Geometry

Running Head : GEOMETRY ASSIGNMENTHistory of Mathematics - AssignmentNAME OF CLIENTNAME OF INSTITUTIONNAME OF PROFESSORCOURSE NAMEDATE OF SUBMISSIONHistory of Mathematics - Assignment (aIf D is between A and B , then AD DB AB (Segment Addition conduct And particle AB has hardly one mid head up which is D (Mid stain PostulateThe midsegment of a triplicity is a segment that connects the centers of dickens posts of a triangle . Midsegment Theorem states that the segment that joins the centres of two sides of a triangle is tally to the third gear side and has a aloofness equal to fractional the length of the third side . In the figure show above (and below , DE lead al itinerarys be equal to half of BCGiven ?ABC with point D the midpoint of AB and point E the midpoint of AC and point F is the midpoint of BC , the unde rmentioned can be concludedEF / ABEF ? ABDF / ACDF ? ACDE / BCDE ? BCTherefore , 4 triangles that atomic number 18 harmonious are varianted (bTwo circles intersecting sassyly are orthogonal curves and called orthogonal circles of severally oppositeSince the tangent of circle is perpendicular to the radius haggard to the middleman point , both radii of the two orthogonal circles A and B drawn to the point of intersection and the line segment connecting the centres form a right on triangleis the condition of the orthogonality of the circles (cA Saccheri four-sided is a quadrilateral that has one set of opposite sides called the legs that are congruent , the other set of opposite sides called the bases that are disjointly latitude , and , at one of the bases , both angles are right angles . It is named after Giovanni Gerolamo Saccheri , an Italian Jesuit priest and mathematician , who attempted to show up Euclid s one-fifth Postulate from the other axioms by the use of a reductio ad absurdum argument by assuming th! e negation of the Fifth Postulateradians .

Thus , in any Saccheri quadrilateral , the angles that are non right angles moldiness be acuteSome examples of Saccheri quadrilaterals in various models are shown below . In each example , the Saccheri quadrilateral is labelled as ABCD and the general perpendicular line to the bases is drawn in blueThe Beltrami-Klein modelRed lines show stoppage of acute angles by using the polesThe Poincary disc modelThe hurrying half plane model (dFor hundreds of years mathematicians tried without advantage to prove the postulate as a theorem , that is , to deduce it from Euclid s ot her tetrad postulates . It was not until the last century or two that intravenous feeding mathematicians , Bolyai , Gauss , Lobachevsky , and Riemann , working independently , discovered that Euclid s parallel postulate could not be proven from his other postulates . Their find paved the way for the development of other kinds of geometry , called non- euclidean geometriesNon-Euclidean geometries differ from Euclidean geometry only in their rejection of the parallel postulate but this hotshot alteration at the axiomatic foundation of the geometry has profound...If you want to rag a profuse essay, order it on our website: OrderCustomPaper.com

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