Archives November 2013

"An enormous amount of water is thrown out... by means of a trifling amount of labor."   Diodorus siculus, historian The Archimedes screw was first mentioned in the writings of Athenaeus of Naucratis in 200 B.C.E. He described the use of a screw mechanism to extract bilge water from a ship named Syracusia, and attributed its invention to Archimedes. Archimedes (c. 287-212 B.C.E.) himself lived in Syracuse, Sicily, and was devoted to the exploration of mathematics and science. The polymath is thought to have spent time studying in Egypt, and the screw named for him is used in the Nile delta to this day, more than 2,000 years later, as a means to raise water from rivers for irrigation purposes. The Archimedes screw consists of a helix within a hollow tube, the lower end of which is placed in a fluid. The screw is then rotated and the fluid is more...

In mathematics a combination is a way of selecting several things out of a larger group, where (unlike permutations) order does not matter. In smaller cases it is possible to count the number of combinations. For example given three fruit, say an apple, orange and pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally a k-combination of a set S is a subset of k distinct elements of S. If the set has n elements the number of k-combinations is equal to the binomial coefficient          which can be written using factorials as   more...

Science has revolutionized our life. It has considerably altered the world by its wonderful discoveries and inventions. It has created mysteries. No aspect of our life remains untouched of science, whether at home or in school or in office. It is predominant in every walk of life. It has done not only concrete services to mankind but also filled us with wonder by making impossible things possible for us. Thus it is science which has make helpless man the king of the universe, removed the darkness of ignorance with light of knowledge and changed Our thorny life into the bed of roses. Science has been a potent factor to shape the history of man's civilization on earth. Our forefathers lived a nomadic life, and we are now living in the atomic age. This long leap from the jungle to the atomic civilization could be possible only through science. It is more...

Possibly in 1834, Robert Anderson of Scotland created the first electric carriage. The following year, a small electric car was built by the team of Professor Stratingh of Groningen, Holland and his assistant, Christopher Becker. More practical electric vehicles were brought onto the road by both American Thomas Davenport (1802-51) and Scotsman Robert Davidson (1804-1894) circa 1842. Both of these inventors introduced non- rechargeable electric cells in the electric car. The Parisian engineer Charles Jentaud fitted a carriage with an electric motor in 1881. William Edward Ayrton and John Perry, professors at the London's City and Guilds Institute, began road trials with an electrical tricycle in 1882; three years later a battery-driven electric cab serviced Brighton. Around 1900, internal combustion engines were only one of three competing-technologies for propelling cars. Steam engines were used, while electric vehicles were clean, quiet, and did not smell. In the United States, electric cabs more...

Useful as it might have been, an indication to drivers of how fast their automobiles were actually moving was not an option for pioneer motorists. The first production cars sported no such frivolous extras, but the race to develop suitable technology had begun. Extrapolating speed from the time taken to travel a given distance had been used for centuries, but it was a system for indicating an automobile's speed in real time—the speedometer proper—that was needed. The electric speedometer, in a form that would be recognized today, appeared between the late nineteenth and early twentieth centuries. Josip Belusic, a Croatian professor from the (then) Aystro- Hungarian region of Labin, was granted a patent for his electric "velocimeter" as early as 188-8. Other inventors were to produce various speedometers over the years that followed, and although most would achieve the required objective—to measure the rotational speed of the wheels or some more...

Definition:  Factorial: The number of sequences that can exist with a set of items, derived by multiplying the number of items by the next lowest number until 1 is reached. In mathematics, product of all whole numbers up to the number considered. The special case zero factorial is defined to have value 0!=1, consistent with the combinatorial interpretation of there being exactly one way to arrange zero objects. The notation n factorial (n!) was introduced by Christian Kramp in 1808. Permutation: An arrangement is called a Permutation. It is the rearrangement of objects or symbols into distinguishable sequences. When we set things in order, we say we have made an arrangement. When we change the order, we say we have changed the arrangement. So each of the arrangement that can be made by taking some or all of a number of things is known as Permutation.  Combination: A Combination is more...

Definition:  Permutation: An arrangement is called a Permutation. It is the rearrangement of objects or symbols into distinguishable sequences. When we set things in order, we say we have made an arrangement. When we change the order, we say we have changed the arrangement. So each of the arrangement that can be made by taking some or all of a number of things is known as Permutation.  Combination: A Combination is a selection of some or all of a number of different objects. It is an un-ordered collection of unique sizes.In a permutation the order of occurence of the objects or the arrangement is important but in combination the order of occurence of the objects is not important.   Formula: 

• Factorial=n! = 1*2*3*...*n.
• Permutation = nPr = n! / (n-r)! 
• Combination = nCr = nPr / r! =n!/(n-r)! r!

where,       more...

Permutation  ï»¿ A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. The number of permutations on a set of nelements is given by n! (n factorial;  For example, there are  2!=2·1=2 permutations of {1,2}, namely {1,2}and {2,1}, and 3!=3·2·1=6 permutations of {1,2,3}, namely {1,2,3}, {1,3,2}, {2,1,3}, {2,3,1}, {3,1,2}, and {3,2,1}.  The number of ways of obtaining an ordered subset of k elements from a set of n elements is given by       You will get a detailed knowledge at the given below different links : http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/factorial-1/1611 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-2/1612 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-3/1613 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-4/1614 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-5/1615 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-6/1616 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-7/1617 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-8/1618 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-9/1619 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-10/1620 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-11/1621 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-12/1622  

BuoyancyIn science, buoyancy  is an upward force exerted by a fluid that opposes the weight of an immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the column than at the top. This difference in pressure results in a net force that tends to accelerate an object upwards. The magnitude of that force is proportional to the difference in the pressure between the top and the bottom of the column, and (as explained by Archimedes' principle) is also equivalent to the weight of the fluid that would otherwise occupy the column,  i.e.,  the displaced fluid. For this reason, an object whose density is greater than that of the fluid in which it is submerged tends to sink. If the more...

An allylic rearrangement or allylic shift is an organic reaction in which the double bond in an allyl chemical compound shifts to the next carbon atom. It is encountered in nucleophilic substitution. In reaction conditions that favor a SN1 reaction mechanism the intermediate is a carbocation for which several resonance structures are possible. This explains the product distribution (or product spread) after recombination with nucleophile Y. This type of process is called an SN1' substitution. Alternatively, it is possible for nucleophile to attack directly at the allylic position, displacing the leaving group in a single step, in a process referred to as SN2' substitution. This is likely in cases when the allyl compound is unhindered, and a strong nucleophile is used. The products will be similar to those seen with SN1' substitution. Thus reaction of 1-chloro-2-butene with sodium hydroxide gives a mixture of 2-buten-1-ol and 1-buten-3-ol. In this video Mr. more...