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There are three basic aspects of a whole number: its name, its numeral, and its elemental nature.

If you put a different letter, a thru j, on each one of someone's thumbs and fingers, there would be 10!=3,628,800 ways to do that. 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824 seconds, or approx. A Trillion, 1,000,000,000,000, can be described as 1000 with 3 (tri) sets of 3 zeros appended.

In between these last two numbers is 1000!, one thousand factorial, a number containing 2568 digits. Click below for an Educational site, which can name any numbers put into it (up to centillion). Thus, (10x10100)3 = cen-tillion, and you will find other examples in the discussions above.

The largest prime number found to date is the one cited above, M43112609 = 243,112,609 - 1. Graham's number is so large than it cannot be conveniently expressed in conventional number notation.

Math students who think about what they are learning, especially those who love to dig deeply in the mines of learning, invariably discover the power and beauty of mathematics. Applied mathematics is the language of the natural sciences, such as physics, chemistry, and astronomy.

While few may explore math at very high levels, the power of pure mathematics is found in powerful mathematical theorems, theorems that have both generality and depth. Mathematics is not only powerful, it is also beautiful. The beauty of math is not often appreciated by non-mathematicians. To be recognized as true, a scientific formula or theory must not only be applicable to the physical world (meaning that it works, it has the power to predict), it must also be beautiful, or elegant.

So, for example, both Ptolemy’s geocentric theory, the idea that the earth is the center of the universe, and Copernicus’s heliocentric theory, the idea that the sun is the center of the solar system, “save the appearances” of the motions of the sun, moon, and planets in the sky. My point here is that these men believed the heliocentric theory to be true for aesthetic reasons: it is a more elegant solution to the problem of describing and predicting planetary motion.

My examples have focused on theories from astronomy, but the point is equally true for other branches of science. When we see patterns in mathematics, especially patterns which reveal solutions to problems, we are struck with a sense of delight.

Teachers of mathematics should bring to the attention of their students the power and beauty of mathematics. If you like this Site about Solving Math Problems, please let Google know by clicking the +1 button.

We call applied mathematics the “language” of those sciences because we use mathematical formulas to describe scientific theories.

A mathematical theorem is general if it is widely applicable, not necessarily applicable to the physical world like applied math, but applicable in the sense that it can be applied to other areas of math; it can be used in solving other theorems.

Ptolemy’s system used 77 circles and epicycles to describe the motion of the planets and the sun around the earth, and was accurate in describing the observed motions to several decimal places. Copernicus was convinced of his theory not primarily because it worked any better than Ptolemy’s, but because it was more beautiful. The theoretical physicist Paul Dirac (1902-1984) admitted that it was primarily his sense of aesthetics which encouraged him to find a more elegant equation to describe the electron, which led to the successful prediction of antimatter. Let the students not only know what math can do, but let them admire it for its elegance and order, and give glory to God for what He has revealed to man through it. He is an elder at Christ Church and lives in Moscow with his wife Giselle and their four children. It represents the number of different ways 10 items can be lined up in a sequence (permutation). While most students realize early on the power of mathematics, at least to solve problems, many have trouble seeing the beauty of the subject. If a particular theorem is needed to solve other theorems, then it is general, and in that sense powerful. Copernicus, however, was convinced that “nature is pleased with simplicity.” Contrary to all appearances and accepted dogma, he placed the sun at the center of the system of planets. He went so far as to say that “it is more important to have beauty in one’s equations than to have them fit experiment.” And all scientists, when presented with two solutions which solve a problem equally well, will prefer the more elegant solution.

If I know the height of a rock above the ground, I can use mathematical formulas to predict the time it will take the rock to fall.

A theorem is also considered to be general if it connects many mathematical ideas together. Deep theorems require a lot of study and creativity to develop, and often require powerful methods of proof.

Hardy (1877-1947) wrote, “It may be very hard to define mathematical beauty, but that is just as true of beauty of any kind – we may not know what we mean by a beautiful poem, but that does not prevent us from recognizing one when we read it.” Let’s consider beauty first in applied math.

Lewis compares medieval and modern cosmology, and writes, “A scientific theory must ‘save’ or ‘preserve’ the appearances, the phenomena, it deals with, in the sense of getting them all in . In the early 1800s, astronomers were aware of aberrations in the orbit of the planet Uranus.

But once they are proven, especially if they can be used elsewhere in mathematics, they are considered to be powerful. His system was more elegant, it made fewer assumptions, and thus Copernicus was convinced it was a superior system – that is, that it was true. When we recognize that a theorem is true, that the conclusion is inescapable, it strikes an aesthetic chord in us; it surprises us.

Through a careful use of mathematics, these astronomers were able to predict the location of Neptune within degrees of its actual position. Clearly, applied mathematics, being so applicable to the physical world, is a powerful tool.

But if we demanded no more than that from a theory, science would be impossible, for a lively inventive faculty could devise a good many different supposals which would equally save the phenomena.

If you put a different letter, a thru j, on each one of someone's thumbs and fingers, there would be 10!=3,628,800 ways to do that. 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824 seconds, or approx. A Trillion, 1,000,000,000,000, can be described as 1000 with 3 (tri) sets of 3 zeros appended.

In between these last two numbers is 1000!, one thousand factorial, a number containing 2568 digits. Click below for an Educational site, which can name any numbers put into it (up to centillion). Thus, (10x10100)3 = cen-tillion, and you will find other examples in the discussions above.

The largest prime number found to date is the one cited above, M43112609 = 243,112,609 - 1. Graham's number is so large than it cannot be conveniently expressed in conventional number notation.

Math students who think about what they are learning, especially those who love to dig deeply in the mines of learning, invariably discover the power and beauty of mathematics. Applied mathematics is the language of the natural sciences, such as physics, chemistry, and astronomy.

While few may explore math at very high levels, the power of pure mathematics is found in powerful mathematical theorems, theorems that have both generality and depth. Mathematics is not only powerful, it is also beautiful. The beauty of math is not often appreciated by non-mathematicians. To be recognized as true, a scientific formula or theory must not only be applicable to the physical world (meaning that it works, it has the power to predict), it must also be beautiful, or elegant.

So, for example, both Ptolemy’s geocentric theory, the idea that the earth is the center of the universe, and Copernicus’s heliocentric theory, the idea that the sun is the center of the solar system, “save the appearances” of the motions of the sun, moon, and planets in the sky. My point here is that these men believed the heliocentric theory to be true for aesthetic reasons: it is a more elegant solution to the problem of describing and predicting planetary motion.

My examples have focused on theories from astronomy, but the point is equally true for other branches of science. When we see patterns in mathematics, especially patterns which reveal solutions to problems, we are struck with a sense of delight.

Teachers of mathematics should bring to the attention of their students the power and beauty of mathematics. If you like this Site about Solving Math Problems, please let Google know by clicking the +1 button.

We call applied mathematics the “language” of those sciences because we use mathematical formulas to describe scientific theories.

A mathematical theorem is general if it is widely applicable, not necessarily applicable to the physical world like applied math, but applicable in the sense that it can be applied to other areas of math; it can be used in solving other theorems.

Ptolemy’s system used 77 circles and epicycles to describe the motion of the planets and the sun around the earth, and was accurate in describing the observed motions to several decimal places. Copernicus was convinced of his theory not primarily because it worked any better than Ptolemy’s, but because it was more beautiful. The theoretical physicist Paul Dirac (1902-1984) admitted that it was primarily his sense of aesthetics which encouraged him to find a more elegant equation to describe the electron, which led to the successful prediction of antimatter. Let the students not only know what math can do, but let them admire it for its elegance and order, and give glory to God for what He has revealed to man through it. He is an elder at Christ Church and lives in Moscow with his wife Giselle and their four children. It represents the number of different ways 10 items can be lined up in a sequence (permutation). While most students realize early on the power of mathematics, at least to solve problems, many have trouble seeing the beauty of the subject. If a particular theorem is needed to solve other theorems, then it is general, and in that sense powerful. Copernicus, however, was convinced that “nature is pleased with simplicity.” Contrary to all appearances and accepted dogma, he placed the sun at the center of the system of planets. He went so far as to say that “it is more important to have beauty in one’s equations than to have them fit experiment.” And all scientists, when presented with two solutions which solve a problem equally well, will prefer the more elegant solution.

If I know the height of a rock above the ground, I can use mathematical formulas to predict the time it will take the rock to fall.

A theorem is also considered to be general if it connects many mathematical ideas together. Deep theorems require a lot of study and creativity to develop, and often require powerful methods of proof.

Hardy (1877-1947) wrote, “It may be very hard to define mathematical beauty, but that is just as true of beauty of any kind – we may not know what we mean by a beautiful poem, but that does not prevent us from recognizing one when we read it.” Let’s consider beauty first in applied math.

Lewis compares medieval and modern cosmology, and writes, “A scientific theory must ‘save’ or ‘preserve’ the appearances, the phenomena, it deals with, in the sense of getting them all in . In the early 1800s, astronomers were aware of aberrations in the orbit of the planet Uranus.

But once they are proven, especially if they can be used elsewhere in mathematics, they are considered to be powerful. His system was more elegant, it made fewer assumptions, and thus Copernicus was convinced it was a superior system – that is, that it was true. When we recognize that a theorem is true, that the conclusion is inescapable, it strikes an aesthetic chord in us; it surprises us.

Through a careful use of mathematics, these astronomers were able to predict the location of Neptune within degrees of its actual position. Clearly, applied mathematics, being so applicable to the physical world, is a powerful tool.

But if we demanded no more than that from a theory, science would be impossible, for a lively inventive faculty could devise a good many different supposals which would equally save the phenomena.

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