| Fascinating
numbers
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The essence of mathematics resides
in its freedom. |
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On this page you will find a list of the 10 most interesting numbers, based on surveys and interviews with mathematicians. |
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| 1. 0 | Invented around A.D. 200 by the
Hindus, possibly with Arab help, it is the greatest of all mathematical
inventions. The number 0 makes it possible to differentiate between 11,
101 and 1001 without the use of additional symbols.
All the numbers can be expressed in terms of 10 symbols, the numerals from 1 to 9, plus 0, making calculations easier. By the early 17th century, Hindu numerals were used by everyone. |
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| 2. Pi (p) | Pre 17th century humanity thought it corresponded to the ratio of the circumference of a circle to its diameter. Today, p relates to unaccountably many areas in number theory, probability, complex numbers, and series of simple fractions. More recently, it has turned up in equations that describe subatomic particles, light, and other quantities that have no obvious connection to circles. Here is a little trick to
remember the first decimals of pi. In this sentence the number of letters
in each word corresponds to the digits of pi: 3.14159265358979... |
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| 3. e | The base of the natural system of
logarithms. Its numerical value is 2.7182...
e like p is a transcendental number (numbers that cannot be expressed as the root of any algebraic equation with rational coefficients.) Numerous growth processes in physics, biology, chemistry, and the social sciences exhibit exponential growth expressed by the formula y = e^x. |
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| 4. i | Imaginary unit. When you try to
find the solution of the square root of a negative number, you realize
that no real solution exists. Heron of Alexandria was the first to
formally present such a solution. At first, people were not sure of the
validity of such numbers, but today imaginary numbers are everywhere in
science.
The space shuttle's flight software uses them for navigation. They are used by chemists for spatially manipulating models of protein structure. Gauss was the first to use the word "complex" to describe numbers with both real and imaginary components, in 1832. |
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| 5. Square root of 2 | It has a numerical value of
1.414214...
When it was shown that it could not be expressed as the ratio of two integers, in other words that it was irrational, it allowed the development of a whole new area of mathematics. Irrational numbers are non-terminating, non-repeating decimals. Disciples of Pythagoras were the first to realize that the diagonal of a square with sides length of 1 is not a rational number. This was so shocking that those who knew were sworn to secrecy for fear that it might disrupt the fabric of society. The problem caused an existential crisis in the ancient Greek mathematics. |
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| 6. 1 | 1 has no factors but itself, and
is also a factor of all numbers.
It is the multiplicative identity for 1 x a = a. |
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| 7. 2 | The only even prime number. It is
the basis of the binary system of numbers upon which all computers are
built.
Powers of 2 appear more frequently in mathematics and physics than those of any other number. |
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| 8. Euler's gamma (g) | This number is the link between the exponentials and logs to number theory. Its numerical value is 0.5772... This number plays a role in probability, and in addition, in many infinite series, products, and definite integral representations. Because it is more difficult to evaluate this number, it is only known to several thousand decimal places, compared to the billions that are known for pi. |
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| 9. Chaitin's constant (W) | It is an irrational number which
gives the probability that a "universal Turing machine" will
halt.
A Turing machine is a theoretical computing machine that consists of an infinitely long magnetic tape on which instructions can be written and erased, a single-bit register of memory, and a processor capable of carrying out certain simple instructions. This number has implications for the development of human and natural languages and it gives insight into the ultimate potential of machines. |
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| 10. Aleph naught | A transfinite number.
Even though there are an infinite number of rational and irrational numbers, the infinite number of irrationals is in some sense greater than the infinite number of rationals. To indicate this difference, mathematicians refer to the infinity of rationals as Aleph naught, and the infinite numbers of irrationals as C (continuum). Transfinite numbers are used to qualify the different "levels" of infinity. |
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