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1Geometry

a branch of mathematics that deals with the measurement, properties, and relationshipsof points, lines, angles, surfaces, and solids; broadly: the study of properties of givenelements that remain invariant under specified transformations

Geometry is a part of mathematics is to study some idealizations of the space in whichwe live, which are points, lines and planes, and other conceptual elements derived fromthem, such as polygons or polyhedra.

2.AArchimedes of Syracuse (ca.287-ca.212 BC)

Among the many thinkers and innovators of ancient Greece, Archimedes of Syracuse isstill honored nearly 2,300 years after his death for his contributions to geometry,

physics, mechanics and technology. He calculated the value of pi, devised the notion ofmathematical exponents, and famously discovered the principle of water displacementin a "eureka" moment while taking a bath.

B Thales of Miletus was the first known Greek philosopher, scientist andmathematician. Some consider him to be the teacher of of Pythagoras, though it may beonly that he advised Pythagoras to travel to Egypt and Chaldea.

From Eudemus of Rhodes (fl ca. 320 B.C) we knowthat he studied in Egypt and brought these teachings to Greece. He is unanimouslyascribed the introduction of mathematical and astronomical sciences into Greece.

He is unanimously regarded as

having been unusally clever--by general agreement the first of the Seven Wise Men, apupil of the Egyptians and the Chaldeans. None of hiswriting survives; this makes it is difficult to determine his philosophy and to be certainabout his mathematical discoveries. Thereis, of course, the story of his successful speculation in oil presses -- as testament to hispractical business acumen.

It is reported that he predicted an eclipse of the Sun on May 28, 585 BC, startlingall of Ionia.

He is credited with five theorems of elementary geometry.

C WHAT IS EUCLIDEN GEOMETRY?

Euclidean, or classical, geometry is the most commonly known geometry, and is the

geometry taught most often in schools, especially at the lower levels. Euclid described

this form of geometry in detail in "Elements," which is considered one of the

cornerstones of mathematics. The impact of "Elements" was so big that no other kind of

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geometry was used for almost 2,000 years.

D.what is element?

Elements was the first systematic discussion of geometry

, the Elements is one of the oldest extant Greek mathematical treatises

The word 'element' is in the Greek language the same as 'letter

kinds of geometry

Euclidean Geometry

Euclidean, or classical, geometry is the most commonly known geometry, and is thegeometry taught most often in schools, especially at the lower levels. Euclid describedthis form of geometry in detail in "Elements," which is considered one of the

cornerstones of mathematics. The impact of "Elements" was so big that no other kind ofgeometry was used for almost 2,000 years.

Non-Euclidean Geometry

Non-Euclidean geometry is essentially an extension of Euclid's principles of geometry tothree dimensional objects. Non-Euclidean geometry, also called hyperbolic or ellipticgeometry, includes spherical geometry, elliptic geometry and more. This branch ofgeometry shows how familiar theorems, such as the sum of the angles of a triangle, arevery different in a three-dimensional space.

Analytic Geometry

Analytic geometry is the study of geometric figures and constructions using a coordinatesystem. Lines and curves are represented as set of coordinates, related by a rule ofcorrespondence which usually is a function or a relation. The most used coordinatesystems are the Cartesian, polar and parametric systems.

Differential Geometry

Differential geometry studies planes, lines and surfaces in a three-dimensional spaceusing the principles of integral and differential calculus. This branch of geometryfocuses on a variety of problems, such as contact surfaces, geodesics (the shortestpath between two points on the surface of a sphere), complex manifolds and manymore. The application of this branch of geometry ranges from engineering problems to

the calculation of gravitational fields.

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B Analytic Geometry

1Analytic geometry is the study of geometric figures and constructions using acoordinate system. Lines and curves are represented as set of coordinates, related by arule of correspondence which usually is a function or a relation. The most used

coordinate systems are the Cartesian, polar and parametric systems.

2 two founder

Ren Descartes (1596-1650) is generally regarded as the father of Analytical Geometry

. His name in Latin is Renatius Cartesius so you can see that our terminology

Cartesian plane and Cartesian coordinate system are derived from his name!

Analytical Geometry is also often called Cartesian Geometry or Coordinate geometry.

Pierre de Fermat (French:[pj dfma]; 17[1]August 1601 or 1607/8[2] 12 January

1665) was aFrenchlawyer at theParlementofToulouse,France, and anamateur

mathematicianwho is given credit for early developments that led toinfinitesimal

calculus, including hisadequality. In particular, he is recognized for his discovery of an

original method of finding the greatest and the smallestordinatesof curved lines, which

is analogous to that of the then unknowndifferential calculus, and his research

intonumber theory. He made notable contributions toanalytic geometry,probability,

andoptics. He is best known forFermat's Last Theorem, which he described in a note

at the margin of a copy ofDiophantus'Arithmetica.

2a

The la geometria Spanish word means geometry

4 two section of analytic geometry that broke up

Analytic geometry is broken up into two sections, "finding an equation to match points

and finding points to match equations."

http://en.wikipedia.org/wiki/Wikipedia:IPA_for_Frenchhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_Frenchhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_Frenchhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_Frenchhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_Frenchhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_Frenchhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_Frenchhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_Frenchhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_Frenchhttp://en.wikipedia.org/wiki/Pierre_Fermat#cite_note-1http://en.wikipedia.org/wiki/Pierre_Fermat#cite_note-1http://en.wikipedia.org/wiki/Pierre_Fermat#cite_note-barner-2http://en.wikipedia.org/wiki/Pierre_Fermat#cite_note-barner-2http://en.wikipedia.org/wiki/French_peoplehttp://en.wikipedia.org/wiki/French_peoplehttp://en.wikipedia.org/wiki/French_peoplehttp://en.wikipedia.org/wiki/Parlementhttp://en.wikipedia.org/wiki/Parlementhttp://en.wikipedia.org/wiki/Parlementhttp://en.wikipedia.org/wiki/Toulousehttp://en.wikipedia.org/wiki/Toulousehttp://en.wikipedia.org/wiki/Toulousehttp://en.wikipedia.org/wiki/Francehttp://en.wikipedia.org/wiki/Francehttp://en.wikipedia.org/wiki/Francehttp://en.wikipedia.org/wiki/List_of_amateur_mathematicianshttp://en.wikipedia.org/wiki/List_of_amateur_mathematicianshttp://en.wikipedia.org/wiki/List_of_amateur_mathematicianshttp://en.wikipedia.org/wiki/Infinitesimal_calculushttp://en.wikipedia.org/wiki/Infinitesimal_calculushttp://en.wikipedia.org/wiki/Infinitesimal_calculushttp://en.wikipedia.org/wiki/Infinitesimal_calculushttp://en.wikipedia.org/wiki/Adequalityhttp://en.wikipedia.org/wiki/Adequalityhttp://en.wikipedia.org/wiki/Adequalityhttp://en.wikipedia.org/wiki/Ordinatehttp://en.wikipedia.org/wiki/Ordinatehttp://en.wikipedia.org/wiki/Ordinatehttp://en.wikipedia.org/wiki/Differential_calculushttp://en.wikipedia.org/wiki/Differential_calculushttp://en.wikipedia.org/wiki/Differential_calculushttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Analytic_geometryhttp://en.wikipedia.org/wiki/Analytic_geometryhttp://en.wikipedia.org/wiki/Analytic_geometryhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Opticshttp://en.wikipedia.org/wiki/Opticshttp://en.wikipedia.org/wiki/Opticshttp://en.wikipedia.org/wiki/Fermat%27s_Last_Theoremhttp://en.wikipedia.org/wiki/Fermat%27s_Last_Theoremhttp://en.wikipedia.org/wiki/Fermat%27s_Last_Theoremhttp://en.wikipedia.org/wiki/Diophantushttp://en.wikipedia.org/wiki/Diophantushttp://en.wikipedia.org/wiki/Diophantushttp://en.wikipedia.org/wiki/Arithmeticahttp://en.wikipedia.org/wiki/Arithmeticahttp://en.wikipedia.org/wiki/Arithmeticahttp://en.wikipedia.org/wiki/Arithmeticahttp://en.wikipedia.org/wiki/Diophantushttp://en.wikipedia.org/wiki/Fermat%27s_Last_Theoremhttp://en.wikipedia.org/wiki/Opticshttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Analytic_geometryhttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Differential_calculushttp://en.wikipedia.org/wiki/Ordinatehttp://en.wikipedia.org/wiki/Adequalityhttp://en.wikipedia.org/wiki/Infinitesimal_calculushttp://en.wikipedia.org/wiki/Infinitesimal_calculushttp://en.wikipedia.org/wiki/List_of_amateur_mathematicianshttp://en.wikipedia.org/wiki/List_of_amateur_mathematicianshttp://en.wikipedia.org/wiki/Francehttp://en.wikipedia.org/wiki/Toulousehttp://en.wikipedia.org/wiki/Parlementhttp://en.wikipedia.org/wiki/French_peoplehttp://en.wikipedia.org/wiki/Pierre_Fermat#cite_note-barner-2http://en.wikipedia.org/wiki/Pierre_Fermat#cite_note-1http://en.wikipedia.org/wiki/Wikipedia:IPA_for_French

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