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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 ( , ; ; 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 Modern science, science. Mathematics was paramou ... devised the Cartesian exponent notation, which is still used today. This is a list of Recorde's terms. By ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
8 (number)
8 (eight) is the natural number following 7 and preceding 9. Etymology English ''eight'', from Old English '', æhta'', Proto-Germanic ''*ahto'' is a direct continuation of Proto-Indo-European '' *oḱtṓ(w)-'', and as such cognate with Greek and Latin , both of which stems are reflected by the English prefix oct(o)-, as in the ordinal adjective ''octaval'' or ''octavary'', the distributive adjective is '' octonary''. The adjective ''octuple'' (Latin ) may also be used as a noun, meaning "a set of eight items"; the diminutive '' octuplet'' is mostly used to refer to eight siblings delivered in one birth. The Semitic numeral is based on a root ''*θmn-'', whence Akkadian ''smn-'', Arabic ''ṯmn-'', Hebrew ''šmn-'' etc. The Chinese numeral, written ( Mandarin: ''bā''; Cantonese: ''baat''), is from Old Chinese ''*priāt-'', ultimately from Sino-Tibetan ''b-r-gyat'' or ''b-g-ryat'' which also yielded Tibetan '' brgyat''. It has been argued that, as the cardinal ... [...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. Mathematics Twenty-one is the fifth distinct semiprime, and the second of the form 3 \times q where q is a higher prime. It is a repdigit in quaternary (1114). Properties As a biprime with proper divisors 1, 3 and 7, twenty-one has a prime aliquot sum of 11 within an aliquot sequence containing only one composite number (21, 11, 1, 0). 21 is the first member of the second cluster of consecutive discrete semiprimes (21, 22), where the next such cluster is ( 33, 34, 35). There are 21 prime numbers with 2 digits. There are a total of 21 prime numbers between 100 and 200. 21 is the first Blum integer, since it is a semiprime with both its prime factors being Gaussian primes. While 21 is the sixth triangular number, it is also the sum of the divisors of the first five positive integers: \begin 1 & + 2 + 3 + 4 + 5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
20 (number)
20 (twenty) is the natural number following 19 and preceding 21. A group of twenty units is sometimes referred to as a score. In mathematics Twenty is a composite number. It is also the smallest primitive abundant number. The Happy Family of sporadic groups is made up of twenty finite simple groups that are all subquotients of the friendly giant, the largest of twenty-six sporadic groups. Geometry An icosagon is a polygon with 20 edges. Bring's curve is a Riemann surface, whose fundamental polygon is a regular hyperbolic icosagon. Platonic solids The largest number of faces a Platonic solid can have is twenty faces, which make up a regular icosahedron. A dodecahedron, on the other hand, has twenty vertices, likewise the most a regular polyhedron can have. This is because the icosahedron and dodecahdron are duals of each other. Other fields Science 20 is the third magic number in physics. Biology In some countries, the number 20 is used as an index in m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19 (number)
19 (nineteen) is the natural number following 18 (number), 18 and preceding 20 (number), 20. It is a prime number. Mathematics Nineteen is the eighth prime number. Number theory 19 forms a twin prime with 17 (number), 17, a cousin prime with 23 (number), 23, and a sexy prime with 13 (number), 13. 19 is the fifth Trinomial triangle#Central trinomial coefficients, central trinomial coefficient, and the maximum number of fourth powers needed to sum up to any natural number (see, Waring's problem). It is the number of Composition (combinatorics), compositions of 8 into distinct parts. 19 is the eighth strictly non-palindromic number in any Numeral system, base, following 11 (number), 11 and preceding 47 (number), 47. 19 is also the second octahedral number, after 6, and the sixth Heegner number. In the Engel expansion of pi, 19 is the seventh term following and preceding . The sum of the first terms preceding 17 (number), 17 is in equivalence with 19, where its prime Sequen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
18 (number)
18 (eighteen) is the natural number following 17 (number), 17 and preceding 19 (number), 19. It is an even composite number. Mathematics 18 is a semiperfect number and an abundant number. It is a largely composite number, as it has 6 divisors and no smaller number has more than 6 divisors. There are 18 One-sided polyomino, one-sided pentominoes. In the classification of finite simple groups, there are 18 infinite families of groups. In science Chemistry * The 18-Electron rule, 18-electron rule is a rule of thumb in transition metal chemistry for characterising and predicting the stability of Metal complex#Metal complexes, metal complexes. In religion and literature * The Hebrew language, Hebrew word for "life" is (''Chai (symbol), chai''), which has a gematria, numerical value of 18. Consequently, the custom has arisen in Jewish circles to give donations and monetary gifts in multiples of 18 as an expression of blessing for long life. * In Judaism, in the Talmud; Pirkei Avot ... [...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. 17 was described at MIT as "the least random number", according to the Jargon File. This is supposedly because, in a study where respondents were asked to choose a random number from 1 to 20, 17 was the most common choice. This study has been repeated a number of times. Mathematics 17 is a Leyland number and Leyland number#Leyland primes, Leyland prime, using 2 & 3 (23 + 32) and using 4 and 5, using 3 & 4 (34 - 43). 17 is a Fermat prime. 17 is one of six lucky numbers of Euler. Since seventeen is a Fermat prime, regular heptadecagons can be constructible polygon, constructed with a compass and unmarked ruler. This was proven by Carl Friedrich Gauss and ultimately led him to choose mathematics over philology for his studies. The minimum possible number of givens for a sudoku puzzle with a unique solution is 17. Geometric properties Two-dimensions *There are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
16 (number)
16 (sixteen) is the natural number following 15 (number), 15 and preceding 17 (number), 17. It is the 4, fourth power of two. In English speech, the numbers 16 and 60 (number), 60 are sometimes confused, as they sound similar. Mathematics 16 is the ninth composite number, and a square number: 4 (number), 42 = 4 × 4 (the first non-unitary fourth-power prime number, prime of the form ''p''4). It is the smallest number with exactly five divisors, its proper divisors being , , and . Sixteen is the only integer that Equation x^y = y^x, equals ''m''''n'' and ''n''''m'', for some unequal integers ''m'' and ''n'' (m=4, n=2, or vice versa). It has this property because 2^=2\times 2. It is also equal to 32 (see tetration). The aliquot sum of 16 is 15 (number), 15, within an aliquot sequence of four composite members (16, 15 (number), 15, 9 (number), 9, 4 (number), 4, 3 (number), 3, 1 (number), 1, 0) that belong to the prime 3-aliquot tree. *Sixteen is the largest known integer , for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
15 (number)
15 (fifteen) is the natural number following 14 (number), 14 and preceding 16 (number), 16. Mathematics 15 is: * The eighth composite number and the sixth semiprime and the first odd and fourth discrete semiprime; its proper divisors are , , and , so the first of the form (3.q), where q is a higher prime. * a deficient number, a lucky number, a bell number (i.e., the number of partitions for a set of size 4), a pentatope number, and a repdigit in Binary numeral system, binary (1111) and quaternary numeral system, quaternary (33). In hexadecimal, and higher bases, it is represented as F. * with an aliquot sum of 9 (number), 9; within an aliquot sequence of three composite numbers (15,9 (number), 9,4 (number), 4,3 (number), 3,1 (number), 1,0) to the Prime in the 3 (number), 3-aliquot tree. * the second member of the first cluster of two discrete semiprimes (14 (number), 14, 15); the next such cluster is (21 (number), 21, 22 (number), 22). * the first number to be Polygonal numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
14 (number)
14 (fourteen) is the natural number following 13 (number), 13 and preceding 15 (number), 15. Mathematics Fourteen is the seventh composite number. Properties 14 is the third distinct semiprime, being the third of the form 2 \times q (where q is a higher prime). More specifically, it is the first member of the second cluster of two discrete semiprimes (14, 15 (number), 15); the next such cluster is (21 (number), 21, 22 (number), 22), members whose sum is the fourteenth prime number, 43 (number), 43. 14 has an aliquot sum of 10 (number), 10, within an aliquot sequence of two composite numbers (14, 10 (number), 10, 8 (number), 8, 7 (number), 7, 1 (number), 1, 0) in the prime 7-aliquot tree. 14 is the third Pell number, companion Pell number and the fourth Catalan number. It is the lowest even n for which the Euler totient \varphi(x) = n has no solution, making it the first even nontotient. According to the Shapiro inequality, 14 is the least number n such that there exist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
13 (number)
13 (thirteen) is the natural number following 12 (number), 12 and preceding 14 (number), 14. Folklore surrounding the number 13 appears in many 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 a prime number, happy number and a lucky number. It is a twin prime with 11 (number), 11, as well as a cousin prime with 17 (number), 17. It is the second of only 3 Wilson prime, Wilson primes: 5, 13, and 563 (number), 563. A 13-sided regular polygon is called a tridecagon. List of basic calculations In languages Grammar * In all Germanic languages, 13 is the first Compound (linguistics), compound number; the numbers 11 and 12 have their own names. * The ... [...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 the 3rd superior highly composite number, the 3rd colossally abundant number, the 5th highly composite number, and is divisible by the numbers from 1 (number), 1 to 4 (number), 4, and 6 (number), 6, a large number of divisors comparatively. 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 pres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
