The Palindrome Numbers

Palindromes are words or numbers that read the same forwards and backwards eg. EYE, RACECAR, 1221.

The Sator Square

A Roman graffiti artist, in the first century AD, made a square grid of some mysterious words in the city of Pompeii. This is what it looked like

                                            
                                            SATOR
                                            AREPO
                                            TENET
                                            OPERA
                                            ROTAS

The words can be read horizontally or vertically and if all the words are put together they form a sentence which reads the same forwards and backwards :

                   SATOR AREPO TENET OPERA ROTAS

This when translated reads " The sower Arepo holds the wheels with effort". There are many more interpretations to this. 

But enough of this historical trivia ! The point is that Palindromes are so much fun. Although,  most of us have been aware of the palindromes in words, very few know that some of the numbers can be palindromic as well. There are many ways in which  numbers can be toyed around with to get palindromes. Quickly grab your calculator and punch the following :

                                              3 x 7 x 11 x 13 x 37

So what did you get? Isn't it amazing! You can make patterns in numbers appear from nowhere. Are you able to figure out anything more intriguing about this palindromic answer you got ? Confused? Let me come to your rescue.

The answer to the above operation is 111,111.

Interestingly, the number 11 makes some striking patterns.

1  x 1 =                                               1

11  x 11 =                                         1 2 1

111  x 111 =                                   1 2 3 2 1

1111  x 1111 =                             1 2 3 4 3 2 1

11111  x 11111 =                       1 2 3 4 5 4 3 2 1

This will keep on continuing till you reach number 111111111. Do you want to have more fun with this palindromic pattern? If you square the above number, you will get 12,345,678,987,654,321 which is of course a Palindrome. Only problem being, you will have to do the above calculation manually as your regular faithful calculator will not display numbers beyond 12 digits !

As mentioned earlier, there are many palindromic number patterns out there, which would be constantly discussed here.  Do you know of any interesting number palindromes you would like to share here? 

Bubble Magic

Photo courtesy Neetu Aggarwal

Now there would hardly be a being on this planet who hasn't played with Bubbles. Ah those refreshing childhood memory of dipping the wands in a soap solution and blowing air through them and Whoosh!!  Hundreds of transparent balls flying everywhere. There is surely something magical about Bubbles that even adults rejoice in this activity. I would personally look forward to this activity with my toddler. During one of those times, i was drawn into the science and math of Bubbles. Yes, even these innocent frolicky transparent balls are Mathemagical. You would say "Whats in a Bubble?"
Apparently a lot ! Lets just start with how various people look at Bubbles:

Child                    :  Lovely transparent balls bouncing around 
Parent                  :  Some silly bouncing balls that keep the kids entertained
Artist                    :  Lovely transparent balls trapping the colors of the rainbow
Scientist               :  A stretched thin film of soapy water filled with air.

Mathematician      : Spheres, almost always Spheres!



Simple, isnt it !? Now if you thought that Bubbles were as simple as that, then think again! 

First, some facts. Bubbles consist of a thin film of soapy water filled with air. When you blow a bubble the film expands outward to its maximum capacity and then blows away. 

Did you know that whatever the shape of the wand the bubbles are always spherical in shape. You take a triangular or a rectangular wand but the bubbles that escape out are always Spheres. The Sphere is the shape that minimizes the surface area of the structure, which makes it the shape that requires the least energy to achieve i.e. it encloses the most volume with the least surface area.

Picture courtesy Wikipedia

But wait till you see these Bubbles come together. The moment they form a a cluster (as in foam) they act differently. Lets see the 2-D drawing of layer of bubbles. In a cluster they always stick to each other tightly and hence form hexagonal shape. Regular hexagons fit together perfectly, leaving no gaps thus minimizing surface area. Three neighboring bubbles will together form a Triple Junction i.e. three 120 degree angles. 


  "Soap films always meet in threes along an edge called a Plateau Border, and they do so at an angle of 120 degrees" -Plateau's Law on soap films formulated by the Belgian scientist Joseph Plateau in the Nineteenth century.

         

         

       
Triple Junction 

2-D illustration of layer of bubbles

The detailed mathematics of bubbles is more complex and beyond the scope of this blog.

But why this immense interest in the mathematical behavior of bubbles? Foams are of immense importance in firefighting, mineral processing, radioactive dust recovery, oil recovery, crop spraying, food technology and also the brewing industry( where the formation of foam is not beneficial). 

 

Did you know

   

Many of the processed food we eat are actually foams: bread, chocolate, ice cream, cake, coke, soda and beer !   

          

Trivia

One of the Olympic venues, at the Beijing 2008 Olympics, was the National Aquatic Centre, named the Water Cube. It seems to be sliced from a giant foam of bubbles, an effect that is enhanced when it glows blue against the night sky.

The Water Cube at night. Image © Chris Bosse.       

                                 
So are you ever going to look at bubbles the same way? No way !

Mathematically yours,

Let me confess today publicly that I HATED MATH for the better part of my student life. It bullied me  persistently and unrelentingly through out my exemplary education. It was clear to me very early in my academic life, that this relationship would not last long. Later  in my student life, we parted ways. I was greatly relieved and started enjoying my association with Ms. Life Sciences. I had vowed that I would maintain my ignorance to Mr. Math for good.

I should have known better! Did I mention that Mr. Math is a creepy character who almost always manages to find its way around you? It has a knack of sneaking up on you when you least expect it. As an adult, i started having visions of Math everywhere around me in everything i saw; flowers, buildings, paintings etc. I could feel myself getting drawn towards it against my will. The more i read about its presence around me the more fascinated i became.

I started gradually sharing my learning with children in various talks and workshops. I love to see their enthralled faces once they experience the marvels of Math. It has also been a life changing event personally for me to overcome my fear and hatred for a certain Mr. Math!

Through this blog, i would like to demystify this subject and try to eliminate any negative emotions like fear and hatred associated with it. I would like to further maintain that i am no Math expert !! I just like to look at math from a lighter point of view.

So come join me, adult and children, into this fascinating and fun journey into the World of Math.

Mathematically yours,