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Descripción: Zome Geometry.pdf Hands-on learningh with Zome Models.
Descrição: Tire Geometry
Sacred geometry is the geometry used in the planning and construction of religious structures such as churches, temples, mosques, religious monuments, altars, tabernacles; as well as for sacred spa...
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detail in many texts and not surprisingly in this age of technology there are several web-sites devoted to them. For instance,
is a very interesting attempt at putting Euclid’s Elements on-line using some very clever Java applets to allow real time manipulation of figures; it also contains links to other similar websites. The web-site
http://thales.vismath.org/euclid/
is a very ambitious one; it contains a number of interesting discussions of the Elements. Any initial set of assumptions should be as self-evident as possible and as few as possible so that if one accepts them, then one can believe everything that follows logically logically from them. In the Elements Euclid introduces two kinds of assumptions:
COMMON NOTIONS: 1. Things which are equal to the same thing are also equal to one another. 1. If equals be added to equals, the wholes are equal. 1. If equals be subtracted from equals, the remainders are equal. 1. Things which coincide with one another are equal to one another. 1. The whole is greater than the part. POSTULATES: Let the following be postulated. 1. To draw a straight line from any point to any point. 1. To produce a finite straight line continuously in a straight line. 1. To describe a circle with any center and distance. 1. That all right angles are equal to one another. 1. That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, then the two straight lines if produced indefinitely, meet on that side on which are the angles less than two right angles. Today we usually refer to all such assumptions as axioms. The common notions are surely self-evident since we use them all the time in many contexts not just in plane geometry – perhaps that’s why Euclid distinguished them from the five postulates which are more geometric in character. The first four of these postulates too seem self-evident; one surely needs these constructions and the notion of perpendicularity in plane geometry. The Fifth postulate is of a more technical nature, however. To understand what it is saying we need the notion of parallel lines.