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Number  
  
742   04:27 مساءً   date: 5-8-2020
Author : Barbeau, E. J
Book or Source : Power Play: A Country Walk through the Magical World of Numbers. Providence, RI: Amer. Math. Soc., 1997.
Page and Part : ...


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Date: 7-8-2020 788
Date: 15-12-2020 663
Date: 2-1-2020 998

Number

The word "number" is a general term which refers to a member of a given (possibly ordered) set. The meaning of "number" is often clear from context (i.e., does it refer to a complex number, integer, real number, etc.?). Wherever possible in this work, the word "number" is used to refer to quantities which are integers, and "constant" is reserved for nonintegral numbers which have a fixed value. Because terms such as real number, Bernoulli number, and irrational number are commonly used to refer to nonintegral quantities, however, it is not possible to be entirely consistent in nomenclature.

To indicate a particular numerical label, the abbreviation "no." is sometimes used (deriving from "numero," the ablative case of the Latin "numerus"), as is the less common "nr." The symbol # (known as the octothorpe) is commonly used to denote "number."

While some authors prefer to include "and" between various parts of a number name, in this work, "and"s are omitted. For example, the number 101 is called "one hundred one" rather than "one hundred and one." According to most definitive sources (Schildberger 2001; The Chicago Manual of Style 2003, p. 381; Mish 2003, p. 852), either is acceptable. However, The Associated Press Stylebook gives implicit examples in which the "and" is omitted (Goldstein 1998, p. 145). So the fact of the matter is that different sources use different conventions, with some sources even being internally inconsistent. For example, Conway and Guy (1996) list the "(and)" as optional on p. 15, while writing out "one hundred and sixty-three" on p. 25.

According to The Chicago Manual of Style (2003, p. 380), in nontechnical written contexts, whole numbers from one to one hundred should always be spelled out, and other whole numbers should be written in terms of numerals. In addition, when a number begins a sentence, it is always spelled out unless it appears awkward, in which case the sentence should be recast. In this work, numbers are sometimes spelled out and sometimes written numerically, depending on which appears clearer.

Note that commas should not be used to separate words that are part of one number (Goldstein 1998, p. 145).

The following table summarizes the English names given to the first few positive numbers (Schildberger 2001, Misch 2003).

n name
1 one
2 two
3 three
4 four
5 five
6 six
7 seven
8 eight
9 nine
10 ten
11 eleven
12 twelve
13 thirteen
14 fourteen
15 fifteen
16 sixteen
17 seventeen
18 eighteen
19 nineteen
20 twenty
21 twenty-one
22 twenty-two
23 twenty-three
24 twenty-four
25 twenty-five
26 twenty-six
27 twenty-seven
28 twenty-eight
29 twenty-nine
30 thirty
31 thirty-one
32 thirty-two
33 thirty-three
34 thirty-four
35 thirty-five
36 thirty-six
37 thirty-seven
38 thirty-eight
39 thirty-nine
40 forty
41 forty-one
42 forty-two
43 forty-three
44 forty-four
45 forty-five
46 forty-six
47 forty-seven
48 forty-eight
49 forty-nine
50 fifty
51 fifty-one
52 fifty-two
53 fifty-three
54 fifty-four
55 fifty-five
56 fifty-six
57 fifty-seven
58 fifty-eight
59 fifty-nine
60 sixty
61 sixty-one
62 sixty-two
63 sixty-three
64 sixty-four
65 sixty-five
66 sixty-six
67 sixty-seven
68 sixty-eight
69 sixty-nine
70 seventy
71 seventy-one
72 seventy-two
73 seventy-three
74 seventy-four
75 seventy-five
76 seventy-six
77 seventy-seven
78 seventy-eight
79 seventy-nine
80 eighty
81 eighty-one
82 eighty-two
83 eighty-three
84 eighty-four
85 eighty-five
86 eighty-six
87 eighty-seven
88 eighty-eight
89 eighty-nine
90 ninety
91 ninety-one
92 ninety-two
93 ninety-three
94 ninety-four
95 ninety-five
96 ninety-six
97 ninety-seven
98 ninety-eight
99 ninety-nine
100 one hundred
101 one hundred one
102 one hundred two
103 one hundred three
104 one hundred four
105 one hundred five
106 one hundred six
107 one hundred seven
108 one hundred eight
109 one hundred nine
110 one hundred ten
111 one hundred eleven
112 one hundred twelve
113 one hundred thirteen
114 one hundred fourteen
115 one hundred fifteen
116 one hundred sixteen
117 one hundred seventeen
118 one hundred eighteen
119 one hundred nineteen
120 one hundred twenty
121 one hundred twenty-one
122 one hundred twenty-two
123 one hundred twenty-three
124 one hundred twenty-four
125 one hundred twenty-five
126 one hundred twenty-six
127 one hundred twenty-seven
128 one hundred twenty-eight
129 one hundred twenty-nine
130 one hundred thirty
131 one hundred thirty-one
132 one hundred thirty-two
133 one hundred thirty-three
134 one hundred thirty-four
135 one hundred thirty-five
136 one hundred thirty-six
137 one hundred thirty-seven
138 one hundred thirty-eight
139 one hundred thirty-nine
140 one hundred forty
141 one hundred forty-one
142 one hundred forty-two
143 one hundred forty-three
144 one hundred forty-four
145 one hundred forty-five
146 one hundred forty-six
147 one hundred forty-seven
148 one hundred forty-eight
149 one hundred forty-nine
150 one hundred fifty

Note that two differing conventions exist for the naming of large numbers (e.g., the American system terms 10^9 "a billion," while the British system terms it "a milliard").

American British power of 10
million million 10^6
billion milliard 10^9
trillion billion 10^(12)
quadrillion   10^(15)
quintillion trillion 10^(18)
sextillion   10^(21)
septillion quadrillion 10^(24)
octillion   10^(27)
nonillion quintillion 10^(30)
decillion   10^(33)
undecillion sexillion 10^(36)
duodecillion   10^(39)
tredecillion septillion 10^(42)
quattuordecillion   10^(45)
quindecillion octillion 10^(48)
sexdecillion   10^(51)
septendecillion nonillion 10^(54)
octodecillion   10^(57)
novemdecillion decillion 10^(60)
vigintillion   10^(63)
  undecillion 10^(66)
  duodecillion 10^(72)
  tredecillion 10^(78)
  quattuordecillion 10^(84)
  quindecillion 10^(90)
  sexdecillion 10^(96)
  septendecillion 10^(102)
  octodecillion 10^(108)
  novemdecillion 10^(114)
  vigintillion 10^(120)
centillion   10^(303)
  centillion 10^(600)

NumberCharacters

The numbers of characters (including spaces and dashes) in the English names (written without trailing "and"s) for the numbers 1, 2, 3, ... are 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, 8, 7, 7, 9, 8, 8, 6, 10, 10, ... (OEIS A052360), illustrated above.

NumberLetters

The corresponding numbers of letters are 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, 8, 7, 7, 9, 8, ... (OEIS A005589; Eureka 1974), illustrated above.

The corresponding numbers of syllables are 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 2, ... (OEIS A075774).

Consider the numbers having incrementally largest numbers of letters. This gives the sequence 1, 3, 11, 13, 17, 23, 73, 101, 103, 111, 113, 117, 123, 173, 323, 373, ... (OEIS A052363), which have the corresponding number of digits 3, 5, 6, 8, 9, 11, 12, 13, 15, 16, 18, 19, 21, ... (OEIS A089585).


REFERENCES:

"Problems Drive." Eureka 37, 8-11 and 33, 1974.

The Chicago Manual of Style, 15th ed. Chicago, IL: University of Chicago Press, 2003.

Barbeau, E. J. Power Play: A Country Walk through the Magical World of Numbers. Providence, RI: Amer. Math. Soc., 1997.

Bogomolny, A. "What is a Number." https://www.cut-the-knot.org/do_you_know/numbers.shtml.

Borwein, J. and Borwein, P. A Dictionary of Real Numbers. London: Chapman & Hall, 1990.

Conway, J. H. On Numbers and Games, 2nd ed. Wellesley, MA: A K Peters, 2000.

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, 1996.

Dantzig, T. Number: The Language of Science, 4th rev. ed. New York: Free Press, 1985.

Davis, P. J. The Lore of Large Numbers. New York: Random House, 1961.

De Geest, P. "World!Of Numbers." https://www.worldofnumbers.com/.

Ebbinghaus, H. D.; Hirzebruch, F.; Hermes, H.; Prestel, A; Koecher, M.; Mainzer, M.; and Remmert, R. Numbers. New York: Springer-Verlag, 1990.

Frege, G. Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, 2nd rev. ed. Evanston, IL: Northwestern University Press, 1980.

Goldstein, N. (Ed.). The Associated Press Stylebook and Libel Manual, fully upd. rev. Reading, MA: Addison-Wesley, 1998.

Ifrah, G. From One to Zero: A Universal History of Numbers. New York: Viking, 1987.

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, 1983.

McLeish, J. Number: The History of Numbers and How They Shape Our Lives. New York: Fawcett Columbine, 1992.

Mish, F. C. (Ed.). Merriam-Webster's Collegiate Dictionary, 11th ed. Springfield, MA: Merriam-Webster, 2003.

Munafo, R. "Notable Properties of Specific Numbers." https://home.earthlink.net/~mrob/pub/math/numbers.html.

Phillips, R. Numbers: Facts, Figures & Fiction. Cambridge, England: Cambridge University Press, 1994.

Rosenfelder, M. "Numbers from 1 to 10 in Over 4000 Languages." https://zompist.com/numbers.shtml.

Russell, B. "Definition of Number." Introduction to Mathematical Philosophy. New York: Simon and Schuster, 1971.

Schildberger, G. "English Names for the Numbers from 0 to 1022." Apr. 4, 2001. https://www.research.att.com/~njas/sequences/a000027.txt.

Sloane, N. J. A. Sequences A005589/M2277, A052360, A052363, A075774, and A089585 in "The On-Line Encyclopedia of Integer Sequences."

Smeltzer, D. Man and Number. Buchanan, NY: Emerson Books, 1974.

Weisstein, E. W. "Books about Numbers." https://www.ericweisstein.com/encyclopedias/books/Numbers.html.

Wells, D. W. The Penguin Dictionary of Curious and Interesting Numbers. Harmondsworth, England: Penguin Books, 1986.




الجبر أحد الفروع الرئيسية في الرياضيات، حيث إن التمكن من الرياضيات يعتمد على الفهم السليم للجبر. ويستخدم المهندسون والعلماء الجبر يومياً، وتعول المشاريع التجارية والصناعية على الجبر لحل الكثير من المعضلات التي تتعرض لها. ونظراً لأهمية الجبر في الحياة العصرية فإنه يدرّس في المدارس والجامعات في جميع أنحاء العالم. ويُعجب الكثير من الدارسين للجبر بقدرته وفائدته الكبيرتين، إذ باستخدام الجبر يمكن للمرء أن يحل كثيرًا من المسائل التي يتعذر حلها باستخدام الحساب فقط.وجاء اسمه من كتاب عالم الرياضيات والفلك والرحالة محمد بن موسى الخورازمي.


يعتبر علم المثلثات Trigonometry علماً عربياً ، فرياضيو العرب فضلوا علم المثلثات عن علم الفلك كأنهما علمين متداخلين ، ونظموه تنظيماً فيه لكثير من الدقة ، وقد كان اليونان يستعملون وتر CORDE ضعف القوسي قياس الزوايا ، فاستعاض رياضيو العرب عن الوتر بالجيب SINUS فأنت هذه الاستعاضة إلى تسهيل كثير من الاعمال الرياضية.

تعتبر المعادلات التفاضلية خير وسيلة لوصف معظم المـسائل الهندسـية والرياضـية والعلمية على حد سواء، إذ يتضح ذلك جليا في وصف عمليات انتقال الحرارة، جريان الموائـع، الحركة الموجية، الدوائر الإلكترونية فضلاً عن استخدامها في مسائل الهياكل الإنشائية والوصف الرياضي للتفاعلات الكيميائية.
ففي في الرياضيات, يطلق اسم المعادلات التفاضلية على المعادلات التي تحوي مشتقات و تفاضلات لبعض الدوال الرياضية و تظهر فيها بشكل متغيرات المعادلة . و يكون الهدف من حل هذه المعادلات هو إيجاد هذه الدوال الرياضية التي تحقق مشتقات هذه المعادلات.