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Channa Bankapur
Works at Pragathi InfoTech
Attended IISc., Bangalore
Lives in Bengaluru, India
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Channa Bankapur

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Imagine while filling an official form, just like "Your Religion", you are asked to choose "Your Superhero" too. Those who chose a superhero other than their parent's choice are tagged rebellious. More so if someone doesn't want to choose any because they are all made-up and not entertaining anymore!
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Iron MAN !!!
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Channa Bankapur

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My dentist bro: Do you floss regularly?
Me: Do you back up your computer data regularly?
He: I did it an year back.
Me: Same here!
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#IndiaElections2014  
I don't want Congress to come to power. More so because RaGa may become the PM. AAP can't take majority seats by itself. They are most likely here to prove a point by defeating some highly corrupt politicians. If they get a significant chuck, they may have to make a coalition Government with Congress. Fear of another Congress rule. Coalition Governments are never good. They don't allow development work to happen and more chances of re-election, which is an economical burden to the country. BJP is any day better than Congress and NaMo is a great PM candidate because of his administrative style. So, we should vote for BJP this time. I don't mean to say BJP is corrupt-free. I also fear some Hindu religious enthusiasts may hijack the Government's agenda and affect the development work.

PS: It's just my opinion as of today. I couldn't follow much about politics this time. So, my opinion could be too uninformed!
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Agreed.. If I remember correctly when congress came in power in 2004 the main issues were corruption and FDI in telecom and today they are corruption and FDI in retail.. Nothing has changed
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Have him in circles
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Channa Bankapur

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It takes intelligence to act dumb!
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Are you talking about Man Mohan Singh ?
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Channa Bankapur

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Read somewhere: If religions were true, there wouldn't be so many of them.

Me: If any one religion was true, there wouldn't be any other religions.
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Not only are there so many of them (like fashions) but they contradict each other, but are nevertheless taken seriously by their adherents and by society as a whole (unlike fashion).
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Channa Bankapur

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Neat!
 
Adding cubes

If you add up the first n numbers and square the result, this produces the same answer as adding the first n cubes. The picture gives a wordless proof of this result.

The picture shows the case n=5. In this case, the sum of the first 5 natural numbers is 1+2+3+4+5=15, which squares to 15x15=225. On the other hand, the sum of the first n cubes is (1x1x1)+(2x2x2)+(3x3x3)+(4x4x4)+(5x5x5)=1+8+27+64+125, which also adds up to 225. There is nothing special about the number 5 here: an analogous identity holds for any other positive integer, and it can be illustrated by a similar picture.

So how exactly does the picture illustrate the equation? Well, the big square is a grid whose area is 15x15=225, where our unit of length is the side length of the smallest box appearing in the picture. The vertical strip to the right of the square and the horizontal strip below the square are each 1+2+3+4+5=15 boxes long. It follows that the total number of boxes in the big square is (1+2+3+4+5)^2.

On the other hand, consider the area of the red part of the big square. There are 5 red squares, each of which measures 5x5. The total red area is thus 5x5x5=125, or 5 cubed. Something similar happens for the dark blue squares, provided that the two half-squares on the left edge and top edge are combined to form one big 4x4 square. We then have 4 dark blue squares, each of which measures 4x4, giving a total dark blue area of 4x4x4=64, or 4 cubed. Adding up the areas of each colour gives a total area of 1+8+27+64+125, which is the sum of the first five cubes.

We have counted the integer-valued area of the big square in two ways. Both methods must produce the same answer, from which it follows that the equation must hold. This technique of counting a quantity in two different ways and equating the two results is what mathematicians call a combinatorial proof. The “sum of cubes” identity can be proved in a fairly mechanical way using the standard technique of mathematical induction, but that proof does not give any intuition for why the result should be true. A combinatorial proof, such as the one in the picture, gives a better idea of why the result should be true, and is therefore more satisfying to a mathematician than the other proof.

One might expect, given that there are cubes of integers appearing on one side of the equation, that a combinatorial proof of the result would involve summing volumes, but remarkably, it reduces to summing areas.

Combinatorial proofs are also known as counting arguments. Here's another post by me in which I explain, using a counting argument, why it is not possible for everybody on Google+ to have more than 5,000 followers (https://plus.google.com/101584889282878921052/posts/YV7j9LRqKsX). That post provoked some surprisingly negative reactions.

The picture is based on a picture from Brian R. Sears' website (http://users.tru.eastlink.ca/~brsears/math/oldprob.htm#p32). I found the picture in a recent paper by Johann Cigler (http://arxiv.org/abs/1403.6609) which examines some generalizations of the sum of cubes result.

#mathematics #scienceeveryday
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Channa Bankapur

commented on a video on YouTube.
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What's the buggy behavior here? Looks like it's working as intended!
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accuracy is off by far especially near edges
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Channa Bankapur

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Kannada movies actor Charanjeevi Sarja visited my brother's dental clinic.
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your bro's clinic is now celebrity's clicni
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People
Have him in circles
3,541 people
Work
Occupation
Software Engineer Manager
Employment
  • Pragathi InfoTech
    Co-Founder & Engineering Manager, 2013 - present
  • Google
    Software Engineer, 2010 - 2013
  • Adobe Systems
    Software Engineer, 2009 - 2010
  • Cisco Systems
    Software Engineer, 2005 - 2008
  • Mistral Solutions, Bangalore
    Software Engineer, 2001 - 2002
Places
Map of the places this user has livedMap of the places this user has livedMap of the places this user has lived
Currently
Bengaluru, India
Previously
Bangalore, India - Davanagere, India - Davangere, India - Noida, India
Story
Tagline
Building cool products that matter!
Introduction
Rationalist at heart, Atheist by choice.
India is my motherland, Kannada is my mother-tongue.
English is used more, Hindi is used rare.
Davanagere is my hometown, Bengaluru is where my home is.
Software-Engineer for a living, Married for living life.
Father of a boy to survive my genes, Nice-Guy to survive in the modern world.

Disclaimer: The views expressed by me in Google+ or elsewhere are mine (all mine!) and not my employer's.
Bragging rights
Worked in Google+ team at Google
Education
  • IISc., Bangalore
    Computer Science
  • BIET, Davanagere
    Computer Science
Basic Information
Gender
Male
Relationship
Married
Other names
ಚನ್ನ ಬಂಕಾಪುರ, Channabasavanna Bankapur Subhashchandra, ಚನ್ನಬಸವಣ್ಣ ಬಂಕಾಪುರ ಸುಭಾಷಚಂದ್ರ
Channa Bankapur's +1's are the things they like, agree with, or want to recommend.
Karthik Fashion
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Total Pool Free
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Simply the best touchscreen pool game in the world.- Realistic pool ball physics - 4 levels of difficulty against which to play - Intuitive

Karnataka anti-superstitious bill: 13 rituals considered evil practices ...
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The draft law — The Karnataka Prevention of Superstitious Practices Bill, 2013 — proposes death sentence for human sacrifice in the name of

Pragathi Infotech
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Pragathi Infotech hasn't shared anything on this page with you.

Chrome Browser - Google
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Browse fast with the Chrome web browser on your Android phone and tablet. Sign in to sync your Chrome browser experience from your computer

Battle Alert - Empire Defense
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Battle Alert is a real-time strategy (RTS) game which could bring back the nostalgia of having the World War II in a fun and challenging way

My nephew Varun Bankapur ate SAND while playing in it for the first time
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Normally, he gets excited to see my cell phone and runs to grab it. But, this is the first time I saw him not caring about my cell phone! Th

'Women invite sexual harassment': Madhya Pradesh Congress leader's shocker
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A Congress leader in Madhya Pradesh woman has made shocking remarks, blaming women for harassment.

Google Green
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Google is creating a better web that's better for the environment. We’re greening our company by using resources as efficiently as possible

Google Web Academy .
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Educational resources to succeed in internet economy

Galaxy Nexus
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Galaxy Nexus. First phone with Android 4.0, Face Unlock, Android Beam, an amazing HD screen and 4G LTE fast.

Google+ - Apps on Android Market
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Real-life sharing rethought for the web, wherever you are. Google+ for mobile makes sharing the right things with the right people a lot sim

Google +1 Button
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Recommendations when you want them. Learn more about the +1 button. The +1 button is shorthand for "this is pretty cool" or "

Google+: real life sharing, rethought for the web.
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Google+ aims to make sharing on the web more like sharing in real life. Check out Circles, Messenger and Hangouts, just a few of the things

Yahoo! Mail
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Stay connected - Access your inbox in just one tap - Stay on top of your new messages with notifications - Quickly scan messages in your inb

Google Chrome - Get a fast new browser. For PC, Mac and Linux
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Google Chrome is a browser that combines a minimal design with sophisticated technology to make the web faster, safer and easier.

Google India
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Updates and news from Google India

Faking News
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Leading news satire website of India

Google Politics & Elections
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Google Politics & Elections. Your elections hub to study, watch, discuss, participate in and make your impact on the digital campaign trail.

Google Search
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The fastest, easiest way to find what you need on the web and on your device.Google Search app for Android: The fastest, easiest way to find

Food: Very goodDecor: GoodService: Very good
Public - a year ago
reviewed a year ago
Great food :)
Food: ExcellentDecor: Very goodService: Very good
Public - a year ago
reviewed a year ago
Authentic North Indian food :)
Atmosphere: Very goodDecor: Very goodService: Very good
Public - a year ago
reviewed a year ago
Food: GoodDecor: Very goodService: Good
Public - a year ago
reviewed a year ago
17 reviews
Map
Map
Map
Satisfying Indian meal if you are okay with the average decor and look of the food.
Quality: ExcellentAppeal: GoodService: Good
Public - a year ago
reviewed a year ago
Public - a year ago
reviewed a year ago
Great ambience!
Food: GoodDecor: ExcellentService: Very good
Public - a year ago
reviewed a year ago