before I end, just wanted to note that the one number total for today's date 09/30/2010 is 6! A quick check --> 9+3+0+2+0+1+0 =  15 --> 1+5 = 6!
15 is divisible by 5 and 3, hence i chose 5 for today!!
On a personal note, i just added three classes to my semester which is going to make it a little difficult to update as often as i would like. But keep checking!

Just happy...

Yesterday, I sat down and sketched out the visuals for each single digit number that I use when remembering each number. All will be revealed in time. But for now, i simply changed the blog picture to reflect a green heart lying sideways to demonstrate 3.

Since it is the weekend, i figured that i am not going to write any new details about specific numbers. Thus, the question arises...what do i write about? Well, i decided to write about today's date! It is 25th of September, 2010. In letters only it can be written as 09252010 (U.S. style) and 25092010 (other styles). As you can note, there is a big difference between the two numbers if you consider them simply numbers rather than dates:

9,252,010

2,50,92,010

1st version: 9,252,010 translates to violet-lt. blue-black-lt. blue-white-red-white.
If you notice, i have written the number in the version that is most common in United States - commas before every 3 numbers (am I the only one who sees the craziness of three all around me??). Thus, we read the number as Nine million, Two hundred, Fifty-Two thousand, Ten.


2nd version: 2,50,92,010 translates to lt.blue-black-white-violet-lt.blue-white-red-white. This is a longer number and i have written it out in the style of writing numbers that i learned growing up...a comma before the last three numbers and consecutive commas before 2 digits thereafter. This number would be read as Two crores, Fifty lakhs, Ninety-Two thousand, Ten.

The bands i have shown above are the kind of bands that will help visual learners memorize numbers better. So let us try to find out what is unique (mathematically) about today's numbers - i am going to use the 1st version to begin with. The number is obviously an even number, and is divisible by 1, 2, 5, 10. After dividing by 10, it is easy to see that the result 925201 is an extremely odd number to play with. A website helped me find the other positive factors - 1, 2, 5, 10, 71, 83, 142, 157, 166, 314, 355, 415, 710, 785, 830, 1570, 5893, 11147, 11786, 13031, 22294, 26062, 29465, 55735, 58930, 65155, 111470, 130310, 925201, 1850402, 4626005, 9252010. Remember that the negative versions of all these numbers are also factors! Interestingly, the basic (upto three digits) prime factors of 9252010 are 1, 2, 5, 71, 83, 157. The spacing between 5 and 71 is big!! I guess what i am trying to accomplish here is to demonstrate how every number is special and unique, no matter how large it is!

For the 2nd version; 25092010 - again, even number divisible obviously by 1,2,5,10.  But beyond that, the number becomes more interesting than the first version of today's date. Upon finding factors (thank God for wonderful computing applications, it is easy to do!) we obtain 1, 2, 5, 10, 1013, 2026, 2477, 4954, 5065, 10130, 12385, 24770, 2509201, 5018402, 12546005, 25092010. Considering the prime factors in this case, we get a distance of 1008 between 5 and 1013 and the next prime number 2477 is 1464 spaces away from 1013!! Talk about large numbers, eh?

Anyways, my 3rd factor is about to wake up...so i will stop my number-mania for today...

Till tomorrow, or later...ADIOS!!

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!!

Of colors and numbers...

I have been thinking for a while, why some people are better with numbers than others. I saw a show on The Science Channel sometime back which stated that some people associate numbers with a variety of visual objects. The condition is called Synesthesia. Once i heard that, it all made sense to me. I have ALWAYS associated numbers with colors. However, unlike people with synesthesia, I do not have any other signs. If I look back on my childhood, I must have heard or seen someone associate colors with numbers and picked it up as a conscious habit. In fact, i remember thinking around the age of 6 or so that if there are 7 colors in the rainbow, and only 10 single digits in the world (0-9), how come we don't associate colors with numbers?

Another commonly used associative behavior is that of numbers and music notes (think "Close Encounters of the Third Kind"). But my music abilities are best left unexplored! LOL.

I cannot predict or confirm if it always works. However, i have found that associating numbers with colors makes it easier to perform mathematical functions and memorize sequences. This all aids only short-term memory for me, but studies show that in many cases, even long term memory is affected.

Let me try to give you an insight into how this works. And perhaps remembering phone numbers or order tracking numbers or confirmation numbers when you don't have a pen handy might become just a teeny bit easier.

First and foremost, let me give you my color spectrum:
0 = White
1 = Red
2 = Light Blue
3 = Green
4 = Yellow
5 = Black
6 = Indigo or Dark Blue
7 = No Color
8 = Orange
9 = Violet

If you notice, all of these colors are basically derived from VIBGYOR or the sequence of colors in the rainbow - violet, indigo, blue, green, yellow, orange, and red. The other three numbers have Black, White, and No color. I refer you again to the first paragraph of this post that clearly states that for me color association was a conscious effort and i have been fairly successful.

Now, suppose you need to remember a number, say 53. In this case imagine a black stripe and a green stripe next to each other. I often will associate a small number with a food item. For instance, mint chocolate (think pillow chocolates in hotel rooms or dessert chocolates given in restaurants) is dark brown (almost black) and green in color. Thus, 53 corresponds to a mint chocolate as does 35. However, 35 in an "reverse mint chocolate." Does this make sense?

Let's take a bigger example. Let's consider the number 3,125,597,845. As we can see this is a 10 digit number and is most likely to show in phone number formats. Therefore, first break it down into the format we are used to seeing 10-digit numbers in --> 312-559-7845. Now, the first band of numbers is Green-Red-Blue; second band is Black-Black-Violet; and the last band is None-Orange-Yellow-Black. If you think in "stripes" of color corresponding to each number, you will find that the green-red-blue will remind you of many a childhood toy (children are attracted towards basic colors). The black-black-violet corresponds to a thick black stripe with a violet border - to me, it translates into a beautiful saree i had seen someone wear a long time ago. The last set of numbers is tricky because the first stripe has no color. However, Orange-yellow-black typically reminds me of bees or taxi-cabs (with a major nod to So----, who knitted a beautiful hat in those colors for my son). Thus, now i have to think of three objects instead of the sequence of numbers - favorite toy, saree, and taxi-cab hat. Thus, the sequence of numbers is 312-559-7845 (i wrote this from memory)...and double-checked... VOILA!!

I am going to let you all play around with this method...and make sure to post comments if you have questions about the method or need to clarify some visuals.

For the "Factor of 3" bandwagon, i am on: I have always associated the number 3 with green. Three looks like the top portion of a heart laid sideways. But it also looks like 2 consecutive petals of a flower. To me, 3 also represents femininity (think about it - it is an obvious reason why). All of these in my opinion have always represented fertility - which is embodied in the color 'green' - one of the first lessons we had on the Indian flag. "Green represents fertility and growth." Anyways, my point here being that when my son was born, he completed my circle of 3, and guess what his favorite color is? Remember, that my favorite number is 1 and favorite color is Red. Thus, my sub-conscious efforts were always to encourage him towards Red. However, i am proud to admit that despite my manipulations (they were not too many), my 3rd factor prefers the color green and learned how to say "Three" before any other number!!

Till tomorrow, or later...ADIOS!

And thus, it starts...

First and foremost, I want to thank my hubby and my awesome friends on Facebook (and in real life) whose encouragement was invaluable in beginning this blog! Now that acknowledgments are out of the way, let me get to the core concept of this blog.

Obviously, the name "a factor of 3" can mean so many things to so many people. Later in this post are some examples that you have all heard but probably never connected. My hope is to connect some of these dots and demonstrate the prowess of not only the number 3, but eventually other numbers as well.

My favorite number of all time, in the entire world, in every context is the beautiful number "1". One is a prime number, is its own infinite multiple, and its own infinite factor. It stands tall and proud, and dominates binary systems as well as decimal systems. I will eventually write a post entirely devoted to the beauty of one...

My second favorite number of all time is "2". The majestic two looks like a patient swan on water, surveying all around it and yet standing apart from it all. Two is also the first and only even prime number and has the power to cut any other even number to size! Again, i will eventually write a post devoted to the number two...

This begs the question, i hope, as to why i have titled this blog "A Factor of 3" rather than focusing on either 1 or 2. (Yes, i know that Reader's Digest and other grammar fanatics despise the use of "begs the question", but its my style, and I am going to stick with it! LOL).

Let me start by defining the word "Factor." A quick Google search results in multiple definitions and I want to encompass all of these within this blog.

3 is a powerful number, and the actual beauty of this number will be covered in the course of various posts. However, for a straightforward start - 3 is a prime number (only has factors 1 and 3) and is a summation of 1 and 2. It is the fifth element in the Fibonacci series and plays an important role in many aesthetic, religious, philosophical, and design elements. Most of us have seen the factor of 3 play a role in many of our beliefs and expressions, and yet it is not always conscious. Let us consider some examples:
1. All bad things happen in threes...
2. The Holy Trinity factor exists in every major religion and culture globally
3. All good things happen in threes...
4. If you are unsure about design, make sure to have 3 of each element type...
5. A triangular construction (3 sides, 3 angles) brings the eye to the apex...
6. Multiple food and diet pyramids are all constructed basically with three sides...
7. For my readers who have some exposure to political, managerial, or economic theory, the triangular element is often one of the best ways to demonstrate hierarchy...
8. A large majority of people can give you the third power of three (=27) but usually not beyond that...
9. 3 are the dimensions we deal with everyday in everything we do...

The list can go on...but my 3rd element (my son) is beckoning me to "wake up!!" - he forgets the difference between get up and wake up...so I will get going...

Till tomorrow, or later...adios!