GUPTA's FORMULA

GUPTA's FORMULA

To find a², we can use the following formula :-

a² = (a+b)(a-b)+b²
b can be any number

VERIFICATION

This formula is useful to find squares of numbers like 99

99² = (99+1)(99-1)+1²
=100*98+1
=9801

Done fast, easily, and accurately!!!

SHAMBO'S RULE

If a number x is a square of another number y then the square of  y+1 is {x+(2y+1)}

EXAMPLE:

1024² =1048576 then [1048576+{(2*1024)+1}]=1050625=1025²

What a Fact!!!

• In Tokyo, a bicycle is faster than a car for most trips of less than 50 minutes!
• A lightning bolt generates temperatures five times hotter than those found at the sun's surface!
• Forest fires move faster uphill than downhill!
• Peanuts are one of the ingredient in dynamite
• The two-foot long bird called a Kea that lives in New Zealand likes to eat the strips of rubber around car windows.
• A group of geese on the ground is a gaggle, a group of geese in the air is a skein!
• Clinophobia is the fear of beds
• The Earth weighs around 6,600,000,000,000,000,000,000 tons (5,940 billion billion metric tons)

WHAT IS SCIENCE

Science (from Latin scientia, meaning "knowledge") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. In an older and closely related meaning, "science" also refers to a body of knowledge itself, of the type that can be rationally explained and reliably applied.

 In an effort to understand the history of the natural world and how the natural world works, with observable physical evidence as the basis of that understanding. It is done through observation of natural phenomena, and/or through experimentation that tries to simulate natural processes under controlled conditions.

Mass of photon

A  mass of a photon can be calculated by Einstein's equation

E = mc²

m = e/c² 

and 

Energy of a photon = h(Planks Constant) * c(speed of light ) / wavelength

.

so mass of a photon = (hc/wavelength )/c²

m = 6.626*10^-34/wavelength / 299792458

for a light ray of red colour

wavelength = approx 400nm = 4 * 10^-7m

so 

m =( 6.626*10-34 / 4 * 10^-7 )/ 299792458 

= 5.525489236957388701219428275277 * 10-36 kg

for a photon of red colour with wavelength = 400nm

this way we can calculate the mass of any photon with a known value of wavelength or frequency

Das' rule Version 2

any number multiplied by 3,4,5 and the result arranged in ascending order will be a Pythagorean triplet.

eg-  2
2(3,4,5) = 6,8,10 (arranged in ascending order from the starting).

6,8,10 is a Pythagorean triplet.


45
45(3,4,5) = 135, 180, 225

so 135, 180, 225 is definitely a Pythagorean triplet.



NOTE: this rule is also true for 5,12,13

eg

2(5,12,13) = 10,24,26

also 10,24,26 is a Pythagorean triplet

it seems We are not alone

NASA just found something strange!! About 2 BILLION Earth like planets found(WOW)

Are conservation laws correct!

case - In an isolated system, a 5 kg ball 'A'  with 10 m/s velocity is made to hit a 10 kg ball 'B' at rest. After collision the balls move together in the same direction .The plane and the balls are friction less and there is vacuum in the system( zero drag).

According to conservation of energy:
 Total energy after collision = Total energy of the system initially 
                                         =  energy of ball A + energy of ball B 
                                         = 1/2 mv*v  + 1/2 mv*v
                                         = (1/2 x 5kg x 10m/s x 10m/s) + (1/2 x 10kg x 0m/s x 0m/s)
                                        =  250 J  --------------( 1)

According to conservation of momentum:
     Total momentum of 2 balls before collision = Total momentum of balls after collision
=> mu(A) + mu(B)                       =   v[m(A) +m(B)]       { u = initial velocity ; v = final velocity of the balls}
=> 5kg x 10m/s + 10kg x 0m/s     =   v[5kg + 10kg]
=> 50kg m/s                                 =   v[15kg]                   
=> v                                             =   10/3 m/s

Now , Total energy after collision  = 1/2  * m(A+B)  * v * v
                                                    = 1/2  * (5kg +10kg)  *10/3 m/s  *10/3 m/s
                                                    = 83.33 J  --------------------(2)
(1) and (2) contradicts each other .

Hence either of the laws is wrong !

  

Finding roots of quadratic equations

As we know for a quadratic equation ax² + bx + c = 0 , where a is not = 0 , have many ways of solving them ( finding roots ), those methods include factorization (mid term splitting ) , completing squares and quadratic formula , now here is a method made by me for finding roots.
Take any quadratic Equation , for example
x² - x - 6 = 0
here a = 1 , b = -1 , x = -6
 α+ß = -b/a = 1
αß = c/a = -6

now
(α + ß )² = α² + ß² + 2αß
1 = α² + ß² - 12
α² + ß²  = 13

(α - ß)² = α² + ß² - 2αß
(α - ß)² = 13 + 12
α - ß = ±5

on subtracting the equations
Case 1 where α - ß = 5
(α + ß) - (α - ß) = 2ß = -4 , ß = -2 , so one root of the polynomial is -2 , α - 2 = 1 , α = 3 , this is another root .
Case2 where α - ß = -5
(α + ß) - (α - ß) = 2ß = 6 , ß = 3 , so one root of the polynomial is 3 , α + 3 = 1 , α = -2 , this is another root . so if we take any one case , we will get the roots of the polynomial

White holes

White holes, unlike their black hole neighbors, have not been studied because they only exist in an extremely hypothetical situation. In fact, there’s not even a clear understanding what a white hole could be. Is it the other end of a black hole? Is it a wormhole? Is it something else entirely?
Generally, white holes are thought to spit out matter, much like black holes eat matter. For this to happen, the matter that passes through a black hole would have to be protected during the voyage, avoiding the process of merging into singularity. No white holes have ever been detected, up to this point, and no black holes have been seen without an event horizon (the guarding force around a black hole that prevents us from seeing them) that may show us just how matter passes through. To do that, white holes would have to break a few laws of physics and reinstitute some ideas that have been discarded; that’s asking a lot. Until then, white holes are best left for hypothetical ideas or naughty jokes.

Amazing Facts

• A strong jet stream can add or subtract microseconds from a day
• Amyotrophic lateral sclerosis is an illness that only 4 % of the people that have it live for more than 10 years. However, Stephan Hawking has survived for over 50 years with it! Making him one of the strongest human beings around.
• For over 150 years, scientists have known that fires can be extinguished with sound waves, but they still don't know how

Coal Ash Is More Radioactive than Nuclear Waste

• By burning away all the pesky carbon and other impurities, coal power plants produce heaps of radiation
• Neurologist Oliver Sacks reported a case of a man whose perception of time was so radically skewed that it took him several hours to wipe his nose, even though he felt like he was doing it at a normal rate.
• Although you might not want to leave your protective gear(helmet) at home, just know that if you do, drivers will be a lot more scared of hitting you.

Protein TITIN

Titin is the biggest protein found till now and it's scientific name is 189,819 letters long.  189,819 letters long.

It can't be posted in the blog and so check out this link below:-

http://www.sarahmcculloch.com/luminary-uprise/2009/longest-word/

 It's only a single word!!!

You wont be able read the full of it as it is sooooooooo long!!

Branches of SCIENCE

SCIENCE is divided in 4 parts one of which is natural science.
It is further divided to what we study majorly:

1. Physical

•   Physics
•   Chemistry

    2.  Earth

•   Ecology
•             oceanography
•             meteorology
•             geology

    3.  Life

•  Biology
•             zoology
•             botany
•             human biology

Scientists bind photons to create new state of matter

The physicists were exploring the properties of photons – an elementary particle that is the most basic constituent of light and all other types of electromagnetic radiation – when they managed to create molecules formed from photons bound together.What they have done is that create a special type of medium in which photons interact with each other so strongly that they begin to act as though they have mass, and they bind together to form molecules.To get the photons to interact with one another , physicists cooled rubidium atoms in a vacuum chamber to just a few degrees above absolute zero – the coldest possible temperature at which particles do not move. When two photons were fired at the cloud they did not pass through it and exit individually (as had been expected) but emerged on the other side as a single molecule. This was due to the Rydberg blockade, which states that when an atom is excited (has energy imparted to it) nearby atoms cannot be excited to the same degree.

Our Brain to heart wire connections

Everything in our body is controlled by the brain, even the functioning(pumping) of the Heart. Now our brain uses electrical impulses to to give such commands. Now is a person's heart is not working then he/she is considered dead. The pumping of the heart is involuntary and is controlled by the mid-brain. My saying is that if we can send an impulse of the same current and frequency that the mid-brain sends to the heart then we can make the heart pump.