Pi Day - Once In Hundread Years Celebration

Happy Pi Day wishes to everyone ...

pi value = 3.1415926 ... & so celebrate the pi value on 3-14-15 @ 9:26 AM which occurs only once in hundred years ...And today is the day ... lets celebrate it ...

Check out the Origin & History of Pi

1/8 Vs. 1/4 ( 1/8 LARGER than 1/4 )

1/8 Vs. 1/4 (1/8 LARGER than 1/4)

Can anyone can tell me which is greater among 1/4 and 1/8 ? Normally we will answer this question with 1/4 . Lets make a difference in this . I say 1/8 is larger than 1/4 . Let me Prove 1/8 is larger than 1/4 .

We Know that ,

3 > 2   
3 log(1/2) > 2 log(1/2)    // Multiply log (1/2) on both sides ..( log means log base 10 )
log[(1/2)³] > log[(1/2)²]  // Property of logrithms
(1/2)³ > (1/2)²   // Take anti-log on both sides
1/8 > 1/4

Here is my solution to prove something not possible . Can you find the fallacy I have used in this Proof ? 

Ans :  The Answer is that the multiplication of log(1/2) in the second step is the fallacy . In reality , log(1/2) is a negative value .

1 Equals 0 (FALLACY)

1=0

(n+1)2 = n2+2n+1
                                //Expansion

(n+1)2-(2n+1) = n2

                                //Subtract from both sides

(n+1)2-(2n+1)-n(2n+1) = n2-n(2n+1)
                                //Add to both sides

(n+1)2-(n+1)(2n+1) = n2-n(2n+1)
                                //Factor

(n+1)2-(n+1)(2n+1)+(2n+1)2/4 = n2-n(2n+1)+(2n+1)2/4
                                //Add to both sides

[(n+1)-(2n+1)/2]2 = [n-(2n+1)/2]2
                                //Factor

(n+1)-(2n+1)/2 = n-(2n+1)/2
                                //Take square roots of both sides

n+1 = n
                                //Subtract from both sides

1 = 0

Impossible!

The operations listed above utilize basic arithmetics to arrive at the false conclusion. Starting by simply expanding a squared equation, we can subtract 2n+1 from both sides to isolate n2. Subtracting n(2n+1) from both sides now allows the left side to be factored. Adding (2n+1)2/4 to both sides once again will enable both sides of the equation to be factored down to squared forms. By taking the square roots and then subtracting the n-(2n+1)/2, the proof is complete and 1=0.

If two numbers are equal, their squares are also equal. However, the reverse form of such a statement does not hold. In short, u = v does not imply square root of u equals square root of v due to the fact that the result of a square root is not unique. Without this fact, the above proof becomes actually legitimate.

Is Zero A Prime Number Or A Composite Number ?

Zero - Prime Or Composite

                   Most of us will be wondering whether the number (awesome & unique number) is either prime or composite . The general explanation you might have received is that ZERO is not a natural number and so it is neither prime nor composite . Well , of course , the answer is correct . Zero is Neither Prime Nor Composite but the way of explaining is not correct and is not logically valid .

                   We all know the definition of the PRIME Number . The Prime Number is a number which has exactly two factors 1 and itself . But Zero has infinitely many factors i.e., zero is divisible by all numbers except zero and so zero can never be a Prime Number .

                    Now lets jump on to the definition of a COMPOSITE Number . The Composite Number is a number which can be represented by the product of any two positive integers , neither of which can be itself . Since Zero can never be represented as a product of two non-zero positive integers , it can also never be a Composite Number . 

                     As ZERO can never be a Prime number and also a Composite number , ZERO is NEITHER PRIME NOR COMPOSITE .

Different Methodology In Multiplication

Different Methodology In Multiplication


           This is a new methodology in Multiplication used to make the kids understand the multiplication more clearly and perfectly . This can help the kids do the multiplication correctly using this method .

Image Of A Number

Image of a Number

                  The image of a number is constructed in the way that the image contains as many angles (curve) as the value number . For example , consider zero which does not contain any angle (curve) as that of its value .... But currently most of us are not using the actual image to denote the numbers .

The Mysterious Zero / Infinity

THE  MYSTERIOUS  ZERO  /  INFINITY 




Zero is behind all of the big puzzles in physics. In thermodynamics a zero became an uncrossable barrier: the coldest temperature possible. In Einstein's theory of general relativity, a zero became ablack hole, a monstrous star that swallows entire suns and can lead us into new worlds. The infinite density of the black hole represents a division by zero. The big bang creation from the void is a division by zero. In quantum mechanics, the infinite energy of the vacuum is a division by zero and is responsible for a bizarre source of energy -- a phantom force exerted by nothing at all. Yet dividing by zero destroys the fabric of mathematics and the framework of logic -- and threatens to undermine the very basis of science.


The biggest challenge to todays physicists is how to reconcile general relativity and quantum mechanics. However, these two pillars of modern science were bound to be incompatible. "The universe of general relativity is a smooth rubber sheet. It is continuous and flowing, never sharp, never pointy. Quantum mechanics, on the other hand, describes a jerky and discontinuous universe. What the two theories have in common -- and what they clash over -- is zero." "The infinite zero of a black hole -- mass crammed into zero space, curving space infinitely -- punches a hole in the smooth rubber sheet. The equations of general relativity cannot deal with the sharpness of zero. In a black hole, space and time are meaningless."


"Quantum mechanics has a similar problem, a problem related to the zero-point energy. The laws of quantum mechanics treat particles such as the electron as points; that is, they take up no space at all. The electron is a zero-dimensional object, and its very zerolike nature ensures that scientists don't even know the electron's mass or charge." But, how could physicists not know something that has been measured? The answer lies with zero. According to the rules of quantum mechanics, the zero-dimensional electron has infinite mass and infinite charge. As with the zero-point energy of the quantum vacuum, "scientists learned to ignore the infinite mass and charge of the electron. They do this by not going all the way to zero distance from the electron when they calculate the electron's true mass and charge; they stop short of zero at an arbitrary distance. Once a scientist chooses a suitably close distance, all the calculations using the "true" mass and charge agree with one another." This is known as renormalization -- the physicist Dr. Richard Feynman called it "a dippy process."


The leading approach to unifying quantum theory and general relativity is string theory. In string theory each elemental particle is composed of a single string and all strings are identical. The "stuff" of all matter and all forces is the same. Differences between the particles arise because their respective strings undergo different resonant vibrational patterns -- giving them unique fingerprints. Hence, what appear to be different elementary particles are actually different notes on a fundamental string. In string theory zero has been banished from the universe; there is no such thing as zero distance or zero time. Hence, all the infinity problems of quantum mechanics are solved.


But, there is a price that we must pay to banish zero and infinity. The size of a typical string in string theory is the Planck length, i.e., about 10^-33 centimeters. This is over a thousand trillion times smaller that what the most advanced particle detection equipment can observe. Are these unifying theories, that describe the centers of black holes and explain the singularity of the big bang, becoming so far removed from experiment that we will never be able to determine their correctness? The models of the universe that string theorists and cosmologists develop might be mathematically precise, beautiful and consistent and might appear to explain the nature of the universe -- and yet be utterly wrong. Scientific models/theories, philosophies, and religions will continue to exist and be refined. However, because of zero and infinity, we can never have "proof". All that science can know is that the cosmos was spawned from nothing, and will return to the nothing from whence it came.