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Wilbur Knorr
Wilbur Richard Knorr (August 29, 1945 – March 18, 1997) was an American historian of mathematics and a professor in the departments of philosophy and classics at Stanford University. He has been called "one of the most profound and certainly the most provocative historian of Greek mathematics" of the 20th century. Biography Knorr was born August 29, 1945, in Richmond Hill, Queens. He did his undergraduate studies at Harvard University from 1963 to 1966 and stayed there for his Ph.D., which he received in 1973 under the supervision of John Emery Murdoch and G. E. L. Owen... After postdoctoral studies at Cambridge University, he taught at Brooklyn College, but lost his position when the college's Downtown Brooklyn campus was closed as part of New York's mid-1970s fiscal crisis. After taking a temporary position at the Institute for Advanced Study, he joined the Stanford faculty as an assistant professor in 1979, was tenured there in 1983, and was promoted to full professor in 199 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilbur Knorr 1973 Headshot
Wilbur may refer to: Places in the United States * Wilbur, Indiana, an unincorporated town * Wilbur, Trenton, New Jersey, a neighborhood in the city of Trenton * Wilbur, Oregon, an unincorporated community * Wilbur, Washington, a small farming town * Wilbur, West Virginia Other uses * Wilbur (name) * The codename given to the HTML 3.2 standard * Wilbur (comics), ''Wilbur'' (comics), a long-running comic book published by Archie Comics from 1944 to 1965 * Wilbur Kookmeyer, Wilbur (Kookmeyer), cartoon strip about a 'kook' (poser surfer) created by Bob Penuelas, which first appeared in ''Surfer'' magazine in 1986 * Wilbur (TV series), ''Wilbur'' (TV series), a children's TV show on Kids' CBC * Wilbur Chocolate Company, a chocolate company based in Lititz, Pennsylvania * Wilbur Dam, a hydroelectric dam on the Watauga River, Tennessee * Wilbur Theatre, a historic theatre in Boston, Massachusetts See also * Wilber (other) * Wilbor (other) * Wilbour * Samuel Wilbo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thebes, Greece
Thebes (; ell, Θήβα, ''Thíva'' ; grc, Θῆβαι, ''Thêbai'' .) is a city in Boeotia, Central Greece. It played an important role in Greek myths, as the site of the stories of Cadmus, Oedipus, Dionysus, Heracles and others. Archaeological excavations in and around Thebes have revealed a Mycenaean settlement and clay tablets written in the Linear B script, indicating the importance of the site in the Bronze Age. Thebes was the largest city of the ancient region of Boeotia and was the leader of the Boeotian confederacy. It was a major rival of ancient Athens, and sided with the Persians during the 480 BC invasion under Xerxes I. Theban forces under the command of Epaminondas ended Spartan hegemony at the Battle of Leuctra in 371 BC, with the Sacred Band of Thebes, an elite military unit of male lovers celebrated as instrumental there. Macedonia would rise in power at the Battle of Chaeronea in 338 BC, bringing decisive victory to Philip II over an alliance of Thebes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid
Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus (mathematician), Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics. Very little is known of Euclid's life, and most information comes from the philosophers Proclus and Pappus of Alexandria many centuries later. Until the early Renaissance he was often mistaken f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sabetai Unguru
Sabetai Unguru (, ''Shabtai Unguru''; born 1 January 1931) is an Israeli historian of mathematics and science. Biography Sabetai Unguru was born in 1931 in Podu Iloaiei, Romania. He studied philosophy, philology, history, and mathematics at the University of Iași, before immigrating to Israel in 1961. He obtained his Ph.D. in the history of science from the University of Wisconsin–Madison in 1970, and was an assistant and associate professor in the Department of History at the University of Oklahoma between 1970 and 1982. Unguru was appointed associate professor at Tel Aviv University in 1983, and became full professor Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professors ... in 1987. He served as Director of the Cohn Institute for the History and Philosophy of Science and Ideas at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golden Section
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( or \phi) denotes the golden ratio. The constant \varphi satisfies the quadratic equation \varphi^2 = \varphi + 1 and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli, and also goes by several other names. Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of \varphi—may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural objects ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eudoxus Of Cnidus
Eudoxus of Cnidus (; grc, Εὔδοξος ὁ Κνίδιος, ''Eúdoxos ho Knídios''; ) was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato. All of his original works are lost, though some fragments are preserved in Hipparchus' commentary on Aratus's poem on astronomy. ''Sphaerics'' by Theodosius of Bithynia may be based on a work by Eudoxus. Life Eudoxus was born and died in Cnidus (also spelled Knidos), which was a city on the southwest coast of Asia Minor. The years of Eudoxus' birth and death are not fully known but the range may have been , or . His name Eudoxus means "honored" or "of good repute" (, from ''eu'' "good" and ''doxa'' "opinion, belief, fame"). It is analogous to the Latin name Benedictus. Eudoxus's father, Aeschines of Cnidus, loved to watch stars at night. Eudoxus first traveled to Tarentum to study with Archytas, from whom he learned mathematics. While in Italy, Eudoxus visited Sicily, where he studied medicine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Mean
In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired. The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, and 4 is : \left(\frac\right)^ = \frac = \frac = 2\,. Definition The harmonic mean ''H'' of the positive real numbers x_1, x_2, \ldots, x_n is defined to be :H = \frac = \frac = \left(\frac\right)^. The third formula in the above equation expresses the harmonic mean as the reciprocal of the arithmetic mean of the reciprocals. From the following formula: :H = \frac. it is more apparent that the harmonic mean is related to the arithmetic and geometric means. It is the reciprocal dual of the arithmetic mean for positive inputs: :1/H(1/x_1 \ldots 1/x_n) = A(x_1 \ldots x_n) The harmonic mean is a Schur-con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Mean
In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results of an experiment or an observational study, or frequently a set of results from a survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics, because it helps distinguish it from other means, such as the geometric mean and the harmonic mean. In addition to mathematics and statistics, the arithmetic mean is used frequently in many diverse fields such as economics, anthropology and history, and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population. While the arithmetic mean is often used to report central tendencies, it is not a robust statistic, meaning that it is greatly influe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the th root of the product of numbers, i.e., for a set of numbers , the geometric mean is defined as :\left(\prod_^n a_i\right)^\frac = \sqrt /math> or, equivalently, as the arithmetic mean in logscale: :\exp For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product, that is, \sqrt = 4. As another example, the geometric mean of the three numbers 4, 1, and 1/32 is the cube root of their product (1/8), which is 1/2, that is, \sqrt = 1/2. The geometric mean applies only to positive numbers. The geometric mean is often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as a set of growth figures: values of the human population or inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theaetetus (dialogue)
The ''Theaetetus'' (; el, Θεαίτητος) is one of Plato's dialogues concerning epistemology, written BCE. In this dialogue set in a wrestling school, Socrates and Theaetetus discuss three definitions of knowledge: knowledge as nothing but ''perception'', knowledge as ''true judgment'', and, finally, knowledge as a '' true judgment with an account.'' Each of these definitions is shown to be unsatisfactory. Socrates declares Theaetetus will have benefited from discovering what he does not know, and that he may be better able to approach the topic in the future. The conversation ends with Socrates' announcement that he has to go to court to face a criminal indictment. The framing of the dialogue The dialogue is framed by a brief scene in which Euclid of Megara tells his friend Terpsion that he has a written record of a dialogue between Socrates and Theaetetus, which occurred when Theaetetus was quite a young man. This dialogue is then read aloud to the two men by a sl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plato
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution of higher learning on the European continent. Along with his teacher, Socrates, and his student, Aristotle, Plato is a central figure in the history of Ancient Greek philosophy and the Western and Middle Eastern philosophies descended from it. He has also shaped religion and spirituality. The so-called neoplatonism of his interpreter Plotinus greatly influenced both Christianity (through Church Fathers such as Augustine) and Islamic philosophy (through e.g. Al-Farabi). In modern times, Friedrich Nietzsche diagnosed Western culture as growing in the shadow of Plato (famously calling Christianity "Platonism for the masses"), while Alfred North Whitehead famously said: "the safest general characterization of the European philosophical tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity (mathematics)
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because \begin -2 \cdot 2 &= -4 \\ 0 \cdot 2 &= 0 \\ 41 \cdot 2 &= 82 \end By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
