Einstein's concept of non-euclidean

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Einstein came along and discovered
that these non-Euclidean geometries were just the thing to describe
the real-world interactions of objects with mass - that is, to
describe gravity. examples on math forum; This is a case where the mathematical system was
invented with no consideration of the real world (and therefore no
faith element), but it turned out that this system does appear to
describe the real world.

The experiments to show that Einstein's theory of general relativity
do describe the real world better than any other mathematical system
are very tricky; it is still possible that another system would do
better. We can be absolutely sure that the results of general
relativity theory follow from its assumptions; the only question is
whether or not those assumptions match the way the real world is.
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law of trichotomy

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The law of trichotomy still isn't covered. It can be split into two parts: at most one of the three cases can occur, and at least one of the three cases occurs. more examples on math forum; The first can be stated as an axiom of addition as

It is not the case that x = x + y.

And that says it is not the case that x > x. The other half requires the axiom

For each x and y, either x = y or there is some z such that x + z = y, or there is some z such that x = y + z.

With these axioms, all the properties of magnitudes needed in the first few books of the Elements can be proved. For instance, we can prove

If 2x = 2y, then x = y.

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Euclid's square theory

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The only figure defined here that Euclid actually uses is the square. The other names of figures may have been common at the time of Euclid's writing, or they may have been left over from earlier authors' versions of the Elements. Euclid makes much use of parallelogram, or parallelogrammic area, which he does not define, but clearly means quadrilateral with parallel opposite sides. Parallelograms include rhombi and rhomboids as special cases. get more examples on help in math; And rather than oblong, he uses rectangle, or rectangular parallelogram, which includes both squares and oblongs.

Squares and oblongs are defined to be "right-angled." Of course, that is intended to mean that all four angles are right angles. Sometimes Euclid's definitions are too brief, but the intended meaning can easily be determined from the way the definitions are used. In particular, proposition I.46 constructs a square, and all four angles are constructed to be right, not just one of them. read more on free math tutoring.

Figures and there boundry

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The definition of figure needs to be fleshed out. In order to be a figure, a region must be bounded, that is, held in by a boundary. For instance, an infinite plane is unbounded, so it is not intended to be a figure. Neither is the region between two parallel lines even though that region has the two parallel lines as its extremities.

Other figures may be considered if other ambient spaces are allowed, although Euclid only uses plane and solid figures. online math forum; For a one-dimensional example, a line segment could be considered to be a figure in an infinite line with its endpoints as its boundary. Also, a hemisphere could be considered to be a figure on the surface of a sphere with the equator as its boundary. read more on math forum.

Plane surface elements

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We see now that a plane surface, usually abbreviated to the single word "plane," is a kind of surface. Perhaps the remainder of the statement is a definition of content, but, if so, some words are missing.

One interpretation often given is that if a plane surface contains two points, then it contains the line connecting the two points. If that were the meaning, then it would be just as well to make that the explicit definition or to make it a postulate. examples on online math tutors ; But that does not seem to be Euclid's intent. His proposition XI.7 has a detailed proof that the line joining two points on two parallel lines lies in the plane of the two parallel lines. No proof at all would be necessary if that line were by definition or by postulate contained in a plane that contained its ends.

Note that a plane surface may be infinite, but needn't be infinite. It can be a square, a circle, or any other plane figure. more examples on math tutors online.

Geometrical point

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A "point" in geometry can be thought of as something
with no length, width, or breadth. Everything in the real world has
some length, width, and breadth; we can only approximate a point by
making a dot with the sharpest pencil we can get. free math; (Physicists now
think that electrons may actually be points, but electrons obey the
laws of quantum physics, which is rather more complicated than
ordinary geometry.)

Still, somehow, geometry is very useful in describing the real world,
even though strictly speaking, it describes things that don't exist in
the real world. more explanation on math forum.

Counting calender numbers

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In short, since the historical/calendric situation is so messy, I
believe that we should measure the millennium by noticing when the big
party is, and Prince doesn't party like it's 2000. I think we're in
the new millennium now.

It's also worth noting that since there was no year zero, the years
transitioning from BCE to CE are numbered ... -3, -2, -1, 1, 2, 3, ...
But some people, free math; notably astronomers, want the math to work out
better, so they actually use a year zero (... -2, -1, 0, 1, 2, ...),
so they're one year off from the rest of us in negative-land.
Learn more on online math forum.

Understanding math

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It wasn't until I got to college, where they started dealing with the
components of molecules (atoms and electrons) that chemistry started
making sense. That's where they should have started, and there is no
telling how many kids had their interest in the subject killed by
starting at the other end.

Similarly, mathematics is, by and large, taught backward. You are
drilled on little skills, which turn out to be important, but without
ever really being shown the bigger picture, which would help you
understand _why_ they are important.

Can you imagine trying to teach
someone to play chess by having them practice moving the individual
pieces, math helper ;without ever letting them know that there was such a thing as
a chess 'game', or even letting them see a board with more than one
piece on it? Who would bother to learn it? That's something like the
way we currently go about teaching math. Is it any wonder that so many
students lose interest so early?
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Learn to enjoy math

Welcome to free online math help,
Actually, math starts to get _fun_ in 7th and 8th grade. You stop
dealing with particular numbers, and start dealing with patterns,
which are much more powerful, and therefore much more interesting. meet free online math tutors.

I don't believe that anyone can stay focused for long on a subject
that she doesn't like, so my advice would be to learn to enjoy math,
instead of looking at it as something that you're 'supposed' to learn.
more examples on math forum.

Philosophy of Mathematics

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There is a philosophy whose purpose is to help people get past this
"freezing" business. It's called Zen Buddhism. (I know, that _sounds_
like a religion, but it isn't.) You can read a really nice, short,
simple introduction to the ideas of Zen Buddhism in a book called _Zen
in the Martial Arts_, by Joe Hyams. online math tutors ;(I know, that _sounds_ like it's
going to be a book about karate, or judo, but it isn't. At least, not
mostly.) It's a pretty popular book, so you should be able to find it
in most libraries or bookstores. It would be well worth your time to
read it.

This probably isn't what you wanted to hear, but it's better that you
should find out sooner rather than later. learn more with free online math tutoring.

Chess related to math

Welcome to free math tutoring,
It's a little like what you do when you invent a board game like
chess. You specify that there are such-and-such pieces, and they can
move in such-and-such ways, and then you let people explore which
board positions are possible or impossible to achieve. 

The main difference is that in chess, you're trying to win, while in
math help, you're just trying to figure out what kinds of things can - and
can't - happen. So a 'chessamatician', instead of playing complete
games, might just sit and think about questions like this:

 If I place a knight (the piece that looks like a horse, and moves
 in an L-shaped jump) on any position, can it reach all other
 positions?

 What is the minimum number of moves that would be required to get
 from any position to any other position?

Think, get more examples on free online math tutoring.

Introduction of Mathematics

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I am your math helper,

mathematics is the derivation of
theorems from axioms.

So what does that mean?

It means that mathematics is a collection of extended, collaborative
games of 'what if', played by mathematicians who make up sets of rules
(axioms) and then explore the consequences (theorems) of following
those rules, more examples in math forum,

For example, you can start out with a few rules like:

A point has only location.
A line has direction and length.
Two lines interesect at a point.

Hope the above explanation was interesting, get connected with free math tutors online

Different numbers in India

Welcome to free math tutoring online, let us study about indian numericals,

The Hindu-Arabic numeral system is a positional decimal numeral system. Many of the countries adopted the Indian numerals.

Most of the positional base 10 numeral systems in the world have originated from India, where the concept of positional numerology was first developed. The Indian numeral system is commonly referred to in the West as the Hindu-Arabic numeral system or even Arabic numerals, since it reached Europe through the Arabs. you can find these examples of help in math numericals below,
I hope the above explanation was useful, math forum helps you with more examples.

Introduction to factoring quadratic equation

Let us study about Factoring quadratic equation,

An equation is in the form of y= ax² + bx + c, where a, b, c are variables with a not equal to zero is called as quadratic equations. When we graph the quadratic equation, we will get a curve called as parabola.

Parabolas are the curvature that be able to open upward or downward depending the sign of a and it may vary in its "girth", but all the parabolas have the same basic "U" shape.

I hope the above explanation was useful, now let me explain Quadratic Equation Problems

What is Odd function

Let us study about Odd function,
Here we are going to learn even and odd functions. Even and odd functions are very useful in graphing and symmetry. Whether a function is even or odd can be said using some algebraic calculations.
Every plot may not have symmetry so there is no need that every function should be even or odd. That is a function can be even or odd or might not be both. Now we will separately learn even and odd functions.

I hope the explanation was useful, now let me explain decimal place value chart.

Geometry Parts of a Circle

Let us study about the Parts of a circle,
A line to create a circle contains no start otherwise finish; it is a easy closed curve.
* Either point lying on the circumference of a circle is the equal distance as of the middle of the circle.
* A line section as of a point lying on the circumference of a circle to its middle is known as the radius.
* Both line segment to start and ends on the circle’s circumference is known as a chord.
* A chord to exceeds during the middle of a circle is known as the diameter.
The diameter of either circle is double as long as circle within the radius. Each circle contain an infinite number of radii also diameters. For a known circle, every diameters are congruent also every radii are congruent. A chord is a line part that connecting two points on a curve. Within geometry, a chord is frequently utilized to illustrate a line part connecting two endpoints that lie on a circle.
I hope the above explanation helped you.

Explain Interval notation

Let us study what is Interval notation,

An interval can be shown using set notation. For instance, the interval that includes all the numbers between 0 and 1, including both endpoints, is written 0 ≤ x ≤ 1, and read "the set of all x such that 0 is less than or equal to x and x is less than or equal to 1."

The same interval with the endpoints excluded is written 0 <>

Replacing only one or the other of the less than or equal to signs designates a half-open interval, such as 0 ≤ x <>intervals. In this notation, a square bracket is used to denote an included endpoint and a parenthesis is used to denote an excluded endpoint. For example, the closed interval 0 ≤ x ≤ 1 is written [0,1], while the open interval 0 <: x <>
I hope the above explanation was useful, now let me explain Factorisation.

Perimeters

Let us learn what is perimeter,

The term perimeter refers either to the curve constituting the boundary of a lamina, or else to the length of this boundary.

The perimeter of a circle is called the circumference.

The perimeters of some common laminas are summarized in the table below. In the table, e is the eccentricity of an ellipse, a is its semimajor axis, and E(k) is a complete elliptic integral of the second kind.
I hope the above explanation was useful.

Area of circle

Let us study about area of circle,
The distance around a circle is called its circumference. The distance across a circle through its center is called its diameter. We use the Greek letter π (pronounced Pi) to represent the ratio of the circumference of a circle to the diameter. In the last lesson, we learned that the formula for circumference of a circle is: C = πd. For simplicity, we use π = 3.14. We know from the last lesson that the diameter of a circle is twice as long as the radius. This relationship is expressed in the following formula: d = 2r

The area of a circle is the number of square units inside that circle. If each square in the circle to the left has an area of 1 cm², you could count the total number of squares to get the area of this circle. Thus, if there were a total of 28.26 squares, the area of this circle would be 28.26 cm² However, it is easier to use one of the following formulas:


if the radius of this circle is r, the area, A of the circle will be:
A = πr²
a circle with the radius r

where π is a constant that is approximately equals to 3.14.


I hope the above explanation was useful.

Frequency Polygon

Let us study about Frequency polygon,
Relative frequencies of class intervals can also be shown in a frequency polygon. In this chart, the frequency of each class is indicated by points or dots drawn at the midpoints of each class interval. Those points are then connected by straight lines.

The frequency polygon shown in Figure 1 uses points, rather than the bars you would find in a frequency histogram.Figure 1

Frequency polygon display of items sold at a garage sale.

Whether to use bar charts or histograms depends on the data. For example, you may have qualitative data—numerical information about categories that vary significantly in kind. For instance, gender (male or female), types of automobile owned (sedan, sports car, pickup truck, van, and so forth), and religious affiliations (Christian, Jewish, Moslem, and so forth) are all qualitative data. On the other hand, quantitative data can be measured in amounts: age in years, annual salaries, inches of rainfall. Typically, qualitative data are better displayed in bar charts, quantitative data in histograms. As you will see, histograms play an extremely important role in statistics.
Hope the above explanation was useful.