Continued fractions are a fascinating way to represent never ending, never-repeating decimal expansions like pi or e.
As a fun exercise on this Friday evening, take out your smart phone and open the calculator app and try this :
What do you get? Do you recognize this number? If you did, then try answering why it mysteriously popped out of nowhere to represent this continued fraction.
It’s not possible unfortunately to catch a rainbow. They are not objects and are not located at specific distance from the observer that one can physically approach.
Rainbows stems from an optical illusion caused by any water droplets viewed from a
certain angle relative to a light source.
They are user-specific and everyone sees a different rainbow.
The monochrome rainbow
Not all rainbows that occur in nature are multicolored. Under specific
atmospheric conditions, one can spot the Mono-chrome rainbow i.e It has
only one color.
A Moonbow / Lunar rainbow /White rainbow is a
rainbow produced by light reflected off the surface of the moon (as
opposed to direct sunlight) refracting off of moisture-laden clouds in
the atmosphere / from waterfalls.
Just as no two people see exactly the same rainbow, even if they’re
standing next to each other, the few inches between your eyes make a
difference in what you are viewing.
There is no color- indigo ( sort of )
One can distinguish almost all colors in a rainbow but Indigo.
Legend has it that Newton
included indigo because he felt that there should be seven rather than six colors in a rainbow due to his strong religious beliefs.
Origins of ‘Iris’
The Greeks and Romans thought a rainbow was the path made
by Iris, the goddess of the rainbow, between heaven and earth, linking
gods with humans. “Rainbow” in Latin is arcus iris or arcus pluvius, a “rainy arch”.
The iris of the eye is named after her, because of its
colour.
The
Greeks used the word “iris” to describe any coloured circle, such as
the “eye” of a peacock’s tail. The flower called iris gets its name from
the Greek, as does the chemical iridium (Ir), compounds of which are
highly coloured. Iris is also the root of “iridescent”.
Pulsating Rainbows
Place a linear polarizer over the camera whilst capturing a rainbow and you get pulsating rainbows.
A double rainbow is a phenomenon in which two rainbows appear. They are caused by a double reflection of sunlight inside the raindrops. Similarly multiple rainbows are a possibility as well.
This video of a man witnessing a double rainbow for the first time went viral, featuring on numerous popular talk shows. Pure ecstasy!
The full rainbow
Whilst standing on earth, we see rainbows as magical arcs across the sky, but rainbows are full circles. The bottom part of the full circle is usually blocked by the horizon.
Pilots however do not face this difficulty. Under the right sky conditions, pilots are spectators to one of nature’s most beautiful spectacles – The full rainbow.
There doesn’t seem to be a shadow casted on the wall in the above image of a burning matchstick. So, does that mean that fires don’t cast shadows at all?
One common argument that follows is:
Fire is a source of light, hence cannot cast a shadow
But, that arguments falls apart, when you realize that:
Sure, fire is a source of light but it is not the brightest
Why does this phenomenon occur when the light source behind the flame is brighter ?
I could reveal the answer, but Its even better when you think about it and comprehend it for yourself. Wouldn’t want to deprive you of that excitement , now would I ?
There doesn’t seem to be a shadow casted on the wall in the above image of a burning matchstick. So, does that mean that fires don’t cast shadows at all?
One common argument that follows is:
Fire is a source of light, hence cannot cast a shadow
But, that arguments falls apart, when you realize that:
Sure, fire is a source of light but it is not the brightest
Why does this phenomenon occur when the light source behind the flame is brighter ?
I could reveal the answer, but Its even better when you think about it and comprehend it for yourself. Wouldn’t want to deprive you of that excitement , now would I ?
Why are wheels circular? Why aren’t they triangular or square shaped?
That is a question that you might have pondered at some point in your life ( perhaps as a shower-thought? ) But sometimes even the most simple questions have the most elegant answers!
A square wheel can roll smoothly if the ground consists of evenly shaped inverted catenaries of the right size and curvature.
What is a Catenary?
Well, it is the curve that a hanging cable assumes under its own weight when supported only at its ends. You find these everywhere!
Those chains on the pavement,
those hanging cables on a power transmission station,
or maybe a chandelier is of your type
All are catenaries!
Although it superficially resembles a parabola, it is NOT!
Practicality
The mythbusters (like always) decided to give the four wheel vehicle a try.
And found out that, get this – with speed, a truck fitted with square wheels can deliver a relatively smooth ride, despite that bouncy start!
Well, although circular wheels still remain as the king of wheels, it is nice to know that we do have some alternatives up our sleeve!
If you were like me, it took me some thinking after the episode to grasp the intricacies of this joke. The scripting of the show is truly remarkable in these retrospects. Here’s what it means:
If you look at a screw, one piece of metal (an inclined plane ) wraps around another metal ( an axis ) in a spiral ( helically ).
I recorded a new pattern on my smart phone a couple of days ago, known as the Knight’s tour and wish to share my ecstasies of this pattern in this post.
A knight’s tour is a sequence of moves of a knight on a chessboard
such that the knight visits every square only once.
If the knight ends
on a square that is one knight’s move from the beginning square (so that
it could tour the board again immediately, following the same path),
the tour is closed, otherwise it is open.
Here is the knights tour on a 5×5 board:
And on a 8×8 board:
Stop right there!
We always look for inspirations to start anything:
If you have noticed, my pattern is not exactly a true knights tour because I was not smart enough to come up with one. Can you ?
Also I couldn’t get it to work with 4×4 too. Maybe you can help me out.
Like most things in mathematics and sciences, you need to experience it for yourself to truly appreciate the profundity of the Knight’s tour.
You can start with 3×3 and move on to higher orders.
It often comes as a surprise to people when i tell them that the space station can be seen with the naked eye! Flying at 400 km above your head, the ISS looks like a really fast moving airplane in the sky.
The ISS isn’t brighter than the day sky and hence cannot be seen during the day. But in the night, it’s the third brightest object in the sky! It reflects the sunlight off the solar panels on its surface.
Spot the station!
If you would like to see the ISS for yourself, NASA ‘s Spot the station! is at your disposal. Register with your email address/mobile number and every time the ISS passes by your town/city, you will get a notification with the time, duration and inclination.
Have fun!
(Extras: There are mobile phone apps which you could use too, like the ISS detector satellite detector for android. At the end of the day all that matters is what is convenient to you.
Ecstasy Shots 
