Math Regular polygon

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Now move to a regular polygon. We lose just a little bit of
generality, because we see that only with an even number of sides can
we call one SIDE opposite another; but otherwise all the definitions I
can see yield the same result. We haven't clarified the definition at
all.

Now make the polygon slightly irregular, and we're forced to make some
decisions. There probably won't be any parallel side, so that's out.
Halfway around the perimeter, or cutting the polygon into equal
halves, may give you an intuitively "opposite" side, but may also give
a vertex, help in math ; leaving the choice uncertain - and both ways would be very
hard to calculate. Actually, once the sides have different lengths,
such a definition applies only to points not sides; and that's the key
to our choice. Since we're talking about sides, our definition ought
to relate to sides.

So we go back to the most basic possible
definition, one that relies only on counting sides - count half the
sides, and you're at the opposite side. This is the "topological,"
rather than "metric" definition - one that doesn't depend on
measuring any distances, but only on how the sides are connected. For
some special purposes a different definition (especially for 'opposite
point') might be useful, but since we're accustomed to thinking of
polygons topologically, this feels so natural to most mathematicians
that we don't bother mentioning it. more on math forum.

Polygon opposite sides

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Let us study about Polygon opposite sides on math help com,

It might help to know the context in which you have seen the phrase;
but I would say that, in a polygon with an even number of edges, the
side opposite a given side is the side that is separated from that
side by the same number of sides in each direction. Perpendicularity
or convexity is not required, only an even number of edges. You could
define it a bit more formally by saying that, for a 2n-gon, more examples on help in math;
the
opposite side is the nth side counting from the given side in either
direction.

In a pentagon, there is a vertex opposite each side, but not a side
opposite a side.

Math analogy

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To use an imperfect analogy -- don't try to push this too far -- when
you have an attractive melody, there are lots of other 'similar'
melodies that aren't attractive at all. It appears that attractive
melodies -- and useful mathematical systems -- are little islands
surrounded by seas of unattractive -- and useless -- ones.

The question that Minsky is addressing in his article is: Why should
this be the case?

In a sense, then, a mathematician is like an explorer looking for
islands in the Pacific, examples on free math homework help ;
back in the days before airplanes and
satellites. There's no way to know where they'll be, or just what
they'll be like, but -- to an explorer, at least -- there's nothing
quite as exciting as finding one. math forum.

True Math

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Let us study what is mathematics with math helper,

Mathematics can be defined as the construction and exploration of
formal systems. The advantage of this definition is that it emphasizes
the somewhat subtle point that mathematics IS formal -- which is just
another way of saying that it has no NECESSARY relation to anything in
'the real world'.

What all this means is that what is 'true' in mathematics depends
entirely on what axioms you start with, and what rules you use to
combine them. To take your example of 'proving' that the product of
two negatives is positive -- your result is true given the system you
set up, but it may be false in other systems.

I hope the above explanation was useful, now let us study more examples on math forum.

Math and Art related

Math and Art related :

We all need math help and we use it every day, sometimes without even realizing it! Here are some situations that you may find yourself in on any given day. Each one involves the use of help in math skills. Don't be scared! The checkout lady will not give you a test on your math skills on the spot. These are just examples of how a basic knowledge of math can come in handy.
Almost any artist will tell you that there is some kind of mathematical or symmetrical pattern involved in creating pictures. Art doesn't necessarily require addition, subtraction, division, or multiplication. There is, however, a great need for geometric shapes and figures. Notice the picture at the top of the screen. There are some triangles, squares, rectangles, and parallelograms found in each of the images found in the picture.

Hopefully after viewing this stack free math tutoring online, you will understand a little better how math and art can be related through geometry!

Introduction for Poisson equation

Let us study about Poisson Equation,

Poisson distribution is a limiting case of Binomial distribution under the following conditions.

(i) n the number of trials is indefinitely large ie., n → ∞.

(ii) p the constant probability of success in each trial is very small ie., p → 0.

(iii) np = λ is finite where λ is a positive real number. When an event occurs rarely, the distribution of such an event may be assumed to follow a Poisson distribution.

Definition: A random variable X is said to have a Poisson distribution if the probability mass function of X is

P(X = x) =e−λ λx/x!, x = 0,1,2, …for some λ > 0.

I hope the above explanation was useful, now let us study linear programing

How to solve radical fractions

Let us study how to solve radical fractions,

Mainly addition and subtraction problems are solved using the radical fractions.

For the addition problems, the numerator term are simplified first.

* Then, in the next step, we have to take the conjugate for the given problem.
* After that the multiplication are made to the obtained result.
* Then finally simplify the obtained terms.

For the subtraction problems, the numerator term are simplified first.

* Then, in the next step, we have to take the conjugate for the given problem.
* After that the multiplication are made to the obtained result.
* Then finally simplify the obtained terms.