June 11, 2013
March 25, 2013
Mind Boggling Math Problems
For people who hate Math (like me,) Math has always been mind-boggling but not in a good way. So I was pleasantly surprised to see it goes from boring clerical numbers to the realm of magic (almost.)
So here are the facts from Live Science website:
So here are the facts from Live Science website:
Boring or Not?
Mathematics is one of the only areas of knowledge that can objectively be described as "true," because its theorems are derived from pure logic. And yet, at the same time, those theorems are often extremely strange and counter-intuitive.
Some people find math boring. As these examples show, it's anything but.
Some people find math boring. As these examples show, it's anything but.
Random Patterns
Weirdly, random data isn't actually all that random. In a given list of numbers representing anything from stock prices to city populations to the heights of buildings to the lengths of rivers, about 30 percent of the numbers will begin with the digit 1. Less of them will begin with 2, even less with 3, and so on, until only one number in twenty will begin with a 9. The bigger the data set, and the more orders of magnitude it spans, the more strongly this pattern emerges.
Because prime numbers are indivisible (except by 1 and themselves), and because all other numbers can be written as multiples of them, they are often regarded as the "atoms" of the math world. Despite their importance, the distribution of prime numbers among the integers is still a mystery. There is no pattern dictating which numbers will be prime or how far apart successive primes will be.
The seeming randomness of the primes makes the pattern found in "Ulam spirals" very strange indeed.
In 1963, the mathematician Stanislaw Ulam noticed an odd pattern while doodling in his notebook during a presentation: When integers are written in a spiral, prime numbers always seem to fall along diagonal lines. This in itself wasn't so surprising, because all prime numbers except for the number 2 are odd, and diagonal lines in integer spirals are alternately odd and even. Much more startling was the tendency of prime numbers to lie on somediagonals more than others — and this happens regardless of whether you start with 1 in the middle, or any other number.
Even when you zoom out to a much larger scale, as in the plot of hundreds of numbers below, you can see clear diagonal lines of primes (black dots), with some lines stronger than others. There are mathematical conjectures as to why this prime pattern emerges, but nothing has been proven.
SPHERE EVERSION
In an important field of mathematics called topology, two objects are considered to be equivalent, or "homeomorphic," if one can be morphed into the other by simply twisting and stretching its surface; they are different if you have to cut or crease the surface of one to reshape it into the form of the other.
Consider, for example, a torus — the dougnut-shape object shown in the intro slide. If you turn it upright, widen one side and indent the top of that side, you then have a cylindrical object with a handle. Thus, a classic math joke is to say that topologists can't tell their doughnuts from their coffee cups.
On the other hand, Moebius bands — loops with a single twist in them — are not homeomorphic with twist-free loops (cylinders), because you can't take the twist out of a Moebius band without cutting it, flipping over one of the edges, and reattaching.
Topologists long wondered: Is a sphere homeomorphic with the inside-out version of itself? In other words, can you turn a sphere inside out? At first it seems impossible, because you aren't allowed to poke a hole in the sphere and pull out the inside. But in fact, "sphere eversion," as it's called, is possible. Watch the video above to see how it's done.
Incredibly, the topologist Bernard Morin, a key developer of the complex method of sphere eversion shown here, was blind.
Prime Spirals
The seeming randomness of the primes makes the pattern found in "Ulam spirals" very strange indeed.
In 1963, the mathematician Stanislaw Ulam noticed an odd pattern while doodling in his notebook during a presentation: When integers are written in a spiral, prime numbers always seem to fall along diagonal lines. This in itself wasn't so surprising, because all prime numbers except for the number 2 are odd, and diagonal lines in integer spirals are alternately odd and even. Much more startling was the tendency of prime numbers to lie on somediagonals more than others — and this happens regardless of whether you start with 1 in the middle, or any other number.
Even when you zoom out to a much larger scale, as in the plot of hundreds of numbers below, you can see clear diagonal lines of primes (black dots), with some lines stronger than others. There are mathematical conjectures as to why this prime pattern emerges, but nothing has been proven.
SPHERE EVERSION
In an important field of mathematics called topology, two objects are considered to be equivalent, or "homeomorphic," if one can be morphed into the other by simply twisting and stretching its surface; they are different if you have to cut or crease the surface of one to reshape it into the form of the other.
Consider, for example, a torus — the dougnut-shape object shown in the intro slide. If you turn it upright, widen one side and indent the top of that side, you then have a cylindrical object with a handle. Thus, a classic math joke is to say that topologists can't tell their doughnuts from their coffee cups.
On the other hand, Moebius bands — loops with a single twist in them — are not homeomorphic with twist-free loops (cylinders), because you can't take the twist out of a Moebius band without cutting it, flipping over one of the edges, and reattaching.
Topologists long wondered: Is a sphere homeomorphic with the inside-out version of itself? In other words, can you turn a sphere inside out? At first it seems impossible, because you aren't allowed to poke a hole in the sphere and pull out the inside. But in fact, "sphere eversion," as it's called, is possible. Watch the video above to see how it's done.
Incredibly, the topologist Bernard Morin, a key developer of the complex method of sphere eversion shown here, was blind.
Wall Math
Though they may be decorated with an infinite variety of flourishes, mathematically speaking, there's just a finite number of distinct geometric patterns. All Escher paintings, wallpapers, tile designs and indeed all two-dimensional, repeating arrangements of shapes can be identified as belonging to one or another of the so-called "wallpaper groups." And how many wallpaper groups are there? Exactly 17
The Sonnet
"Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's Equation reaches down into the very depths of existence."
Stanford mathematician Keith Devlin wrote these words about the equation to the left in a 2002 essay called "The Most Beautiful Equation." But why is Euler's formula so breath-taking? And what does it even mean?
First, the letter "e" represents an irrational number (with unending digits) that begins 2.71828... Discovered in the context of continuously compounded interest, it governs the rate of exponential growth, from that of insect populations to the accumulation of interest to radioactive decay. In math, the number exhibits some very surprising properties, such as — to use math terminology — being equal to the sum of the inverse of all factorials from 0 to infinity. Indeed, the constant "e" pervades math, appearing seemingly from nowhere in a vast number of important equations.
Next, "i" represents the so-called "imaginary number": the square root of negative 1. It is thus called because, in reality, there is no number which can be multiplied by itself to produce a negative number (and so negative numbers have no real square roots). But in math, there are many situations where one is forced to take the square root of a negative. The letter "i" is therefore used as a sort of stand-in to mark places where this was done.
Pi, the ratio of a circle's circumference to its diameter, is one of the best-loved and most interesting numbers in math. Like "e," it seems to suddenly arise in a huge number of math and physics formulas. What Makes Pi So Special?]
Putting it all together, the constant "e" raised to the power of the imaginary "i" multiplied by pi equals -1. And, as seen in Euler's equation, adding 1 to that gives 0. It seems almost unbelievable that all these strange numbers — and even one that isn't real — would combine so simply. But it's aproven fact.
The Sonnet
 |
| Euler Identity |
"Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's Equation reaches down into the very depths of existence."
Stanford mathematician Keith Devlin wrote these words about the equation to the left in a 2002 essay called "The Most Beautiful Equation." But why is Euler's formula so breath-taking? And what does it even mean?
First, the letter "e" represents an irrational number (with unending digits) that begins 2.71828... Discovered in the context of continuously compounded interest, it governs the rate of exponential growth, from that of insect populations to the accumulation of interest to radioactive decay. In math, the number exhibits some very surprising properties, such as — to use math terminology — being equal to the sum of the inverse of all factorials from 0 to infinity. Indeed, the constant "e" pervades math, appearing seemingly from nowhere in a vast number of important equations.
Next, "i" represents the so-called "imaginary number": the square root of negative 1. It is thus called because, in reality, there is no number which can be multiplied by itself to produce a negative number (and so negative numbers have no real square roots). But in math, there are many situations where one is forced to take the square root of a negative. The letter "i" is therefore used as a sort of stand-in to mark places where this was done.
Pi, the ratio of a circle's circumference to its diameter, is one of the best-loved and most interesting numbers in math. Like "e," it seems to suddenly arise in a huge number of math and physics formulas. What Makes Pi So Special?]
Putting it all together, the constant "e" raised to the power of the imaginary "i" multiplied by pi equals -1. And, as seen in Euler's equation, adding 1 to that gives 0. It seems almost unbelievable that all these strange numbers — and even one that isn't real — would combine so simply. But it's aproven fact.
Business Insider: Startup Advice from Successful Entrepreneur
This article on Business Insider is good advice worth filing.
"You need space to try things and create. It takes a long time to recalibrate if you let people pull at you all the time. A lot of stress comes from reacting to stuff. You have to keep a certain guard [up], if you're a creative person. " - Pete Cashmore, Creator and CEO of Mashable.
"Many [business] people focus on what is static, black and white. Yet great algorithms can be rewritten. A business process can be defined better. A business model can be copied. But the speed of execution is dynamic within you and can never be copied. When you have an idea, figure out the pieces you need quickly, go to market, believe in it, and continue to iterate." - Gurbaksh Chahal.
"Pick a good market. The idea for approaching that market may change, but find a meaty problem to solve. You can try to attack it a bunch of different ways. Don't be too narrow." - Caterina Fake.
"Something worth doing might take a while, so really flesh out the potential of the business and be honest about whether it's worth doing. If it's not a $100 million company in five years, maybe it'll take 10 or 15 years. If you're doing something that has a universal, timeless need, then you need to think of the company in a timeless way." - Scott Heiferman, Meetup CoFounder.
"Don't spend money until you have money. When we used to put candy in our media kits, I would go to the Duane Reade store the day after Easter because the candy was on sale. Of course, it's important to spend on certain things in the beginning. You need good servers but you don't need Aeron desk chairs." - Daily Candy, Founder Dany Levy.
"A good idea is not enough. Business aren't just about ideas, businesses are about execution. Don't get too enamored with your own idea. Other people are going to have that same idea or something similar. You have to build a better team to execute it. You're only human, nobody has all the skills required to make a business work. [Ask yourself] what people are required to make it work for this idea, for this business?" - Brian Sharples.
"What I learned from Rockefeller that's off-the-hook important is: You need to know exactly where you stand in a business at all times. Measure everything, because everything that is measured and watched improves." - Bob Parsons, Go Daddy Founder.
The joy is in the getting there. The beginning years of starting your business, the camaraderie when you're in the pit together, are the best years of your life. So rather than being so focused on when you get big and powerful, if you can just get the juice out of that… don't miss it." - Barbara Corcoran.
"Don't be afraid to fail. My dad encouraged us to fail. Growing up, he would ask us what we failed at that week. If we didn't have something, he would be disappointed. It changed my mindset at an early age that failure is not the outcome, failure is not trying. "
"Get everything in writing, especially with business partners. When you're starting out, things can be quite friendly and exciting, but people's memory can change due to money. Obviously, better to have a lawyer do it, but at least have some written recollection that you are partners, who's responsible for what, and how much money each of you put in." - Marcia Kilgore
"You have a viable business only if your product is either better or cheaper than the alternatives. If it's not one or the other, you might make some money at first, but it's not a sustainable business."
- Jim Koch.
"Be true to yourself. If you follow that principle, a lot of decisions are actually pretty easy." - Tony Hsieh.
"Many [business] people focus on what is static, black and white. Yet great algorithms can be rewritten. A business process can be defined better. A business model can be copied. But the speed of execution is dynamic within you and can never be copied. When you have an idea, figure out the pieces you need quickly, go to market, believe in it, and continue to iterate." - Gurbaksh Chahal.
"Pick a good market. The idea for approaching that market may change, but find a meaty problem to solve. You can try to attack it a bunch of different ways. Don't be too narrow." - Caterina Fake.
"Something worth doing might take a while, so really flesh out the potential of the business and be honest about whether it's worth doing. If it's not a $100 million company in five years, maybe it'll take 10 or 15 years. If you're doing something that has a universal, timeless need, then you need to think of the company in a timeless way." - Scott Heiferman, Meetup CoFounder.
"Don't spend money until you have money. When we used to put candy in our media kits, I would go to the Duane Reade store the day after Easter because the candy was on sale. Of course, it's important to spend on certain things in the beginning. You need good servers but you don't need Aeron desk chairs." - Daily Candy, Founder Dany Levy.
"A good idea is not enough. Business aren't just about ideas, businesses are about execution. Don't get too enamored with your own idea. Other people are going to have that same idea or something similar. You have to build a better team to execute it. You're only human, nobody has all the skills required to make a business work. [Ask yourself] what people are required to make it work for this idea, for this business?" - Brian Sharples.
"What I learned from Rockefeller that's off-the-hook important is: You need to know exactly where you stand in a business at all times. Measure everything, because everything that is measured and watched improves." - Bob Parsons, Go Daddy Founder.
The joy is in the getting there. The beginning years of starting your business, the camaraderie when you're in the pit together, are the best years of your life. So rather than being so focused on when you get big and powerful, if you can just get the juice out of that… don't miss it." - Barbara Corcoran.
"Don't be afraid to fail. My dad encouraged us to fail. Growing up, he would ask us what we failed at that week. If we didn't have something, he would be disappointed. It changed my mindset at an early age that failure is not the outcome, failure is not trying. "
"Get everything in writing, especially with business partners. When you're starting out, things can be quite friendly and exciting, but people's memory can change due to money. Obviously, better to have a lawyer do it, but at least have some written recollection that you are partners, who's responsible for what, and how much money each of you put in." - Marcia Kilgore
"You have a viable business only if your product is either better or cheaper than the alternatives. If it's not one or the other, you might make some money at first, but it's not a sustainable business."
- Jim Koch.
"Be true to yourself. If you follow that principle, a lot of decisions are actually pretty easy." - Tony Hsieh.
October 7, 2009
ILLEGAL MDEDICINES IN INDIA
Please read very carefully -
inform all your friends and family members
India has become a dumping ground for banned drugs; also the business for production of banned drugs is booming. Please make sure that you buy drugs! Only if prescribed by a doctor (also, ask which company manufactures it, this would help to ensure that u get what is prescribed at the drug store) and that also from a reputed drug store. Not many people know about these banned drugs and consume them causing a lot of damage to themselves. This is far more important.
Dangerous drugs have been globally discarded but are available in India... The most common ones are action 500 & Nimulid!
Phenylpropanolamine: Cold and cough. Reason for ban: stroke.
Brand name: Vicks action-500
Cisapride: Acidity, constipation. Reason for ban : irregular heartbeat
Brand name : agarol
India has become a dumping ground for banned drugs; also the business for production of banned drugs is booming. Please make sure that you buy drugs! Only if prescribed by a doctor (also, ask which company manufactures it, this would help to ensure that u get what is prescribed at the drug store) and that also from a reputed drug store. Not many people know about these banned drugs and consume them causing a lot of damage to themselves. This is far more important.
Dangerous drugs have been globally discarded but are available in India... The most common ones are action 500 & Nimulid!
Phenylpropanolamine: Cold and cough. Reason for ban: stroke.
Brand name: Vicks action-500
________________________________________________________________________
Analgin: This is a pain-killer. Reason for
ban: bone marrow depression.Cisapride: Acidity, constipation. Reason for ban : irregular heartbeat
____________________________________________________________
Droperidol: Anti-depressant. Reason for ban :
irregular heartbeat.
______________________________________________________________
Furazolidone: Antidiarrhoeal. Reason for ban :
cancer.
_____________________________________________________________
Nimesulide:
________________________________________________________________________
Nitrofurazone: Antibacterial cream... Reason for
ban : cancer.
________________________________________________________________________
Phenolphthalein:Brand name : agarol
Brand name: enteroquinol
August 8, 2008
Cloud Computing Basics
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| Cloud Computing In 3 Lines |
The process from buying a computer to installing the Internet is so common that we do not realise that it is a complex process. And once we get used to it, we do not expect that it could get any easier than this. But it can, and the answer is in cloud computing.
How does the current system work?
Before we understand why cloud computing is a good alternative, let us just understand how the computer commonly works. First we buy a computer which is the hardware. But just the hardware will render the PC useless so we will need application software. There is a range of operating software available through the market such as Windows or Linux, and along with the operating software we will also need to buy the licences. And of course an Internet Connection through a service provider is absolutely essential. And through all this you will require a professional, first to assemble your computer and then to install the software and configure your computer as per requirement. And the whole process has to work every time you buy a new computer. Imagine how tedious the process will be for a company to go through the process with the number of computers in their office. What we don’t realise is the cost at each point of the process and how interdependent it is.
We can have a less complicated and easy process and this is where Cloud Computing comes into picture. In fact we happen to know and work with the predecessor of Cloud Computing. Let us say you disconnect the Internet will you still be able to use the Word or Excel sheet. Yes but if you were to disconnect the Internet and try to access the email, can we? No, because we are accessing the data through a remote server where all our email account data is exists. You use a web enabled program to access your account through various web-based email services like Hotmail, Yahoo or Gmail. Cloud Computing runs on a very similar line but a macro scale. Moreover, this will not require any new investment as it runs on all current computer devices. It will be extremely beneficial to big companies as it will be a big solution to data storage.
What is Cloud Computing?
Cloud Computing is a technology that will simplify this process. Cloud computing is a system by which all of this services are built-in into your computer by a web-based program. How it simplifies the process is, it removes the hassles of installation, licenses and configuration. And simplicity is not just the only factor, but it is cost-effective too, because the same system can be used on multiple computers at once. What Cloud Computing does is, it rules out the concept of application software altogether as there is no need for version upgrades or license management on individual client computing devices. And since all of the data can be remotely stored external storage devices like CD or Flash Drives will be redundant.
So How Does Cloud Computing Work?
A person who will be using the Cloud Computing Technology, let’s call them Cloud Users. The Cloud User will need a device like computer, laptop, or a tablet and a connection to the Internet. The cloud user will login to a cloud provided by their service provider or by their company. Just like the current function the output of all processes can be observed on the monitor or the display of the user’s device. The cloud services are internet based can you can easily access them on your current Windows or Macintosh or Linux system. A person is billed according his usage.
Cloud computing has made a paradigm shift in the use of computers and data storage. Many major companies are adopting the technology and many big players are tilting in its favour. It does seem like Cloud Computing is the technology of the future.
August 1, 2008
The New Entrepreneur
Do you think all those successful entrepreneurs out there have an MBA degree? Now, everyone knows that Bill Gates was a drop out.
Degrees can get you jobs but if you want to venture out all by yourself you'll definitely need more than degrees.
I am a novice too. And learning everyday. And I can see myself making steady progress.
Here's a list of things to keep in mind before you venture out:
Do a reality check of the concept. Is it saleable, will anyone sponsor it (for ads or funds)?
You will surely need more than yourself to belive in the idea for it work.
Planning your finance
You really have to count out all the money you and your family will need to survive. The rest can go to business. You can sell your car and probably the gold but do not put your house at stake.
Your visiting card
You will be surprised but getting a visiting card is very vital to your business. I suffered a major setback because I was focussing so much on staff, advertising and other stuff. But in chance that I lost I realised without a visiting card I really don't exist. It is as essential as registering yourself or trademarking your logo. You can get an average style V card for as less as 800 bucks in India.
Degrees can get you jobs but if you want to venture out all by yourself you'll definitely need more than degrees.
I am a novice too. And learning everyday. And I can see myself making steady progress.
Here's a list of things to keep in mind before you venture out:
Do a reality check of the concept. Is it saleable, will anyone sponsor it (for ads or funds)?
You will surely need more than yourself to belive in the idea for it work.
Planning your finance
You really have to count out all the money you and your family will need to survive. The rest can go to business. You can sell your car and probably the gold but do not put your house at stake.
Your visiting card
You will be surprised but getting a visiting card is very vital to your business. I suffered a major setback because I was focussing so much on staff, advertising and other stuff. But in chance that I lost I realised without a visiting card I really don't exist. It is as essential as registering yourself or trademarking your logo. You can get an average style V card for as less as 800 bucks in India.
Advertising
They say, "If your business is doing well it's good to advertise, but if your business is doing bad you must advertise." It's true. Basically, advertising means visibility. And the mass psychology is more the visible you are, better your product is.
But on modest budget traditional ways of advertsing like tv, hoardings and newspapers etc. seem out of reach. But the key element here is Innovation. I gave out mugs embossed with my company logo and URL on it. I put a bumper sticker on my husband's car with my company name and URL. You can give out calenders, bookmarks or handouts. Believe me, for small, local businesses it works.
You can share your tips here too...
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