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What is clockwise and anticlockwise circular permutation and why sometimes it effects the number of permutations and sometimes not?
Nadirlaskar
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Will the number of permutations alwaysbe greater than the number of distinguisible permutations?
No, sometimes they will be equal (when all items being permutated are all different, eg all permutations of {1, 2, 3} are distinguishable).
Can angle measurements be negative?
Yes, although it may seem strange. Conventionally, on a Cartesian plane, angles are measured in an anticlockwise dirction, from the x-axis. Consequently, an angle in the clockwise direction could be considered a negative angle. It might be simpler to think of an angle of 359 degrees as one of -1 degrees, instead. Sometimes you need to subtract one angle from another and in that context, a negative measure for the angle is implicit.
What is Greek mathematical symbol e?
The greek letter closest to representing the latin letter e is epsilon (ɛ). In math's, epsilon is mainly used to represent very small positive numbers (e.g. when working with proofs), and used as the Levi-Civita symbol (a.k.a. the permutation symbol, used in tensor calculus, sometimes uses upper epsilon E, instead of lower epsilon ɛ). It is also often used in statistics and numerical analysis to represent errors.
Are nonadjacent angles congruent?
Sometimes they are, sometimes they are not.
Are no adjacent angles congruent?
Sometimes they are, sometimes not.
What is the examples of circular permutation?
The most popular questions involving circular permutations are... How many ways can you seat n people around a round dinner table? Given n different colored beads, how many different bracelets can you make? Given n different Christmas ornaments, how many different door reefs can you make? Sometimes they ask you to pick k out of a set of n to form the permutation.
What is circular permutation?
A circular permutation is a type of permutation which has no starting point and no ending point. It is a set of elements that has an order, but no reference point. It circles back around on itself and encloses.For example, think of the number of ways of sitting 5 people around a circular table. If the chairs themselves are ordered then its a regular permutation problem, and is equivalent to sitting in a row at the movie theatre because the seats are as unique as the people who are to be sat. Any object, be it a main course or the hosts seat at a dinner party, or the ends of a row of seats, adds a reference point which makes it a linear permutation problem.If, on the other hand, the chairs are NOT ordered, the table is round, and all the people are unique... its a circular permutation problem because no seat is unique. There is no reference point that is independent of the people sitting. The uniqueness in seating is a result of a persons placement in relation to other people. It is in fact the first person to sit which creates the reference point in which all other sitters sit relative to.Another example. Flags on a flag pole can be arranged like a regular (linear) permutation problem, because it is linear in shape and thus has a top (a reference point). But suppose you have 10 Christmas ornaments to arrange on a reef. If there is a reference point, such as a top to the reef whereby we hang the reef, then it is still a regular permutation problem. The hook is the reference point and all ornaments are placed relative to it.But if the reef has no top or reference, and you can hang the reef any which way you want... then its a circular permutation problem. Once the reef is made it has a fixed ornament order (a circular permutation) but may still be hung differently - depending on how you orientate the reef on the door and where you place the top, it may appear to be a different reef each time. This is because the top reference makes for a different linear permutation for a given circular permutation. Simply put, only so many reefs can be made with 10 Christmas ornaments. If rotating the reef is the only difference between two reefs, then they have the same circular permutation and are in fact the same reef design.That is the basic idea of a circular permutation.Suppose there are n objects and we wish to pick kof them to arrange in a circular permutation. The number of circular permutations are...(k-1)! * nCk =nPk / kAnd is sometimes denoted nP'k with a little prime tack mark above the P.For circular permutations, all elements have to be unique and so without replacement. Unfortunately, I do not know how to solve a circular permutation with replacement problem... nor can I find such references online.Anyway, the basis of the formula is to take a regular permutation and adjust it for the fact that there is no reference point... any arbitrary starting point is just as good as another and does not increase the multiplicity of the pattern. The pattern on whole is what matters, not where it starts. Regular linear permutations count the same circular pattern k times, once for each of the k unique starting places in that pattern.An explanation of the math. The nCkfunction computes the number of ways to choosing, without order, k objects from n unique objects. Of those kunique objects, there are (k-1)! circular permutations. We multiply, as per the fundamental counting principle, to account for all possible orders of all possible combinations of picks. Likewise, nPk is the number of ways of permuting kobjects picked from n unique objects. As explained in the previous paragraph, k objects have the potential for k reference points, and so each circular permutation is counted k times when nPk is computed. Both expressions are algebraically equivalent.If you allow k=n then you are finding the circular permutations of all n-elements of an n-element set, no elements left out. Both expressions simplify into (n-1)!.Then, I suppose, if you need to get why k elements can be arranged in (k-1)! circular permutations in the first place... what relationship between this and the linear permutations of k elements being k! is there? Bare in mind that when the first person of k people sits at a round table, he is creating the reference point. He is arbitrary, but he also turns the circular permutation into a linear permutation. There are k-1 other people to be sat in k-1 other chairs. Voilà, (k-1)! is the number of permutations that exist under these circumstances.Up until now I have talked about what is called Fixed Circular permutations. A reef may not have a top, but it does have a front. This makes it fixed.Now suppose we took something like a bracelet with coloured beads. It is a circular permutation. But you can take that bracelet off of your wrist and turn it around, placing it back on your wrist backwards and so the permutation is now in reverse order. If you are able to do this in your problem, you have what is called Free Circular permutations. Every one unique bracelet, or fixed circular permutation, counts as two: one clockwise and one counter-clockwise. You only need half as many bracelets as there are fixed circular permutations. All you have to do is take the number of fixed circular permutations and divide by two:nP'k / 2
What does clockwise and anticlock wise mean?
These are words which describe the direction of circular motion, by referring to the motion of the hands on an analog clock. Basically, if you are proceeding around the circumference of a circle with the interior of the circle on your right-hand side, you are proceeding clockwise. If you have the interior of the circle on your left side, you are proceeding anticlockwise (sometimes also called counterclockwise).
Will the number of permutations alwaysbe greater than the number of distinguisible permutations?
No, sometimes they will be equal (when all items being permutated are all different, eg all permutations of {1, 2, 3} are distinguishable).
Why nature refers to the anti clock wise direction?
An insightful question. In the northern hemisphere, the gnomon on a sundial will have its shadow travel around the face, and in a clockwise direction! In the southern Hemisphere the travel will be anticlockwise. But the Northern guys got there first, hence clockwise. [Likewise, the northern guys named their pole North, and that settled that issue!] Even arbitrary can sometimes have logic behind it.
Other facts about the snail?
The pond snail nearly always has a right handed (dextral) to its shell but sometimes it is left handed (sinistral). As dextral snails circle anticlockwise and sinistral snails circle clockwise, an unusual consequence is that two 'mirror image' snails will circle in different directions and are frequently unable to mate. -science daily.com
What way do cyclones move?
Cyclones (which are always low pressure weather systems) spin in a clockwise direction in the southern hemsiphere and anticlockwise in the northern hemisphere (as viewed from space). Anticyclone refers to a system rotating on the reverse direction so: anti-clockwise direction in the southern hemsiphere and clockwise in the northern hemisphere. The word typhoon is sometimes used to refer to a cyclone that forms in the Pacific northwest, and the word hurricane to a cyclone that forms in the Atlantic or east Pacific.
Why do athletic runners nascar horseracing run counter clockwise?
Well, I do not know the whole detail to this question but can give some insight. The reason why baseball players run the bases counter clockwise along with NASCAR, INDY, horse racing, dogs, running counter clockwise etc., has a lot to do with the American Revolution. Early Americans hated the British so much they wanted to do almost eveything opposite to their rules. In England and Europe, they run car and horse races clockwise, and I think Cricket runs clockwise as well, although they do not have a diamond like American Baseball. Hope that helps!
Can angle measurements be negative?
Yes, although it may seem strange. Conventionally, on a Cartesian plane, angles are measured in an anticlockwise dirction, from the x-axis. Consequently, an angle in the clockwise direction could be considered a negative angle. It might be simpler to think of an angle of 359 degrees as one of -1 degrees, instead. Sometimes you need to subtract one angle from another and in that context, a negative measure for the angle is implicit.
How do you unscramble Spanish phrases?
- sometimes the words are backwords or the words are shorter - sometimes there are set parts of words, e.g. 'ado' 'ando' 'endo' 'iendo', 'acion', 'para' 'entre' 'por' etc., which can be extracted to lower the number of permutations, though they are not necessarily - in fact probably not - conveniently in the orders given here.
How do you remove a 94 Supra shift knob?
it simply twists off anti-clockwise. but sometimes it is extremely tight. just be careful not to break it but it will twist off. cheers.
What is another term for tornado?
A tornado that spins in the opposite direction from normal (e.g. clockwise in the northern hemisphere) it is called an anticyclonic tornado.
