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The purpose of Euclidean Geometry is to understand plane (2-D) and solid (3-D) geometry with the understanding that things are "flat". Around 300BC Euclid organized the current knowledge of geometry in a series called the "13 elements" . Euclid was a famous Greek mathematician. The Greeks considered geometry to be its pride and joy. They were the first to ask important questions beginning with "How and Why".
Their main goals were to spread their knowledge of Geometry and answer the question relating to the purpose of Geometry. The answer, the purpose of Geometry is to understand the purpose or existence of life (mankind) itself. Geometry is not just about shapes and things that have been created by mankind. Geometry is in nature and even exists in the things we cannot see. "Geo" means Earth and "metry" comes from the word meaning measurement. So, rightfully so geometry mean the measurement of earth. I will leave you with a famous pun- Without geometry, life is pointless.
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Does a line go on forever in both directions?
In Euclidean geometry, yes.In Euclidean geometry, yes.In Euclidean geometry, yes.In Euclidean geometry, yes.
What is a characteristic of non-euclidean geometry?
One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.
What are the similarities in non euclidean and euclidean geometry?
both the geometry are not related to the modern geometry
Famous geometers and their contributions in geometry?
Archimedes - Euclidean geometry Pierre Ossian Bonnet - differential geometry Brahmagupta - Euclidean geometry, cyclic quadrilaterals Raoul Bricard - descriptive geometry Henri Brocard - Brocard points.. Giovanni Ceva - Euclidean geometry Shiing-Shen Chern - differential geometry René Descartes - invented the methodology analytic geometry Joseph Diaz Gergonne - projective geometry; Gergonne point Girard Desargues - projective geometry; Desargues' theorem Eratosthenes - Euclidean geometry Euclid - Elements, Euclidean geometry Leonhard Euler - Euler's Law Katyayana - Euclidean geometry Nikolai Ivanovich Lobachevsky - non-Euclidean geometry Omar Khayyam - algebraic geometry, conic sections Blaise Pascal - projective geometry Pappus of Alexandria - Euclidean geometry, projective geometry Pythagoras - Euclidean geometry Bernhard Riemann - non-Euclidean geometry Giovanni Gerolamo Saccheri - non-Euclidean geometry Oswald Veblen - projective geometry, differential geometry
What is the difference between Euclidean Geometry and non-Euclidean Geometry?
In Euclidean geometry parallel lines are always the same distance apart. In non-Euclidean geometry parallel lines are not what we think of a parallel. They curve away from or toward each other. Said another way, in Euclidean geometry parallel lines can never cross. In non-Euclidean geometry they can.
