What is Radium?

Hi everyone,

I have a doubt in this:

What is radium? Can anybody confirm it?


- Srinidhi

A simple proof of Pythagoras Theorem

Narasimhanna sent this simple proof of Pythagoras theorem. I have drawn pictures that make it easy to understand the already simple proof. If you have questions post them in the comments section.

A lecture on prime numbers

Here is a very accessible lecture for a general audience, on prime numbers, by a very bright young mathematician.
   http://www.youtube.com/watch?v=PtsrAw1LR3E

In the beginning of the video observe the description of his profile.

The key result of his that he talks about is the following:
"Primes contain arbitrarily long arithmetic progressions"

Examples:
   3,5,7 are primes. These are an arithmetic progression of 3 prime numbers spaced 2 apart.
5,11,17,23 are an arithmetic progression of 4 prime numbers with common difference 6.
7,157,307,457,607,757 are an arithmetic progression of 7 prime numbers (the common difference is 150).

The result he proved in 2004 says that among primes, there are arbitrarily long arithmetic progressions. The longest found so far contain 23 prime numbers:
56211383760397 + 44546738095*n  ( n = 0, 1, ... , 22)

I am sure most of you will agree that understanding the result is easy. Notice, in the lecture, that he mentions that there can be arithmetic progressions millions of prime numbers long; no one knows how to find them!!  The best we have got is 23 primes sequence.

 Also, visit his blog http://terrytao.wordpress.com/ and check out the "Career Advice" section for something you may find useful.

WHEN EMPERORS BUILD GREAT PALACES, WE CAN HAVE A ROLE TOO!

Srinidhi's question:

Peddappa, what is your subject of research?


Narasimhanna's reply:

Dear Srinidhi,

     This is a more difficult question to answer and perhaps not very important.

 

I will write about it some time later.

 

You see, all this is a small part of a great human enterprise.

 

It is evolution of ideas/understanding  about various things around us that really makes our lives easier, more comfortable and satisfying, not just as individuals but also in a broader context of communities, societies and even civilizations.

 

The various issues about which one may have to think about, for example,

- life itself,

- nature of man, mind, intelligence,

- the way things are, like how the world around us work, our own body for example,

- the way things change,  

- the way we can adopt ourselves, adopt our institutions around us in view of the growing understanding of such matters

- the suitable tools that we can probably develop to make our lives easier (technology!)

- develop suitable social institutions, like schools/universities, legal system, banking system, etc

- and so on

 I am sure you can add to the list.  Anyway, you get the idea.

 

All scientists, philosophers and thinkers in general generally think about these issues.

 

As you very well understand, each of them is too huge for any individual or even a group of people.

 

So even great thinkers address a very small part of at most one of these aspects. 

 

People like us are like small helpers in this great endeavour. You know a great man once said

 that WHEN EMPERORS BUILD GREAT PALACES, WE, THE SWEEPERS ALSO HELP!! 

 

 

The emperors he was talking about were people like: Budha, the Shankaracharya, Newton, Einstein, Darwin, Christ, Mohammed, Moses, Confuscius, Socrates, etc.

 

You know we do not even know the names of many such `EMPERORS'  in very distant, forgotten civilizations (like Mayans, like many societies in Africa lost to history, preroman European civilizations,  etc)

 

But people like us (you and me!!)  are also important in this enterprise because: 

 we keep these activities alive in the society we live in  (mostly as students, as  teachers and transmitters of these ideas to new generations) .

 

This is why teachers are very important in a society and our forefathers gave such an exhalted position to our GURUS.

 

 

Yours affectionately,

-Narasimha

What is Group Theory?

Srinidhi wrote:

What is the group theory you have invented peddappa?

Dear Srinidhi,

 I have not invented Group theory! I am only a student of  group theory. This subject is atleast two hundred years old.

But its main content-symmetry in nature- is a topic of human interest all through human life.

You might have seen very nice, old buildings with a great deal of symmetry.

In a sense, music is very pleasing because of the symmetry in the sound (raga, tala, as they say). You agree that music can be very pleasant and relaxing and noice is neither pleasant nor relaxing!

Group theory formally is a subject in Mathematics and it largely deals with symmetry in nature. Its main pillars are  Algebra and Geometry. You understand the word symmetry:

a ball is symmetric,

a square is more symmetric than a rectangle,

a symmetric building is nicer to look and perhaps more useful than a building not symmetric,

Vidhana Soudha is very symmetric

nice flowers have a great deal of symmetry,

you may have seen some crystals which are very symmetric;

diamonds derive their beauty by their shining and symmetry, etc.

  Symmetric objects can be very complicated though they are very pleasing. 

Physicists think that our universe is very  symmetric. That is why physicists also study group theory a lot.

Chemists study symmetry to understand the crystals in nature

To impress on you how complicated a symmetric objects could be, I have include a file containing some nice pictures for you. ENJOY!

 [ http://www.math.umass.edu/~gunnells/cells/cells.html ]

(ignore the beginning stuff, only look at the pictures!!)

-Yours affectionately,

Narasimha

On Dimensions, etc

Here is a gist of an email conversation that happened between Srinidhi and Narasimhanna. You are welcome to participate in the discussion.


Srinidhi wrote:
Peddappa, can you explain what fourth dimension is?



Dear Srinidhi,

  I can and I will. It is better when we meet and talk.
  In simple terms, dimension keeps track of the number of `factors'  we have to keep in mind when we are thinking about any particular matter.

  When you walk in a straight line (or when you write), there is only one direction. That is one dimensional.

  When we paint a picture or see a picture in a plain paper, there is both length and breadth. So two dimensions in this case.

   The space we all exist at any given time has three dimensions : there is length, there is breadth and there is height. The house we live in is in three dimension; the cake you eat has length, breadth and height.


   But  if you think a little carefully, we really live in four dimensions : we live at a particular place (that is, three dimensions) and at a given time (that is an additional dimension, the fourth one).

All the changing events you see (like your eating, a plane flying, earth rotating, etc.) take place  in four dimensions. Just as it is important to know
  (i) the length when you buy a string (MALTHADU),
   (ii) the length and breadth when you buy a piece of cloth,
   (iii) the length, breadth and height when you choose a cake to eat,

when you think of the stars or galaxies, you should think of not only the position of that object but also the time of its existence.

Think of this fact, I was amazed when I came across as a teenager. Many rays of light that is falling on you now (as you are reading this) originated from stars which no longer exist!

 When they started, perhaps even our dear sun, let alone our life sustaining earth, did not exist!

It is like you coming across a gift today in your backyard from your fathers, fathers, fathers,... (200 times over)]

So in thinking about such long time phenomena, we should keep track of not only space but also time. You can think of many situations where this may be necessary as thinking about both the length and the breadth is necessary when you are buying a bedsheet.

Think of this: Mudiyanur inhabited by Subbaiahgaru is different than the Mudiyanur inhabited by Subbanna. The space is the space, but time is different.

Think about fourth dimension. I will explain to you some time later why it is important to think of 5 dimensions, 6 dimensions, 7, dimensions, etc.

-Yours affectionately
Narasimha


Srinidhi Wrote:

Peddappa, I understood this. I am eagerly waiting for what is 5th, 6th, 7th etc.,.


Dear Srinidhi,
    As you see,  we use `spaces' to describe things. Dimension of the space chosen depends on the things we want to describe: dimension one if it is a string, dimension two if it is the site you want to purchase, dimension three if you want to describe the size of the ball you want to describe, dimension four if you want to describe the position of a planet, etc.

But you see, each dimension corresponds to an important feature (`parameter') of the object we want to describe. You can easily imagine many objects/situations where more than four important features are need to describe the object effectively.

 Here are some examples:
A. In describing an iron furnace at any given moment (the one used to manufacture iron, like the one in Bhadravathi), the following factors may have to be specified: its temperature, pressure inside the furnace, the quantity of ore inside it, the number of years it has been in use (its age, if you like), the amount of power available to it, number of staff operating that, etc. So you see in describing this we need to keep track of several dimensions.

B. To describe the Bangalore Bus transport system on any particular day : the parameters could be, number of buses available, number of routes, an average number of potential passengers in each route, number of drivers available, number of conductors, amount of fuel available on that day, etc.

The same for a description of Air lines.

The description of the economic profile of a family also needs many dimensions!!

I am sure you can make up many more examples. But, any way, I suppose you get the idea. As the society gets more and more complicated, it is necessary for accurate descriptions (at least as accurate as we can and use that usefully) of various situations.

So, you see,  description of space  is very important in human life and that is why it has played such an important role in all societies (modern, primitive). The subject that studies it is Geometry. That is why from the old civilizations ( like Aryans, Egyptians, Greek) to the modern era, Geometry is at the core of human thinking and has been very useful.

These days, the computers and Information Theory people are fast developing appropriate geometries to suit their needs.

But the GREATEST ATTRACTION OF GEOMETRY IS ITS BEAUTY.

That is why the ancient Greeks said that God was a geometer.

That is what attracts the indulgence of many thinkers at all times.

-Yours affectionately,    
Narasimha

Believe it or not's !!

Peruvian Amazon ants

An unbelievable number of 43 species of ant can be found on a single tree in the Peruvian Amazon, which is equal to the entire ant fauna of the UK!

The Oldest Trees

The Bristlecone Pine is the oldest known tree species in the world. It is found only in the scattered, arid mountain regions of six western states of America, in a harsh windswept environment. The oldest Bristlecone Pines grow at an elevations of 3,000 to 3,300 metres, and the oldest known tree is 'Methuselah', which is 4,789 years old!

Hybrid Animals

List of hybrid animals -

http://www.messybeast.com/genetics/hybrid-cats.htm

Electric Bulb

Why is Thomas Alva Edison considered to be the inventor of the electric bulb?

The actual inventor of the very first electric lighting was Humphrey Davy. In 1809, he invented the original source of electric lighting. Since his invention, many other men had set out to improve this idea and invent their own form of electrical lighting. Many have succeeded, but none were practical or long lasting.
It was only in 1879 that Edison invented a carbon filament that would burn for at least forty hours. With his great mind and wonderful thinking, he had made a longer lasting electric light bulb in 1880. It burned for over 1,200 hours, using a bamboo-derived element.
So, though there were very many men trying to invent longer, safe, and economical electric lighting, it was Thomas Alva Edison who did the best job. He made quite a few improvements on his improvements on his invention too. Edison spent several years after this, putting together the electric industry, so that this new source of lighting would be used throughout the world, on streets, in homes, and in businesses.

Some more fun stuff

The following is for those of you who have learnt some Geometry. I wanted to show you a simple proof of Pythagoras theorem and, for that, you need to understand the following.  Feel free to ask questions if you do not understand something.

In the diagram above, PQ and XY are parallel straight lines (what does it mean?).  

And, AB=BE (that means, if you slide the green parallelogram along the parallel lines as below, you will see that the base of the green parallelogram coincides with the base AB of the rectangle).

FACT:  If you have such a set up as the green parallelogram and the red rectangle as seen here, then the area of the rectangle is same as the area of the parallelogram.

Some fun stuff

INTERESTING FACTS!!!!!!!!!!!!!!!!

DID YOU KNOW THAT?
1. 4.5 pounds of sunlight strike the Earth each day.
2. A ball of glass will bounce higher than a ball made of rubber. (try it outside)
3. . At room temperature, the average air molecule travels at the speed of a rifle bullet.
4. Each day, up to 150 species of life become extinct.
5. Each day is longer than the previous on by 0.00000002 seconds which is 13 seconds each century!
CHECK OUT MORE OF THESE FACTS IN THE FOLLOWING WEBSITE
http://www.funfactz.com/science-facts/

TEST POST!

HI GUYS,

This is Jayesh, Shruthi's brother. I am really looking forward in getting to know all the members from putkutti science club. If you have any questions please feel free to ask me.

Thanks, Bye Bye

Believe it or not!

Bourke's Luck

Bourke's Luck Portholes are swirling whirlpools which occur as the Treur River plunges into the Blyde River. They were named after Tom Bourke, a farmer on whose land the portholes were located. Tom Bourke correctly predicted that large gold deposits would be found at the bottom of his potholes - and he was right!

Image:

http://www.trekearth.com/gallery/Africa/South_Africa/East/Mpumalanga/Blyde_River_Canyon/photo183281.htm

Testing

Hey guys this is Shruthi. I just joined joined the putkutti club. I f you have any questions please feel free to ask me anytime.

What is strange about the lakes of Keli Mutu?

Kelimutu is a small but well-known Indonesian Volcano in central Flores Island with three summit crater lakes. These lakes are startling in that they are of three different colours! The western lake, Tiwi Ata Mbupu, or Lake of Old People is blue while Tiwu Nua Muri Kooh Tai or the Lake of Young Men and Maidens is green and the Tiwu Ata Polo, or 'The Enchanted Lake', is red.

The people who live in the area believe that these lakes are the resting place of souls, of sinners, virgins and babies. What is even stranger is that the lakes have changed colour over the years. Some years back, they were black, maroon and blue, and in the 1960's, they were milky coffee brown, red brown, and blue! No one can explain the cause of such colour changes except to suppose that different minerals are dissolved in the waters of each lake at Kelimutu. Did you know that the word 'Kelimutu is a combination of words 'Keli' which means mountain and 'Mutu' which means boiling?

ಚಿತ್ರ-http://thepowerofindonesia.blogspot.com/2010/02/kelimutu-unique-lake-with-three.html
ಶ್ರೀನಿಧಿ

S Chandra

I read an article on S Chandrashekhar and I got a glimpse of how big minds operate. Check this out when you get a chance:
http://www.ias.ac.in/currsci/apr252000/generalia.pdf

Here is a very lengthy interview with him where he discusses his career in greater detail:
 http://www.aip.org/history/ohilist/4551_1.html


It surely is inspirational material!




PS: Srinidhi, you have disable comments for your posts. Try to enable comments. When you edit the post, click on "Post Options" link you see at the bottom left of edit window. This has an option to enable comments.


The comment I wanted to make is this: The fossils of tree trunks appear to be those that are neatly cut, like from a chain saw. How did that happen when this should be dating back from pre-human days?


I haven't had time to post of late. The following are coming up soon:
1. The universe may end up in a Big Crunch or a Big Freeze or a Big Rip. These are certain ideas that capture our imagination. 
2. Narasimhanna suggested that I draw pictures to depict visual proofs of such things as (a+b)^2=a^2+2ab+b^2 and Pythogoras theorem, etc. 

Amazing!

Garden Eels

Garden Eels are small eels that burrow into the of coral reefs. They moor themselves into trenches in the seabed, and get their name from the fact that they drift in the current like plants. They don't swim around at all, but stay in one place, filtering the water for fish eggs and small shell fish.

धन्यवाद

Believe it or Not !

Wood to Stone - taken from Manorama's 'Tell me why'

Arizona's Petrified Forest is not a forest at all. It is a hauntingly beautiful landscape filled with magnificent specimens of petrified wood. Petrified wood is wood that has turned into stone. How did this happen? Millions of years ago, the forests covering Northern Arizona were buried under a sea of mud, sand, and volcanic ash, and the pressure over a period of time turned the wood into stone, to create a forest of stone trees!

Image - http://www.moore-fun.net/images/Petrified%20Forest.jpg

ధన్యవాదాలు
శ్రీనిధి

Carnivorous plants

Venus fly trap, Pitcher plants (Nepanthes), Sun Dew plants (Drossera) are some of the carnivorous plants.

List of carnivorous plants available at -

http://www.pinguicula.org/pages/pages_principales/SEZNAM%202004.pdf

How these plants trap the prey and digest is available at -

http://www.ehow.com/list_5791411_carnivorous-plants-list.html

ಇಂತಿ
ಶ್ರೀನಿಧಿ