Math natural logarithm

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Logarithms are useful, but there is a particular kind of logarithm
that is used the most often: the *natural* logarithm. This is just the
logarithm to the base [e]. In fact, the natural logarithm is so useful
that people often say "ln(n)" instead of log[e](n). math forum; Now, why is all
this important? It's hard to say without going into a lot of details,
but here's a little hint of the interesting things about e and ln(n):

Think about (1+1/n)^n for some value n. For n=1, this is 2. For n=2,
this is 2.25. For n=5, this is 2.48832. For n=10, this is 2.5937....
For n=100, this is 2.7048.... For n=10000, this is 2.7169.... Can you
guess what happens to (1+1/n)^n as n gets larger and larger? In fact,
it becomes e. A way of expressing this in mathematical notation is

lim (1+1/n)^n = e.
n->infinity

(the "lim" stands for "limit"; we say "the limit as n goes to infinity
of the quantity one plus one over n to the nth power is e.)

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Math modeling and simulations

Welcome to free math,

To help them with modeling and simulations. These days, before
anyone builds anything that costs very much money, they usually
develop some type of mathematical model, and analyze it using a
computer.

A mathematical model is a set of equations that describe what we think
would happen to something if we really built it the way that it is
described in the model. help in math; You may have seen a computerized 'stick
drawing' of the space shuttle on the TV news, where they show the
shuttle turning from side-to-side and it looks like it's
three-dimensional.

Well, that 'stick-drawing' is a graphical
representation of a mathematical model. And NASA did not make that
computer model just so they could see what the shuttle would look
like, they made it so they could learn as much as they could about it
before it was built. Things like how it would fly, how strong certain
parts would have to be, and how hot it would get on re-entry.
Learn more on math help online.

Chemistry, Physics and Math

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To understand chemistry and physics. Civil engineers are
frequently concerned with two fundamental technical questions:
The first question, "How strong is this material?" can be answered
through material science, which is a branch of chemistry. The second,
"How strong will this part need to be?" is usually answered by statics
and dynamics, which are branches of physics.

Now, long before the engineer ever enrolled in his or her first
engineering class, he or she probably had a good understanding of the
basic principals of chemistry and physics (from a high school science
class, perhaps) and virtually all of these fundamental scientific
principals are described, analyzed, proven, and predicted through the
use of one or more form of mathematics. examples on math forum;
And let me stress that the math is not only needed to pass those classes in the first place, but
even as the engineers (and scientists) apply scientific principals in
their respective fields, they continue to use the mathematics which
define these principals. Learn more on online math forum.

Right books to learn math

Welcome to free online tutoring math,
When you're looking for a book to work through, you want to find one
where the problems in the first chapter seem too easy, and the
problems in the last chapter are too hard. That means that the stuff
in the middle is stuff that you need to learn.

Once you've found a few books that seem to be at the right level, open
each one to somewhere in the middle and see how well you can follow
the author's explanation of something you don't know yet. more examples on math forum,
Each author has a different style, and you'll learn faster if you find authors
whose style of teaching matches your style of learning.

If you have
trouble following what's written in one book, don't assume that it's
entirely your fault. Look for another book that better suits your
personal learning style. One nice thing about math is that, no matter
what you're trying to learn, there are a zillion books (to say nothing
of Internet sites) that are waiting to try to help you learn it. (This
in itself is one of the keys to 'making math easy'.) learn more on online math forum.

Opposite in Polygon

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I agree that it seems a little odd that we don't bother to define
'opposite' precisely; but the comparison to 'open' or 'bounded' is not
really fair, since in those cases a simple word is being given a
complicated definition, while 'opposite' is a simple word being given
the simplest possible definition. more definitions on online math tutors.

Also, the definition probably
doesn't enter into any proofs in such a way as to require clarity; you
only need the definition to see what someone is talking about. That's
important, of course, examples on math forum, but there is a lot of ordinary language that
mathematicians use that doesn't need definition just because we use
them enough to know we are using them the same way. Often it's only in
talking to kids that we realize we don't know how to define a word.

Math Concept

Welcome to online math tutors,

This is a great
opportunity to explore how math is done on help with math problems,
at a basic level. The problem
you have, of course, is that the concept of "opposite" is so "obvious"
that mathematicians, as far as I can see, don't bother to state the
definition they all assume is well known. That gives you a chance to
work out a "new" definition as if you were on the cutting edge of
math.

How do we define a mathematical concept? Generally, we start with
common sense, then make it mathematical by turning that into a precise
and general definition. In this case, "opposite" is a natural concept
if we start by looking at a circle. In fact in free math, any definition we choose
will identify the same point as opposite a given point: halfway around
the circumference; having a parallel tangent; at the other end of a
diameter, which divides the interior into equal halves; or whatever
you want to say.

Euclid Geometry

Let us study about Euclid Geometry on free math help,
The greatest value of geometry has nothing to do with
what people use it for. What Euclid did 2300 years ago was
revolutionary because it got people thinking logically and reasoning
things out - thinking about why something is true. In free math geometry,
something is true or it isn't, and you don't prove something by yelling
loud enough to intimidate people, or by being persuasive and winning in
the polls.

Euclid really set the stage for science, for careful examination of the
world, of cause and effect. And every year, when students study
geometry, it once again sets the stage for some of those students to
head into sciences and technical fields that require careful thought.
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Meaning of Geometry

In this session of free math tutoring, Let us study the meaning of Geometry

The very word "geometry" points to its practical origins: it means
"measurement of the earth." A Greek named Eratosthenes, among others,
used it (and its relative, trigonometry, which means "measurement of
triangles") to find the circumference of the earth. (This was crucial
for mapmaking, and it's even more relevant today, with all our
satellites!)

Geometry is still used in its original sense by surveyors. It's used
every second by computers - those GPS devices you may have heard of,
which can pinpoint where you are by triangulation from several
satellites.

People of all sorts use geometry. Just one example on math help: I do some artwork,
and a few months ago I was making a poster that had 3 circles on it.
I had to use high school geometry to figure out just how big to make
the circles and where to place them so it would look right. If geometry
can be used in art, surely it can be used just about anywhere.

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Arithmetic mean

Welcome to online math forum,

Similarly, you could try to make two different numbers be the
same -- say, 139 and 145. But then, to make subtraction work,
you'll have to make 6 the same as 0 and 4 plus 5 equal to 3.
Suddenly, free math ;you'll find that the sum of two positive numbers
is smaller than either of them--and that scarcely resembles
arithmetic at all. (In fact, this leads to modular arithmetic,
which has a certain usefulness in abstract mathematics but is
worse than useless for keeping track of real things.) And so
it goes.

So 'arithmetic', which is one particular system for generating and
combining numbers, appears to be useful, while many 'similar' systems
appear to have all kinds of complications that make them useless.

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Explanation of Mathematics

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Let us study the Explanation of mathematics with free math

One way to define 'mathematics' is to say that it is the practice of
deriving theorems from axioms -- nothing more, nothing less. Some of
the theorems that have been derived in the past have turned out to be
useful for building and designing things, for explaining empirical
phenomena, and for balancing one's checkbook -- but those are
applications of mathematics, not mathematics itself.

So, to answer your question, the name for what you are doing is not
'number theory', unless you are restricting your inquiries to the
properties of integers. The name for what you are doing is
'mathematics'.

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Explain content mathematics

Content math standards can be explained as specific math help topics such as,

Patterns and relationships: Patterns are things that repeat; relationships are things that are connected by some kind of reason.

Number sense and numeration: Number sense is much more than merely counting, it involves the ability to think and work with numbers easily and to understand their uses and relationships.

Geometry and spatial sense: Geometry is the area of mathematics that involves shape, size, space, position, direction, and movement, and describes and classifies the physical world in which we live.

Measurement: Measurement is finding the length, height, and weight of an object using units like inches, feet, and pounds. Time is measured using hours, seconds, and minutes.

Fractions: In free math fractions represent parts of a whole. A very young child will see something cut into three pieces and will believe that there is more after cutting it than before it was cut.

Estimation: To estimate is to make an educated guess as to the amount or size of something. To estimate accurately, numbers and size have to have meaning.

Statistics and probability: Using graphs and charts, people organize and interpret information and see relationships. Graphing is another way to show and see information mathematically.

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Categories of Math

Hi,
Let us study the categories of math & free online math help,

There are two categories of standards: thinking math standards and content math standards. The thinking standards focus on the nature of mathematical reasoning, while the content standards are specific math topics.

The four thinking math standards are problem solving, communication, reasoning, and connections. The content math help standards are estimation, number sense, geometry and spatial sense, measurement, statistics and probability, fractions and decimals, and patterns and relationships.

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Introduction of Geometric Progression

Let us study about Geometric Progression,

Introduction:

Solving online progression is very interesting since we can find the nth term of the particular sequence in much easier way. In this article we shall learn about steps involved in progressions solving.

Moreover we will see in detail about different types involved in progression. There are three types of Progression in math, * Arithmetic progression *Geometric progression * Harmonic progression Let us see these progression and their properties in the following section.

I hope the above explanation was useful, now let us study height in inches

Introduction to congruent polygon

Let us study about Polygon definition,

In congruent polygon definition,the polygons are congruent when they have the equal number of sides, and all corresponding sides and inside angles are congruent.

The polygon will have the same figure and range, but one may be rotate, or be the mirror picture of the other.The spot anywhere they exist is may be different and turning or flip polygons does not adjust the reality so, that they are congruent.

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What is Mathematical Induction

Let us study what is Mathematical induction,

The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones.

Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof.

Mathematical Induction is a principle by which one can arrive at a conclusion about a statement for all positive integers, after proving certain related proposition.

I hope the above explanation was useful, now let me explain about Mathematical Reasoning

Sine and Cosine Laws

Let us study law of sines and cosines,

In trigonometry, we will learn about sine and cosine law is very useful for solving the triangles. In a triangle, there are three sides, and three angles namely a, b, c are the sides of triangle. Here C is the angle opposite to the side c. B is the angle opposite to the side b. A is the angle opposite to the side a.
Sine and Cosine Laws

Law of Sines or Sine Rule:

The sine law can be expressed as





Law of Cosines or Cosine Rule:

The cosine law can be expressed as


I hope the above explanation was useful.

what are real numbers

Let us study what are real numbers,

Real Numbers are just numbers like:

1

12.38

-0.8625

3/4

√2

1998

In fact:

Nearly any number you can think of is a Real Number

Real Numbers include:

	Whole Numbers (like 1,2,3,4, etc)
	Rational Numbers (like 3/4, 0.125, 0.333..., 1.1, etc )
	Irrational Numbers (like π, √3, etc )

Real Numbers can also be positive, negative or zero.

So ... what is NOT a Real Number?

	√-1 (the square root of minus 1) is not a Real Number, it is an Imaginary Number
	Infinity is not a Real Number
And there are also some special numbers that mathematicians play with that are not Real Numbers I hope the above explanation was useful, now let me explain about Similar polygons.

Introduction of Inverse property

Introduction to Inverse property of multiplication:

The inverse property is used to represent as when we multiply the term with inverse number of the given term the product of the operation will be equal to 1. the inverse property of multiplication is always denoted as like the division format. It has two parts like the numerator denominator. The numerator will always 1 and the denominator will be what the term which we are going to multiply.

For example

Inverse property of 5 is [1/ 5] , if we multiply the both value we get the constant answer that is 1.

= 5 x [1/5]

= 1.

I hope the above explanation was useful.

Introduction to mathematical reasoning

An introduction to mathematical reasoning:

In this article let us study the introduction and process of mathematical reasoning. In mathematical language there are two kinds of reasoning- inductive and deductive.Let us discuss some fundamentals of deductive reasoning. The basic unit involved in mathematical reasoning is a mathematical statement.Consider the two sentences.

An elephant weighs more than a human being.

Reading books is a bad habit.

When we read these sentences, we immediately decide that the first sentence is correct and the second is false. There is no confusion regarding these. In mathematics such sentences are called a statements.

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Explain Polynomials

Afraid of polynomials ??
Here's the easy way to learn it. check it out.
Let us learn about arithmetic sequence and polynomial problems
Polynomial is an equation that is formed by adding or subtracting several variables called monomial. Monomial is a variable that is formed with a number and a letter variable to its powers. The example of monomial is 3X³. You can’t add or subtract monomials if they have different exponents such as 3X³ and 4X⁴. But you can multiply or divide them. To multiply monomials, just add the exponents of the variables and multiply the coefficients. 3X³ x 4X⁴ = 12X⁷.

Here are some additional ways to manipulate the monomials:

* (a^m)ⁿ = a^mn
* (ab)^m= a^mb^m
I hope the above explanation was useful, now let me give you some examples on polynomials.