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Topic: Thales theorem

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	Mathematics & Philosophy
		This is the whole story of Thales, who discovered nothing but the precise virtues of the human gaze, just as, somewhat later, Berkeley organized in an erudite manner a spectacle of light beneath his microscope, a rigorous organon of optical representation.
		On the one hand, the theorem is only possible because of the space of similarities; it may only be inscribed on or in that space which is the space of transport.
		Thales, while reading and noting the volume’s traces, deciphers no secret except that of the impossibility of penetrating the volume’s arcana, in which knowledge has been entombed forever, and from which the infinite history of analytical progress bursts forth as if from a spring.
	pratt.edu /~arch543p/readings/mathematics_and_philosophy.html (6169 words)

	Thales' theorem - Wikipedia, the free encyclopedia
		The converse of Thales' theorem is also valid; it states that a right triangle's hypotenuse is a diameter of its circumcircle.
		Thales' theorem can be used to construct the tangent to a given circle that passes through a given point.
		The theorem is named after Thales because he was said to have been the first to prove the theorem, using his own results that the base angles of an isosceles triangle are equal, and that the sum of angles in a triangle is equal to two right angles.
	en.wikipedia.org /wiki/Thales'_theorem (853 words)

	Thales of Miletus [Internet Encyclopedia of Philosophy]
		Second, Thales, who is acknowledged as an observer of the heavens, would have observed that stars which are visible in a certain locality may not be visible further to the north or south, a phenomena which could be explained within the understanding of a spherical earth.
		Thales never invoked a power that was not present in nature itself, because he believed that he had recognized a force which underpinned the events of nature.
		Thales certainly did not 'discover' the seasons, but he may have identified the relationship between the solstices, the changing position during the year of the sun in the sky, and associated this with seasonal climatic changes.
	www.iep.utm.edu /t/thales.htm (9340 words)

	Thales
		Thales of Miletus (circa 635 BC - 543 BC) was a pre-Socratic Greek philosopher.
		Thales is remembered for arguing that water is the essence of all things.
		Herodotus reports that in 585 BC Thales was with the Lydians when they fought the Medes, and was able to forecast that a solar eclipse would occur on May 28 which ended the war (see Alyattes II).
	www.gamesinathens.com /olympics/t/th/thales.shtml (415 words)

	HOW THE GREEKS MEASURED THE INVISIBLE
		It was Thales who forecast the solar eclipse of May 28, 585 B.C. which put an end to the protracted war between the Lydians and the Medes, and ultimately settled a lasting peace between them.
		Furthermore, Thales is reputed to have created the first almanac, giving the solstices, the equinoxes, the phases of the moon, and a long-range calendar with eclipse and weather prediction.
		This is yet another demonstration of the very powerful Thales Theorem, which has been the germ, the "Motiv," for many other discoveries in the history of astronomy and geometry, from Aristarchus, to Pappus of Alexandria, Pascal, Monge, Poncelet, and Steiner, to identify but a few of the main successors of Thales.
	www.geocities.com /antidummy/sub/greeks.html (3058 words)

	Thales of Miletus, Mathematics and Life
		Thales may have been able to observe that at a certain position of the sun an objects height is equal to the length of its shadow.
		Thales has chosen Water for the Primordial Substance the so-called “Arche”, Anaximenes of Miletus Air to describe the One Life which animates it and Heraclitus of Ephesus maintained that the one Principle underlying all physical phenomena is Fire.
		Solon of Athens - Chilon of Sparta - Thales of Miletus - Bias of Priene - Cleobulus of Lindos
	www.mlahanas.de /Greeks/Thales.htm (2199 words)

	Biography of Thales - Math Open Reference
		Thales is acknowledged by a number of sources as the one who defined the constellation Ursa Minor and used it for navigation.
		While Thales was in Egypt, he was supposedly able to determine the height of a pyramid by measuring the length of its shadow when the length of his own shadow was equal to his height.
		O'Connor, J.O. and Robertson, E.F. Thales of Miletus.
	www.mathopenref.com /thales.html (857 words)

	Thales Summary
		Thales was born at Miletus, in Ionia, Greece.
		Thales was born circa 640 B.C. to 620 B.C. in Miletus, a Greek island along the coast of Asia Minor.
		Thales may have accomplished the feat by using the "magic" of the Egyptian shadow stick, which, when placed in the ground, one could use it to calculate the height of an object by establishing a relationship between the height of the stick's shadow and the shadow of the object to be measured.
	www.bookrags.com /Thales (9110 words)

	Thales biography
		Thales of Miletus was the son of Examyes and Cleobuline.
		Thales discovered how to obtain the height of pyramids and all other similar objects, namely, by measuring the shadow of the object at the time when a body and its shadow are equal in length.
		Thales is said to have travelled in Egypt, and to have thence brought to the Greeks the science of geometry.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Thales.html (2222 words)

	Thales (Site not responding. Last check: 2007-10-20)
		Thales seems to be the first known Greek philosopher, scientist, and mathematician, although his occupation was that of an engineer.
		Thales discovered how to obtain the height of pyramids by measuring the shadow of the pyramids at the time when any body's height and its shadow are equal in length.
		It was Thales who first conceived the principle of explaining the multitude of phenomena by a small number of hypotheses for all the various manifestations of matter.
	www.stetson.edu /~efriedma/periodictable/html/Th.html (313 words)

	Thales - Introduction
		Thales was born in 636 B.C. to the parents Examyes and Cleobuline.
		He used a similar triangle theorem, proportions, and the length of the shadow of the pyramid to determine the pyramid’s height.
		Thales also accurately predicted a solar eclipse that occurred in 585 B.C. Aristotle credits Thales with the concept that the earth is spherical, a quite modern idea for an ancient man.
	www.gsgis.k12.va.us /ourdepartments/thales/mathintro.htm (347 words)

	Explore: Greece - Mathematics
		Thales was, by legend, a clever man, who was said to have learned much from the Egyptians and Babylonians.
		He is reputed to have demonstrated that the angle inscribed in a semicircle is a right angle (Theorem of Thales) and put down a series of rules regarding the angles of triangles.
		However, the theorem that is most often credited to Pythagoras (the sum of the squares of the shorter sides of a right triangle is equal to the square of the third side) is in fact not his own.
	library.thinkquest.org /C0122667/greece/maths.html (1408 words)

	Thales of Miletus
		He also proved that a circle is bisected by its diameter, that the angles of the base of an isosceles triangle are equal, and that an inscribed angle in a semicircle is a right angle ("theorem of Thales").
		This seems to imply that Thales thought that the soul was the cause of movement.
		Although Thales' identification of the first principle with water was rather unfortunate, his idea to look for deeper causes was the true beginning of philosophy and science.
	www.livius.org /th/thales/thales.html (600 words)

	Thales of Miletus
		Thales was the first known philosopher, scientist and mathematician although his occupation was that of an engineer.
		The claims that Thales used the Babylonian saros, a cycle of length 18 years 10 days 8 hours, to predict the eclipse has been shown by Neugebauer to be highly unlikely since Neugebauer shows that the saros was an invention of Halley.
		Now of course Thales could have used these geometrical methods for solving practical problems having merely observed the properties and having no appreciation of what it means to prove a geometrical theorem.
	phoenicia.org /thales.html (2551 words)

	The Origin of Geometry (Site not responding. Last check: 2007-10-20)
		The second attempt contemplates Thales at the foot of the Pyramids, in the light of the sun.
		The result is that the theorem and its immersion in Egyptian legend says, without saying it, that there lies beneath the mimetic operator, constructed concretely and represented theoretically, a hidden royal corpse.
		Thales, at the Pyramids, is on the threshold of the sacred.
	acnet.pratt.edu /~arch543p/readings/origin_of_geometry.html (3851 words)

	Egyptian Science, the Greeks, and Mathematical PROOF (Site not responding. Last check: 2007-10-20)
		Second as to Thales: The theorem attributed to Thales is illustrated by the figure of problem 53 of the Rhind Papyrus, written thirteen hundred years before the birth of Thales...
		Theorems in one system may be axioms in another, and vice versa, and the choice is essentially arbitrary.
		It is perhaps not surprising the result of Godel that not all theorems (of arithmetic) are decidable within such a framework.
	www.theafrican.com /Magazine/Athena/1.htm (2182 words)

	Thales (print-only)
		The claims that Thales used the Babylonian saros, a cycle of length 18 years 10 days 8 hours, to predict the eclipse has been shown by Neugebauer to be highly unlikely since Neugebauer shows in [11] that the saros was an invention of Halley.
		On the other hand B L van der Waerden [16] claims that Thales put geometry on a logical footing and was well aware of the notion of proving a geometrical theorem.
		The fifth theorem is believed to be due to Thales because of a passage from Diogenes Laertius book Lives of eminent philosophers written in the second century AD [6]:-
	www-groups.dcs.st-and.ac.uk /~history/Printonly/Thales.html (2060 words)

	WebQuest
		For the purpose of humiliating Thales in the presence of pharaoh, the abbot challenges to Thales and asks: "How high is this pyramid?" Thales takes his scepter and thrusts it into sand at the point where the shadow of the pyramid finishes.
		Thales, as a merchant, takes two sticks nailed into a cross and goes to top of a tower.
		This biography should include information at least about the place that Thales is from, his interests, the time period in which he lived, his interactions with his colleagues or students.
	www.metu.edu.tr /~e136215/friendlyversion.htm (773 words)

	Thales - Wikipedia, the free encyclopedia
		Diogenes Laërtius (1.22) and others say that Thales was the son of Examyas and Cleobulina and that they were of the Thelidae family (hence Thales), who were of noble Phoenician descent from Cadmus of ancient Thebes.
		After repeating a story that Thales had been naturalized, or recently enrolled as a citizen, Diogenes Laërtius asserts that he was "a right-born Milesian".
		According to Diogenes Laërtius (1.25-26) there are two stories about Thales' family life, one that he married and had a son, Cybisthus or Cybisthon, or adopted his nephew of the same name.
	en.wikipedia.org /wiki/Thales (5766 words)

	Munching on Inscribed Angles (Site not responding. Last check: 2007-10-20)
		This is Proposition III.20 from Euclid's Elements which we already used in several places: Sine, Cosine, and Ptolemy's Theorem, Longest segment, Ptolemy's Theorem, Generalization of Napoleon's Theorem.
		What is the locus of the foot of the perpendicular from B onto lines from a given pencil through A? Why, the circle, of course.
		(This is known as Thales' Theorem: an angle inscribed in a semicircle is right, and vice versa.) The formulation is different but the result is the same.
	www.cut-the-knot.org /pythagoras/Munching/inscribed.shtml (709 words)

	Math 390 -- Reveiw topics for exam 4 (Site not responding. Last check: 2007-10-20)
		Know which theorems we've covered are neutral and which are strictly Euclidean
		Be able to explain exactly where the constructions of a rectangle or a circle through three given points require the parallel postulate
		Theorem 5.18 (Pythagorean Theorem -- give the major steps and briefly justify each)
	www.uidaho.edu /math/nielsen/390video/rev4.html (115 words)

	Thales and pyramid height calculus
		The triangles formed by the stick and its shadow, the pyramid and its shadow are homothetic.
		Therefore we can calculate the pyramid height thanks to the Thales theorem.
		To do so we first ask for the length of the known values: the stick and its shadow length, the pyramid shadow length.
	www.univ-savoie.fr /Portail/Groupes/fernandes/demos/2-thales/index.html (678 words)

	Science and Society Picture Library - Search
		Born in Samos, Greece, he was educated in his youth by three philosophers who introduced him to mathematical ideas: Pherekydes, Thales and Anaximander.
		Pythagoras settled in Crotona, Southern Italy, where he founded a moral and religious school.
		Today, Pythagoras is best remembered for his famous geometry theorem which states that for a right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
	www.scienceandsociety.co.uk /results.asp?image=10198238 (178 words)

	Connecting Math to Our Lives Project- International Networking Project sponsored by PSRTEC, De Orilla a Orilla and ...
		When won't they be situated in the same plan any more?
		According to Thales theorem, they will be all the time situated in the same plane because flying in four different directions they will over at any moment a distance proportional to the distance covered by the other three flies.
		Thales' theorem is: If we have two unparallel lines situated in the same plane and a secant, by drawing parallel lines to the given secanta we obtain proportional segment on the unparallel lines.
	www.orillas.org /math/just12.html (131 words)

	Essay topics
		In the course we've touched upon the history of mathematics only in the Western hemisphere, but considerable developments took place also in India and China.
		Find out how Thales proved the theorem that every triangle inscribed in a semicircle with one side at the base of the semicircle is a right triangle.
		Critically discuss Euclid's argument for the Pythagorean theorem.
	www.phil.cmu.edu /~dschlimm/80-110spring02/essay_topics.html (998 words)

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