Welcome to online math tutoring,
Associativity and commutativity together imply that the order that addition is performed is irrelevant. An algebra satisfying only associativity is called a semigroup, while a semigroup that also satisfies commutativity is called a commutative semigroup or an Abelian semigroup.
When other axioms are added for zero and negation, then the algebra is called a group, examples given on online math forum; and when commutative, an Abelian group. Groups are some of the most important algebraic structures in modern mathematics. read more on math forum.
Friday, August 13, 2010
Geometry angles
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Euclid classifies rectilinear figures by their number of sides in this definition. Classifying them by their number of angles could lead to complications since an angle has to be less than two right angles, and a non-convex figure would have an internal angle greater than two right angles.
The modern English names, however, are based an the number of angles (except quadrilateral): triangle, pentagon, hexagon, heptagon, octagon, etc. free math; From pentagon on up these names derive from the Greek, but they're rarely used past octagon. more examples on math forum.
Euclid classifies rectilinear figures by their number of sides in this definition. Classifying them by their number of angles could lead to complications since an angle has to be less than two right angles, and a non-convex figure would have an internal angle greater than two right angles.
The modern English names, however, are based an the number of angles (except quadrilateral): triangle, pentagon, hexagon, heptagon, octagon, etc. free math; From pentagon on up these names derive from the Greek, but they're rarely used past octagon. more examples on math forum.
Magnitude used in angle
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As treated by Euclid, rectilinear angles are magnitudes that can be added together. When the sum of angles happens greater than two right angles, it is continued to be treated as a sum of angles rather than an individual angle. For instance, in proposition it is proved that the sum of the interior angles of a triangle equals two right angles.
Treating angles as magnitudes should not be confused with measuring angles. The angles themselves are the magnitudes. The only measurement of angles in the Elements is in terms of right angles (defined in the next definition). online math forum; Degree measurement and radian measurement were not used until later. In terms of degrees a right angle is 90°, while in terms of radians a right angle is pi/2 radians.
Throughout ancient Greek mathematics, only positive magnitudes were considered. Zero and negative magnitudes were not conceived. For the most part, a lack of zero and negative magnitudes complicates mathematics, but occasionally simplifies it. In any case, the power of a mathematics without zero and negative magnitudes is no less in the sense that any statement made using the language of zero or negative magnitudes can be translated into a statement that doesn't use them, although the translated statement may be longer and less understandable.
read more on math forum.
As treated by Euclid, rectilinear angles are magnitudes that can be added together. When the sum of angles happens greater than two right angles, it is continued to be treated as a sum of angles rather than an individual angle. For instance, in proposition it is proved that the sum of the interior angles of a triangle equals two right angles.
Treating angles as magnitudes should not be confused with measuring angles. The angles themselves are the magnitudes. The only measurement of angles in the Elements is in terms of right angles (defined in the next definition). online math forum; Degree measurement and radian measurement were not used until later. In terms of degrees a right angle is 90°, while in terms of radians a right angle is pi/2 radians.
Throughout ancient Greek mathematics, only positive magnitudes were considered. Zero and negative magnitudes were not conceived. For the most part, a lack of zero and negative magnitudes complicates mathematics, but occasionally simplifies it. In any case, the power of a mathematics without zero and negative magnitudes is no less in the sense that any statement made using the language of zero or negative magnitudes can be translated into a statement that doesn't use them, although the translated statement may be longer and less understandable.
read more on math forum.
Thursday, August 12, 2010
Line element
Welcome to math tutor online free,
"Line" is the second primitive term in the Elements. The description, "breadthless length," says that a line will have one dimension, length, but it won't have breadth or depth. In I.Def.5 a surface is defined with the two dimensions length and breadth, and in XI.Def.1 a solid is defined with the three dimensions length, breadth, and depth.
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One cannot tell from this definition what kind of line is meant by "line," but later a "straight" line defined to be a special kind of line. One can conclude, then, that "lines" need not be straight. Perhaps "curve" would be a better translation than "line" since Euclid meant what is commonly called a curve in modern English, examples on free math; where a curve may or may not be straight.
Also, from the next definition, it is apparent that Euclid's lines may have ends, so they are "line segments" or "curve segments." But they need not have ends in all cases since the entire circumference of a circle is an example of a line. Indeed, lines need not be finite in all cases; there are a few instances in the Elements where a line is not bounded, and that is usually indicated by the language. more on math forum.
"Line" is the second primitive term in the Elements. The description, "breadthless length," says that a line will have one dimension, length, but it won't have breadth or depth. In I.Def.5 a surface is defined with the two dimensions length and breadth, and in XI.Def.1 a solid is defined with the three dimensions length, breadth, and depth.
java applet or image
One cannot tell from this definition what kind of line is meant by "line," but later a "straight" line defined to be a special kind of line. One can conclude, then, that "lines" need not be straight. Perhaps "curve" would be a better translation than "line" since Euclid meant what is commonly called a curve in modern English, examples on free math; where a curve may or may not be straight.
Also, from the next definition, it is apparent that Euclid's lines may have ends, so they are "line segments" or "curve segments." But they need not have ends in all cases since the entire circumference of a circle is an example of a line. Indeed, lines need not be finite in all cases; there are a few instances in the Elements where a line is not bounded, and that is usually indicated by the language. more on math forum.
Euclidean and Hyperbolic Geometry
Welcome to free math help online,
There are some cases in which assuming different sets of axioms will
give you different bodies of mathematics, and that can be fun. For
example, this is the difference between Euclidean and Hyperbolic
geometry; one simple axiom about parallel lines is changed, and it has
huge effects on what the resulting body of mathematics looks like.
Statements of type (2) are pretty tough, but we'll crack 'em. :-)
Statements of type (3) are things that can make you question your
place in the universe. An Austrian mathematician named Kurt Godel
proved in 1931 that there must be statements of mathematics that
cannot be proved or disproved. examples on math helper; The somewhat
irritating thing is that
we don't know which statements these are. The main thing that
mathematicians get out of this is that the forest of mathematics is a
complicated one indeed, and we'll never completely know its landscape.
learn more examples on online math forum.
There are some cases in which assuming different sets of axioms will
give you different bodies of mathematics, and that can be fun. For
example, this is the difference between Euclidean and Hyperbolic
geometry; one simple axiom about parallel lines is changed, and it has
huge effects on what the resulting body of mathematics looks like.
Statements of type (2) are pretty tough, but we'll crack 'em. :-)
Statements of type (3) are things that can make you question your
place in the universe. An Austrian mathematician named Kurt Godel
proved in 1931 that there must be statements of mathematics that
cannot be proved or disproved. examples on math helper; The somewhat
irritating thing is that
we don't know which statements these are. The main thing that
mathematicians get out of this is that the forest of mathematics is a
complicated one indeed, and we'll never completely know its landscape.
learn more examples on online math forum.
When does 3rd millenium start
Welcome to free online math tutoring,
I actually believe that's a better question for an anthropologist than
a mathematician. The word "millennium" simply means any period of 1000
years, though it's natural for us humans to want to start some
millennium at a known point in history and keep dividing the eons into
consecutive millennia thereafter.
Therefore, if we're going to talk about a "true" millennium, we should
probably fix some important event in the past and count forward 1000
and 2000 years. Supposedly, free math ; we've done this with the birth of Christ.
Seems simple enough - just count forward 2000 years from the nativity,
and pencil in a millennium celebration on the calendar. more explanation on math help online.
I actually believe that's a better question for an anthropologist than
a mathematician. The word "millennium" simply means any period of 1000
years, though it's natural for us humans to want to start some
millennium at a known point in history and keep dividing the eons into
consecutive millennia thereafter.
Therefore, if we're going to talk about a "true" millennium, we should
probably fix some important event in the past and count forward 1000
and 2000 years. Supposedly, free math ; we've done this with the birth of Christ.
Seems simple enough - just count forward 2000 years from the nativity,
and pencil in a millennium celebration on the calendar. more explanation on math help online.
geometry help free
In this article you will get free help on tenth grade geometry. Generally geometry applications are mainly used for the everyday life for measuring area, perimeter and volume of the every object like building, land etc measurement are based on according to shape of the objects, object shapes are classified based on the dimension, there are three types of dimension such as one dimension, two dimension and three dimension, line is the best example for the one dimension objects. The following example problems will help for tenth grade geometry help free.
A wall is in the form of a parallelogram whose side length is 19m and breath is 23m. If you are painting the entire wall means, the cost of painting of the entire wall is $29 per square meter, calculate how much cost for painting (parallelogram shaped) wall.
Solution:
Here the side length of the wall is given as 19m and breath of the parallelogram shaped wall is 23m.
The shape of a wall is parallelogram we know that the area of a parallelogram formula it will be written as in below,
The area of a parallelogram is length x breath (online geometry help)
Plug those length and the breath values
Area= 19x23=437m2
Since the cost of painting of 1sq. meter parallelogram shaped wall is $29,
So the cost for painting (square shape) the entire wall is $29
= $12673.
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