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 plane section AB has exclusively one mid head up which is D (Mid crest PostulateThe midsegment of a triangle is a segment that connects the centers of deuce posts of a triangle . Midsegment Theorem states that the segment that joins the snappers of two sides of a triangle is analogue to the thirdly side and has a continuance equal to half the length of the third side . In the figure show preceding(prenominal) (and down the stairs , 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 th e midpoint of BC , the undermentioned can be concludedEF / ABEF ? ABDF / ACDF ? ACDE / BCDE ? BCTherefore , 4 triangles that are harmonious are varianted (bTwo circles intersecting wisely are orthogonal curves and called orthogonal circles of severally other(a)Since the tangent of circle is perpendicular to the radius draw 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 proficient triangleis the condition of the orthogonality of the circles (cA Saccheri quadrilateral 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 correspond , and , at one of the bases , both angles are right angles . It is named later Giovanni Gerolamo Saccheri , an Italian Jesuit priest and mathematician , who attempted to show up Euclid s fifth part Postulate from the other axio ms by the use of a reductio ad absurdum argu! ment by assuming the 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 repoint stoppage of acute angles by using the polesThe Poincary disc modelThe upper half plane model (dFor hundreds of years mathematicians tried without mastery to prove the postulate as a theorem , that is , to deduce it from Euclid s other 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 denudation 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 integrity alteration at the axiomatic foundation of the geometry has profound...If you want to bond a profuse essay, order it on our website: OrderCustomPaper.com

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