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

Welcome to free math tutoring online,

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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