Sunday, January 25, 2009
Mathworld Education
The Educational Website Which would aware you and give you knowledge about maths
geometry
Geometry, branch of mathematics that deals with shapes and sizes. Geometry may be thought of as the science of space. Just as arithmetic deals with experiences that involve counting, so geometry describes and relates experiences that involve space. Basic geometry allows us to determine properties such as the areas and perimeters of two-dimensional shapes and the surface areas and volumes of three-dimensional shapes. People use formulas derived from geometry in everyday life for tasks such as figuring how much paint they will need to cover the walls of a house or calculating the amount of water a fish tank holds.
Algebra
Algebra, branch of mathematics in which symbols (usually letters) represent unknown numbers in mathematical equations. Algebra allows the basic operations of arithmetic, such as addition, subtraction, and multiplication, to be performed without using specific numbers. People use algebra constantly in everyday life, for everything from calculating how much flour they need to bake a certain number of cookies to figuring out how long it will take to travel by car at a certain speed to a destination that is a specific distance away.
Arithmetic alone cannot deal with mathematical relations such as the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of any right triangle is equal to the square of the length of the longest side. Arithmetic can only express specific instances of these relations. A right triangle with sides of length 3, 4, and 5, for example, satisfies the conditions of the theorem: 32 + 42 = 52. (32 stands for 3 multiplied by itself and is termed “three squared.”) Algebra is not limited to expressing specific instances; instead it can make a general statement that covers all possible values that fulfill certain conditions—in this case, the theorem: a2 + b2 = c2.
This article focuses on classical algebra, which is concerned with solving equations, uses symbols instead of specific numbers, and uses arithmetic operations to establish ways of handling symbols. The word algebra is also used, however, to describe various modern, more abstract mathematical topics that also use symbols but not necessarily to represent numbers. Mathematicians consider modern algebra a set of objects with rules for connecting
Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.
Arithmetic alone cannot deal with mathematical relations such as the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of any right triangle is equal to the square of the length of the longest side. Arithmetic can only express specific instances of these relations. A right triangle with sides of length 3, 4, and 5, for example, satisfies the conditions of the theorem: 32 + 42 = 52. (32 stands for 3 multiplied by itself and is termed “three squared.”) Algebra is not limited to expressing specific instances; instead it can make a general statement that covers all possible values that fulfill certain conditions—in this case, the theorem: a2 + b2 = c2.
This article focuses on classical algebra, which is concerned with solving equations, uses symbols instead of specific numbers, and uses arithmetic operations to establish ways of handling symbols. The word algebra is also used, however, to describe various modern, more abstract mathematical topics that also use symbols but not necessarily to represent numbers. Mathematicians consider modern algebra a set of objects with rules for connecting
Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.
Mathematics
Mathematics, a way of describing relationships between numbers and other measurable quantities. Mathematics can express simple equations as well as interactions among the smallest particles and the farthest objects in the known universe. Mathematics allows scientists to communicate ideas using universally accepted terminology. It is truly the language of science.
We benefit from the results of mathematical research every day. The fiber-optic network carrying our telephone conversations was designed with the help of mathematics. Our computers are the result of millions of hours of mathematical analysis. Weather prediction, the design of fuel-efficient automobiles and airplanes, traffic control, and medical imaging all depend upon mathematical analysis.
For the most part, mathematics remains behind the scenes. We use the end results without really thinking about the complexity underlying the technology in our lives. But the phenomenal advances in technology over the last 100 years parallel the rise of mathematics as an independent scientific discipline.
Albert Einstein
Albert Einstein
Physicist Albert Einstein published mathematical explanations of the nature of space, time, and gravitation in his special theory of relativity in 1905 and his general theory of relativity in 1915. These mathematical models opened the way for modern physics.
Encarta Encyclopedia
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Until the 17th century, arithmetic, algebra, and geometry were the only mathematical disciplines, and mathematics was virtually indistinguishable from science and philosophy. Developed by the ancient Greeks, these systems for investigating the world were preserved by Islamic scholars and passed on by Christian monks during the Middle Ages. Mathematics finally became a field in its own right with the development of calculus by English mathematician Isaac Newton and German philosopher and mathematician Gottfried Wilhelm Leibniz during the 17th century and the creation of rigorous mathematical analysis during the 18th century by French mathematician Augustin Louis Cauchy and his contemporaries. Until the late 19th century, however, mathematics was used mainly by physicists, chemists, and engineers.
At the end of the 1800s, scientific researchers began probing the limits of observation, investigating the parts of the atom and the nature of light. Scientists discovered the electron in 1897. They had learned that light consisted of electromagnetic waves in the 1860s, but physicist Albert Einstein showed in 1905 that light could also behave as particles. These discoveries, along with inquiries into the wavelike nature of matter, led in turn to the rise of theoretical physics and to the creation of complex mathematical models that demonstrated physical laws. Einstein mathematically demonstrated the equivalence of mass and energy, summarized by the famous equation E=mc2, in his special theory of relativity in 1905. Later, Einstein’s general theory of relativity (1915) extended special relativity to accelerated systems and showed gravity to be an effect of acceleration. These mathematical models marked the creation of modern physics. Their success in predicting new physical phenomena, such as black holes and antimatter, led to an explosion of mathematical analysis. Areas in pure mathematics—that is, theory as opposed to applied, or practical, mathematics—became particularly active.
ENIAC
We benefit from the results of mathematical research every day. The fiber-optic network carrying our telephone conversations was designed with the help of mathematics. Our computers are the result of millions of hours of mathematical analysis. Weather prediction, the design of fuel-efficient automobiles and airplanes, traffic control, and medical imaging all depend upon mathematical analysis.
For the most part, mathematics remains behind the scenes. We use the end results without really thinking about the complexity underlying the technology in our lives. But the phenomenal advances in technology over the last 100 years parallel the rise of mathematics as an independent scientific discipline.
Albert Einstein
Albert Einstein
Physicist Albert Einstein published mathematical explanations of the nature of space, time, and gravitation in his special theory of relativity in 1905 and his general theory of relativity in 1915. These mathematical models opened the way for modern physics.
Encarta Encyclopedia
Culver Pictures
Full Size
Until the 17th century, arithmetic, algebra, and geometry were the only mathematical disciplines, and mathematics was virtually indistinguishable from science and philosophy. Developed by the ancient Greeks, these systems for investigating the world were preserved by Islamic scholars and passed on by Christian monks during the Middle Ages. Mathematics finally became a field in its own right with the development of calculus by English mathematician Isaac Newton and German philosopher and mathematician Gottfried Wilhelm Leibniz during the 17th century and the creation of rigorous mathematical analysis during the 18th century by French mathematician Augustin Louis Cauchy and his contemporaries. Until the late 19th century, however, mathematics was used mainly by physicists, chemists, and engineers.
At the end of the 1800s, scientific researchers began probing the limits of observation, investigating the parts of the atom and the nature of light. Scientists discovered the electron in 1897. They had learned that light consisted of electromagnetic waves in the 1860s, but physicist Albert Einstein showed in 1905 that light could also behave as particles. These discoveries, along with inquiries into the wavelike nature of matter, led in turn to the rise of theoretical physics and to the creation of complex mathematical models that demonstrated physical laws. Einstein mathematically demonstrated the equivalence of mass and energy, summarized by the famous equation E=mc2, in his special theory of relativity in 1905. Later, Einstein’s general theory of relativity (1915) extended special relativity to accelerated systems and showed gravity to be an effect of acceleration. These mathematical models marked the creation of modern physics. Their success in predicting new physical phenomena, such as black holes and antimatter, led to an explosion of mathematical analysis. Areas in pure mathematics—that is, theory as opposed to applied, or practical, mathematics—became particularly active.
ENIAC
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