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Encyclopedia > Giovanni Gerolamo Saccheri
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Giovanni Gerolamo Saccheri (September 5, 1667October 25, 1733) was an Italian Jesuit priest and mathematician. Jump to: navigation, search September 5 is the 248th day of the year (249th in leap years). ... // Events January 20 - Poland cedes Kyiv, Smolensk, and eastern Ukraine to Russia in the Treaty of Andrusovo that put a final end to the Deluge, and Poland lost its status as a Central European power. ... Jump to: navigation, search October 25 is the 298th day of the year (299th in leap years) in the Gregorian Calendar, with 67 days remaining. ... Events February 12 - British colonist James Oglethorpe founds Savannah, Georgia. ... The Society of Jesus (Latin: Societas Iesu), commonly known as the Jesuits, is a Roman Catholic religious order. ... Jump to: navigation, search Roman Catholic priest LCDR Allen R. Kuss (USN) aboard USS Enterprise A priest or priestess is a holy man or woman who takes an officiating role in worship of any religion, with the distinguishing characteristic of offering sacrifices. ... A mathematician is a person whose area of study and research is mathematics. ...


Saccheri entered the Jesuit order in 1685, and was ordained as a priest in 1694. Events February 6 - James Stuart, Duke of York becomes King James II of England and Ireland and King James VII of Scotland. ... Events February 6 - The colony Quilombo dos Palmares is destroyed. ...


In 1733, shortly before his death, Saccheri published what is now considered the second work in non-Euclidean geometry, Euclides ab omni noevo vindicatus (Euclid Freed of Every Flaw) after the work of the Persian mathematician Omar Khayyám. The book languished in obscurity until it was rediscovered by Eugenio Beltrami. Saccheri borrowed many ideas from Khayyam's Risâla fî sharh mâ ashkala min musâdarât Kitâb 'Uglîdis [1], a fact deliberately ignored in most of the Western references. Despite the fact that Omar Khayyam outlined, introduced and calculated his quadrilateral in his work 700 years earlier than Saccheri, the Western sources insist on referring to this quadrilateral as "the Saccheri quadrilateral". Behavior of lines with a common perpendicular in each of the three types of geometry The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ... Tomb of Omar Khayyám, Neishapur, Iran. ... Eugenio Beltrami (16 November 1835 - 18 February 1900) was an Italian mathematician notable for his work on non-Euclidean geometry, electricity, and magnetism. ...


The intent of Saccheri's work was to provide a reductio ad absurdum proof of Euclid's parallel postulate. He assumed that the parallel postulate was false, and attempted to derive a contradiction. He derived many unlikely results (such as the existence of triangles whose angles add up to more than 180°), but was unable to derive a logical contradiction. His results are instead theorems of hyperbolic geometry. Jump to: navigation, search Reductio ad absurdum (Latin for reduction to the absurd, traceable back to the Greek ἡ εις άτοπον απαγωγη, reduction to the impossible, often used by Aristotle) is a type of logical argument where we assume a claim for the sake of argument, arrive at an absurd result, and then conclude... Jump to: navigation, search Euclid Euclid of Alexandria (Greek: ) (ca. ... a and b are parallel, the transversal t produces congruent angles. ... Jump to: navigation, search A triangle is one of the basic shapes of geometry: a two-dimensional figure with three vertices and three sides which are straight line segments. ... Jump to: navigation, search A triangle immersed in a saddle-shape plane (an hyperbolic paraboloid), as well as two diverging parallel lines. ...


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Reference.com/Encyclopedia/Giovanni Girolamo Saccheri (468 words)
Giovanni Girolamo Saccheri (September 5, 1667 - October 25, 1733) was an Italian Jesuit priest and mathematician.
Many of Saccheri's ideas have precedent in the 11th Century Persian polymath Omar Khayyam's Discussion of Difficulties in Euclid (Risâla fî sharh mâ ashkala min musâdarât Kitâb 'Uglîdis), a fact ignored in most Western sources until recently.
The intent of Saccheri's work was ostensibly to establish the validity of Euclid by means of a reductio ad absurdum proof of any alternative to Euclid's parallel postulate.
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