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- History of science (41710 bytes)
6: ...ve]] process of designing useful objects and systems, which differs from the search for [[empirical]] ...
54: ...o what is now called an [[algorithm]]; the word [[algebra]] is derived from ''al-jabr'', the beginning of t...
61: ...y [[Vesalius]] on human cadavers also found problems with the Galenian anatomy.
78: ...f Newton were shown not to be correct in all circumstances. Beginning in [[1900]], [[Max Planck|Planc...
93: ...tituents of DNA, simple [[amino acid]]s, could themselves be built up from simpler molecules in a [[si... - Mathematics (24164 bytes)
15: ...ich inspired it and can be applied to solve problems in that subject. Mathematics which can be so used...
21: ...tions, with accompanying notation. Some of the terms they use also have a meaning outside of mathemati...
23: ...from happening, mathematicians wanted their theorems to follow mechanically from a few simple incontro...
33: ...r systems (foundations) and to the empirical systems of the various sciences (applied mathematics).
35: ...ized to [[vector space]]s and studied in [[linear algebra]], belongs to the two branches of structure and s... - Leonardo da Vinci (25889 bytes)
9: ...rdo, son of Mister Piero, from Vinci". Leonardo himself simply signed his works "Leonardo" or "Io, Leo...
12: ...ect that whatever he turned his mind to he made himself master of with ease" ([[Giorgio Vasari|Vasari]...
20: ...a close friendship with one. He also surrounded himself with handsome young men throughout his life, a...
45: ...gh there is significant debate whether Leonardo himself painted the Mona Lisa, or whether it was the w...
53: ...o]]" is the technique of modeling and defining forms through contrasts of light and shadow. - Age of Enlightenment (36312 bytes)
4: ...intellectual leaders of this movement regarded themselves as courageous and elite, and regarded their ...
14: ...ge of Reason, which was built on self-evident axioms, reached its height with [[Baruch Spinoza|Baruch ...
18: ...m first principles, Enlightenment thinkers saw themselves as looking into the mind of God by studying ...
22: ...of the observer, expressible in rigorous human terms. The quest for the expression of this truth would...
33: ...tural philosophy that espoused the application of algebra to the study of nature, and the discoveries broug... - Computer (32773 bytes)
3: ...essible in [[number|numerical]] or [[logic]]al terms. Computers are made from [[digital circuit|compon...
12: ... that information are reduced to simple [[Boolean algebra]].
14: ...(and the majority of information processing problems that can be translated into mathematical ones). T...
16: ...problems. [[Alan Turing]] identified which problems could and could not be solved by computers, and i...
24: ...e context of the citation, it is obvious these terms were in use prior to 1946. - Charles Babbage (13539 bytes)
2: ...' [[computer]]. Parts of his uncompleted mechanisms are on display in the [[London Science Museum]]. ...
38: ...ing custom machine tools, many of which Babbage himself designed. He took extensive tours of the indus...
46: Charles' problems with the treasury coincided with numerous disagre...
59: ...mbers. In another, she wrote about a generalized algebra engine that could perform operations on symbols a...
70: ...ate as a divine legislator, making laws (or programs) which then produced species at the appropriate t... - James Cook (14770 bytes)
8: .... While working for Walker, Cook began to study [[algebra]], [[trigonometry]], [[navigation]], and [[astron...
32: ...ke command of Cook's second voyage, but removed himself from the voyage before it began.
39: ...this voyage, while [[Tobias Furneaux]] commanded HMS ''Adventure''. Cook [[circumnavigation|circumnavi...
49: ... Charles Clerke commanded [[HMS Discovery (ship)|HMS ''Discovery'']]. Ostensibly the voyage was planne...
59: ...ook's sailing master, was given command of the [[HMS Bounty]] in [[1787]] to sail to Tahiti and return... - Rene Descartes (17976 bytes)
1: ...sian coordinate system used in plane geometry and algebra.
6: ...ounded [[analytic geometry]], that bridge between algebra and geometry crucial to the invention of the [[ca...
16: ...d thinking about using mathematics to solve problems in physics, Descartes had a vision in a dream thr...
43: ...characteristics change completely. However, it seems that it is still the same thing: it is still a pi...
46: ... based on deduction <i>and</i> perception. In terms of [[epistemology]] therefore, he can be said to ... - Persian Empire (26229 bytes)
15: ...e took [[Lydia]] in Asia Minor, and carried his arms eastward into central Asia. Finally in [[539 BC]]...
23: Achaemenid Persia united people and kingdoms from every major civilization of a vast region. ...
50: During the Parthian period, Hellenistic customs partially gave way to a resurgence of Persian cul...
60: ...g dynasty since the Achaemenids; thus they saw themselves as the successors of Darius and Cyrus. They ...
73: ...rom Persian and [[Byzantine]] administrative systems and moved their capital to [[Damascus]], in the c... - Ancient Indian science and technology (21581 bytes)
9: ...cepts of [[0 (number)|zero]], the techniques of [[algebra]] and [[algorithm]], [[square root]] and [[cube r...
14: ...orollary were emergence of [[music]] and other forms of [[performing art]]s.
24: ...tical concepts, including [[0 (number)|zero]], [[algebra]] and [[algorithm]], [[square root]] and [[cube r...
30: ...ed �''Siddantha Shiromani''� has a chapter on algebra. In [[1816]], [[James Taylor]] translated Bhaska...
61: ...ring from a diameter of 40 cms at the base to 30 cms at the top and is estimated to weigh 6 tonnes. It... - History of science in the Middle Ages (30877 bytes)
16: ...ich were often incomplete and posed serious problems of interpretation. Given the limited scientific a...
18: ...itating classical knowledge by establishing programs of study based upon the seven [[liberal arts]]: t...
137: ... where, influenced by Grosseteste, he dedicated himself to studies where he implemented the observatio...
167: ...what we now call an [[algorithm]], and the word [[algebra]] is derived from ''al-jabr'', the beginning of t...
176: ...]] tables, and techniques and [[algorithm]]s of [[algebra]]. [[Arabic]] translations of his texts were avai... - Timeline of Middle Eastern History (12425 bytes)
50: ...Narmer unifies the Upper and Lower Egyptian Kingdoms, and gives birth to the worlds's first [[nation]]...
149: * [[Algebra]] developed in the Middle East - Golden Ratio (15928 bytes)
40: For those who struggle with algebra but can at least handle the idea of fractions of ...
64: ...'a'' − ''b'') is in even lower terms — a contradiction.
81: ==Alternate forms==
115: ...the root of a [[polynomial equation]], it is an [[algebraic number]]. It can be shown that φ is an [[ir...
120: ... (mathematics)|limit]] of ratios of successive terms of the Fibonacci sequence (or any Fibonacci-like ... - Integer (6458 bytes)
3: == Algebraic properties ==
24: In the language of [[abstract algebra]], the first five properties listed above for add...
32: Again, in the language of abstract algebra, the above says that '''Z''' is a [[Euclidean dom...
40: The ordering of integers is compatible with the algebraic operations in the following way: - Number (4151 bytes)
19: ... [[complex number]]s '''C''', which leads to an [[algebraically closed field]] in which every polynomial wi...
24: ...umber]]s, and those complex numbers which are not algebraic are called [[transcendental number|transcendent...
27: ...us leaving the category of associative [[division algebra]]s.
31: ...f [[function field]]s of finite [[characteristic (algebra)|characteristic]] behave in some ways like number...
43: ...tains the [[group (mathematics)|group]]s, [[ring (algebra)|ring]]s and [[field (mathematics)|field]]s.
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