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Prime Factor Exponent Notation
In his 1557 work ''The Whetstone of Witte'', British mathematician Robert Recorde proposed an exponent notation by prime factorisation, which remained in use up until the eighteenth century and acquired the name ''Arabic exponent notation''. The principle of Arabic exponents was quite similar to Egyptian fractions; large exponents were broken down into smaller prime numbers. Squares and cubes were so called; prime numbers from five onwards were called ''sursolids''. Although the terms used for defining exponents differed between authors and times, the general system was the primary exponent notation until René Descartes René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathem ... devised the Cartesian exponent notation, which is still used today. This is a list of Recorde's terms. By co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Whetstone Of Witte
''The Whetstone of Witte'' is the shortened title of Robert Recorde's mathematics book published in 1557, the full title being ''The whetstone of , is the : The ''Coßike'' practise, with the rule of ''Equation'': and the of ''Surde Nombers. The book covers topics including whole numbers, the extraction of roots and irrational numbers. The work is notable for containing the first recorded use of the equals sign and also for being the first book in English to use the plus and minus signs. Recordian notation for exponentiation, however, differed from the later Cartesian notation p^q = p \times p \times p \cdots \times p. Recorde expressed indices and surds larger than 3 in a systematic form based on the prime factorization of the exponent: a factor of two he termed a ''zenzic'', and a factor of three, a ''cubic''. Recorde termed the larger prime numbers appearing in this factorization ''sursolids'', distinguishing between them by use of ordinal numbers: that is, he defined 5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
8 (number)
8 (eight) is the natural number following 7 and preceding 9. In mathematics 8 is: * a composite number, its proper divisors being , , and . It is twice 4 or four times 2. * a power of two, being 2 (two cubed), and is the first number of the form , being an integer greater than 1. * the first number which is neither prime nor semiprime. * the base of the octal number system, which is mostly used with computers. In octal, one digit represents three bits. In modern computers, a byte is a grouping of eight bits, also called an wikt:octet, octet. * a Fibonacci number, being plus . The next Fibonacci number is . 8 is the only positive Fibonacci number, aside from 1, that is a perfect cube. * the only nonzero perfect power that is one less than another perfect power, by Catalan conjecture, Mihăilescu's Theorem. * the order of the smallest non-abelian group all of whose subgroups are normal. * the dimension of the octonions and is the highest possible dimension of a normed divisio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21 (number)
21 (twenty-one) is the natural number following 20 and preceding 22. The current century is the 21st century AD, under the Gregorian calendar. In mathematics 21 is: * a composite number, its proper divisors being 1, 3 and 7, and a deficient number as the sum of these divisors is less than the number itself. * a Fibonacci number as it is the sum of the preceding terms in the sequence, 8 and 13. * the fifth Motzkin number. * a triangular number, because it is the sum of the first six natural numbers (1 + 2 + 3 + 4 + 5 + 6 = 21). * an octagonal number. * a Padovan number, preceded by the terms 9, 12, 16 (it is the sum of the first two of these) in the padovan sequence. * a Blum integer, since it is a semiprime with both its prime factors being Gaussian primes. * the sum of the divisors of the first 5 positive integers (i.e., 1 + (1 + 2) + (1 + 3) + (1 + 2 + 4) + (1 + 5)) * the smallest non-trivial example of a Fibonacci number whose digits are Fibonacci numbers and whose digit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
20 (number)
20 (twenty; Roman numeral XX) is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score. In mathematics *20 is a pronic number. *20 is a tetrahedral number as 1, 4, 10, 20. *20 is the basis for vigesimal number systems. *20 is the third composite number to be the product of a squared prime and a prime, and also the second member of the (''2''2)''q'' family in this form. *20 is the smallest primitive abundant number. *An icosahedron has 20 faces. A dodecahedron has 20 vertices. *20 can be written as the sum of three Fibonacci numbers uniquely, i.e. 20 = 13 + 5 + 2. *20 is the number of moves (quarter or half turns) required to optimally solve a Rubik's Cube in the worst case. (e.g. the newspaper headline "Scores of Typhoon Survivors Flown to Manila")."CBS News"''Scores of Typhoon Survivors Flown to Manila'' (November 2013) In sports * Twenty20 is a form of limited overs cricket where each team plays only 20 overs. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19 (number)
19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number. Mathematics 19 is the eighth prime number, and forms a sexy prime with 13, a twin prime with 17, and a cousin prime with 23. It is the third full reptend prime, the fifth central trinomial coefficient, and the seventh Mersenne prime exponent. It is also the second Keith number, and more specifically the first Keith prime. * 19 is the maximum number of fourth powers needed to sum up to any natural number, and in the context of Waring's problem, 19 is the fourth value of g(k). * The sum of the squares of the first 19 primes is divisible by 19. *19 is the sixth Heegner number. 67 and 163, respectively the 19th and 38th prime numbers, are the two largest Heegner numbers, of nine total. * 19 is the third centered triangular number as well as the third centered hexagonal number. : The 19th triangular number is 190, equivalently the sum of the first 19 non-zero integers, that is al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
18 (number)
18 (eighteen) is the natural number following 17 and preceding 19. In mathematics * Eighteen is a composite number, its divisors being 1, 2, 3, 6 and 9. Three of these divisors (3, 6 and 9) add up to 18, hence 18 is a semiperfect number. Eighteen is the first inverted square-prime of the form ''p''·''q''2. * In base ten, it is a Harshad number. * It is an abundant number, as the sum of its proper divisors is greater than itself (1+2+3+6+9 = 21). It is known to be a solitary number, despite not being coprime to this sum. * It is the number of one-sided pentominoes. * It is the only number where the sum of its written digits in base 10 (1+8 = 9) is equal to half of itself (18/2 = 9). * It is a Fine number. In science Chemistry * Eighteen is the atomic number of argon. * Group 18 of the periodic table is called the noble gases. * The 18-electron rule is a rule of thumb in transition metal chemistry for characterising and predicting the stability of metal complexes. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
17 (number)
17 (seventeen) is the natural number following 16 (number), 16 and preceding 18 (number), 18. It is a prime number. Seventeen is the sum of the first four prime numbers. In mathematics 17 is the seventh prime number, which makes seventeen the fourth super-prime, as seven is itself prime. The next prime is 19 (number), 19, with which it forms a twin prime. It is a cousin prime with 13 (number), 13 and a sexy prime with 11 (number), 11 and 23 (number), 23. It is an emirp, and more specifically a permutable prime with 71 (number), 71, both of which are also supersingular prime (moonshine theory), supersingular primes. Seventeen is the sixth Mersenne prime exponent, yielding 131,071. Seventeen is the only prime number which is the sum of four consecutive primes: 2,3,5,7. Any other four consecutive primes summed would always produce an even number, thereby divisible by 2 and so not prime. Seventeen can be written in the form x^y + y^x and x^y - y^x, and, as such, it is a Leyland ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
16 (number)
16 (sixteen) is the natural number following 15 and preceding 17. 16 is a composite number, and a square number, being 42 = 4 × 4. It is the smallest number with exactly five divisors, its proper divisors being , , and . In English speech, the numbers 16 and 60 are sometimes confused, as they sound very similar. Sixteen is the fourth power of two. For this reason, 16 was used in weighing light objects in several cultures. The British have 16 ounces in one pound; the Chinese used to have 16 ''liangs'' in one ''jin''. In old days, weighing was done with a beam balance to make equal splits. It would be easier to split a heap of grains into sixteen equal parts through successive divisions than to split into ten parts. Chinese Taoists did finger computation on the trigrams and hexagrams by counting the finger tips and joints of the fingers with the tip of the thumb. Each hand can count up to 16 in such manner. The Chinese abacus uses two upper beads to represent the 5s and 5 low ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
15 (number)
15 (fifteen) is the natural number following 14 and preceding 16. Mathematics 15 is: * A composite number, and the sixth semiprime; its proper divisors being , and . * A deficient number, a smooth number, a lucky number, a pernicious number, a bell number (i.e., the number of partitions for a set of size 4), a pentatope number, and a repdigit in binary (1111) and quaternary (33). In hexadecimal, and higher bases, it is represented as F. * A triangular number, a hexagonal number, and a centered tetrahedral number. * The number of partitions of 7. * The smallest number that can be factorized using Shor's quantum algorithm. * The magic constant of the unique order-3 normal magic square. * The number of supersingular primes. Furthermore, * 15 is one of two numbers within the ''teen'' numerical range (13-19) not to use a single-digit number in the prefix of its name (the first syllable preceding the ''teen'' suffix); instead, it uses the adjective form of five (' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
14 (number)
14 (fourteen) is a natural number following 13 and preceding 15. In relation to the word "four" ( 4), 14 is spelled "fourteen". In mathematics * 14 is a composite number. * 14 is a square pyramidal number. * 14 is a stella octangula number. * In hexadecimal, fourteen is represented as E * Fourteen is the lowest even ''n'' for which the equation φ(''x'') = ''n'' has no solution, making it the first even nontotient (see Euler's totient function). * Take a set of real numbers and apply the closure and complement operations to it in any possible sequence. At most 14 distinct sets can be generated in this way. ** This holds even if the reals are replaced by a more general topological space. See Kuratowski's closure-complement problem * 14 is a Catalan number. * Fourteen is a Companion Pell number. * According to the Shapiro inequality 14 is the least number ''n'' such that there exist ''x'', ''x'', ..., ''x'' such that :\sum_^ \frac < \frac where ''x'' = ''x'', ''x ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
13 (number)
13 (thirteen) is the natural number following 12 and preceding 14. Strikingly folkloric aspects of the number 13 have been noted in various cultures around the world: one theory is that this is due to the cultures employing lunar-solar calendars (there are approximately 12.41 lunations per solar year, and hence 12 "true months" plus a smaller, and often portentous, thirteenth month). This can be witnessed, for example, in the "Twelve Days of Christmas" of Western European tradition. In mathematics The number 13 is the sixth prime number. It is a twin prime with 11, as well as a cousin prime with 17. It is the second Wilson prime, of three known (the others being 5 and 563), and the smallest emirp in decimal. 13 is: *The second star number: *The third centered square number: * A happy number and a lucky number. *A Fibonacci number, preceded by 5 and 8. *The smallest number whose fourth power can be written as a sum of two consecutive square numbers (1192 + 1202). *The s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
12 (number)
12 (twelve) is the natural number following 11 (number), 11 and preceding 13 (number), 13. Twelve is a superior highly composite number, divisible by 2 (number), 2, 3 (number), 3, 4 (number), 4, and 6 (number), 6. It is the number of years required for an Jupiter#Pre-telescopic research, orbital period of Jupiter. It is central to many systems of timekeeping, including the Gregorian calendar, Western calendar and time, units of time of day and frequently appears in the world's major religions. Name Twelve is the largest number with a monosyllable, single-syllable name in English language, English. Early Germanic languages, Germanic numbers have been theorized to have been non-decimal: evidence includes the unusual phrasing of 11 (number), eleven and twelve, the long hundred, former use of "hundred" to refer to groups of 120 (number), 120, and the presence of glosses such as "tentywise" or "ten-count" in medieval texts showing that writers could not presume their readers would no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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