A simple PUZZLE!

 Puzzle: If the area of the outer square is 100 then what is the area of the inner square?

The inner square touches the outer square at the mid-point of each of its four sides.

Answer: 

A square, by definition, has 4 equal sides and it's area is defined as the square of its side.

The outer square has an area of 100 which implies that each of its four sides is of length 10 because 10^2 is 100.

Pythagoras, from ancient Greece, came up with a relationship between the sides of a triangle that has a right angle between two of it's sides. The formula says:

 Hypotenuse ^2 = side1^2 + side2^2

(^2 is the sign for squaring)

Note: The hypotenuse is the longest side of the triangle opposite the right angle.

Why do we need this formula?

Because, we need to find the length of one side of the inner square. Each side of the inner square is a hypotenuse in the four triangles surrounding the inner square! Therefore the Pythagoras theorem applies. Let us choose the rightmost triangle at the bottom (see diagram above)

      Hypotenuse ^2 = 5^2 + 5^2

      Hypotenuse ^2 = 25 + 25 = 50.

5 is the length of each of the two sides that form a right angle in the triangle because the inner square touches the outer square at mid point of its sides.

And because hypotenuse is the same as a side of the inner square, the answer is that the area of the inner square is 50 !!

Life Is Beautiful - a movie review

 Video Source: a free app

Life is beautiful through the eyes of the hero (Benigni) because he is so chirpy and infectiously  positive about everything and seems to be always running around on his bicycle. (I think it is a dubbed Italian movie.)

As the movie progresses, we see him successfully get his girl friend and marry her as well. The movie uses quick editing to indicate the passage of time as we see the heroine enter a room covered with strings of flowers when they have just married and out walks their child about 5 years old and gets on his dad's bicycle ! 

But it was the time of Nazi Germany and so angry German soldiers appear from somewhere and take captive hundreds of Italian men who are taken  to a prison camp. The young boy is forced to stay with his father in a crowded room which has wooden bunk beds where several dozen men are squeezed in! They are separated from the mother who is in another part of the camp !

To avoid the kid from panicking, his dad tells him that this is a game and at the end they will win a tank. He continues this positive charade in front of the kid till the end. Specially hilarious is the scene where he volunteers as a German to English translator for a German soldier without knowing any German! 

In the end, our hero goes out looking for his wife after hiding his son in a metallic box on a street and is shot and killed just like that by a German soldier. Then the streets become empty as the German soldiers seem to have vanished. The young boy comes out from his hiding place and stands on the empty street when he hears the roar of an approaching tank.  He stands his ground when the tank stops very close to him. (This is the tank which his dad had promised he would win at the end of the game.) Out pops the head of a cheerful American soldier from the tank who invites the young boy to climb onto the tank. You see, the Americans are here to save him and his country from the Germans!

Which is why this movie won Oscars! I remember watching slim Benigni jumping over the heads of the seated audience to reach the Oscar stage after hearing his name being announced!

It's a beautifully sad movie.

Trap , the movie.

 Thankfully there is only a hint of violent behavior and not explicit brutality in this movie making it watchable. The main character in this movie is also called Cooper. 

Cooper takes his daughter to a concert by Lady Raven, a pop singer. He is a doting father and indulges his daughter as any American Dad would, I assume. Gradually and confusingly, we discover that Cooper starts doing ‘weird’ stuff like pushing a girl down the stairs for no apparent reason! We also see him observing a captive young man through a camera app on his phone. Which makes him seem even weirder, you see! Did Cooper deliberately lock the man before leaving his house or is that young man an intruder on Cooper's property who gets accidentally trapped?

We see a large team of police officials arrive suddenly and surround the stadium. They are looking for a serial killer named ‘the butcher’ who is also inside the stadium! Our hero, Cooper seems weird but not a butcher yet, we still can't connect the dots.

Then we notice him raising the temperature of the  fryer while passing a fast food joint causing it to explode and burn a server. But before the explosion, we are shown bottles filled with alcohol inside the overheated oil pan. Cooper didn't place those bottles in there .(And because the director only shows the close up of a hand turning the fryer knob higher while Cooper is close by we have to assume that Cooper did it.) Then Cooper saves the life of a  fainting girl by carrying her to a nurse's station after he notices a group of concert workers place her against a railing near Cooper while he is watching his girl dance with lady Raven from the side of the stage. 

Surprisingly, Cooper forces Lady Raven to give him and his daughter a ride (using the life of the captive man as bait) in her limousine so he can escape without being noticed by the police.After a few twists and turns, Lady Raven exposes Cooper as being the butcher and helps the man who was Cooper’s prisoner somewhere escape with the help of her online fans.

Towards the end, Cooper is shown as suffering from a motherly complex which is what the police use to capture him…So the question is, is Cooper a ‘Dr. Jekyll and Mr. Hyde ‘ type of personality or a victim of circumstances with a psychological disorder?!

Anyway, the entire concert was a trap to catch the butcher. We have seen this type of stuff in old psycho thrillers but not in this low key way where the environment ( shops, crowds etc) surrounding the main characters continues as usual with very little hint of a crime unfolding - a unique Shyamalan approach. 

Circles & Squares: A new approach!

By,

Ravindra Loomba 

In high school, we learnt that the area of a circle is Pi (π) times square of its radius(r). I had no clue as to the origin of this formula (π• r squared). All of us learnt it by rote. It was a fundamental formula someone discovered, we rationalized.Just as the formula for the area of a square whose each side equals r is (r times r).

However, recently  I spent some time thinking upon this formula and the mystery unfolded. The formula doesn't seem that mysterious now. If you draw a square with each side equaling 2r, which contains four equal squares with each side r , then the area of the circle with radius r inscribed within will be slightly bigger than the area of three of these squares. Actually, the area of this circle will be 3.1416 times the area of a single square of side r! That is the original formula we mentioned in first para, where the number 3.1416 is represented by the special character π.

With this information we can deduce the areas of squares and circles much easily. If we know the area of square then the area of the circle inscribed within is 78.54 % of the area of that square.

Happy New Year

 To the readers of this blog

.. if you can afford it !

US & WE!

 More than a decade ago I got my first taste of hummus after my daughter suggested trying a wrap. Then it dawned on me that the word hummus has a special meaning if you know Hindi.

Depending on the context in which the Hindi word ‘hum’ is used it can mean 'us' or 'we'.

Therefore, 

        HUM = US (Hummus)

     & HUM = WE (Humvee)

Strange but true!

Merry Xmas 

How Am I!???#@

 The new acquaintance asked me ‘hello, how are you?’

 That upset me beyond repair and I ask her

‘who are you to ask me how I am? Are you my dad or grandpa or my spouse ?Why should I share my personal information with you? Did I ever ask you how you are?! Next you will be waiting in the parking lot with a fake smile and telling me ‘honey, let us go shopping ‘ like we just got married! Do I even know your name ?

Was that your brother who stole part of the exhaust system of my vehicle and is trying to resell it to me for a few thousand. And is that your sister who is using my health insurance to have her kids treated? When your glucose goes high you can give me diabetes as well ‘honey’!