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Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space
Once the poor old 153 limped out of the way, NS 901 blasts off toward Atlanta. The geometry train was powered by ex. BN SD40-2 #3531 leading NS 36 and NS 32.
Euclid (circa 325-265 BC), the 'Father of Geometry' uses a divider and a tablet to explain Geometry to students. He was the most famous of the ancient Greek mathematicians.
Stanza della Segnatura, Musei Vaticani; July 2019
The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts. The earliest known texts on geometry are the Egyptian Rhind Papyrus (2000–1800 BC) and Moscow Papyrus (1890 BC), the Babylonian clay tablets such as Plimpton 322 (1900 BC). For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, or frustum. South of Egypt the ancient Nubians established a system of geometry including early versions of sun clocks.
In the 7th century BC, the Greek mathematician Thales of Miletus used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. Pythagoras established the Pythagorean School, which is credited with the first proof of the Pythagorean theorem, though the statement of the theorem has a long history Eudoxus developed the method of exhaustion, which allowed the calculation of areas and volumes of curvilinear figures, as well as a theory of ratios that avoided the problem of incommensurable magnitudes, which enabled subsequent geometers to make significant advances. Archimedes of Syracuse used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave remarkably accurate approximations of Pi. He also studied the spiral bearing his name and obtained formulas for the volumes of surfaces of revolution.
In the Middle Ages, mathematics in medieval Islam contributed to the development of geometry, especially algebraic geometry and geometric algebra. Al-Mahani conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra. Thābit ibn Qurra dealt with arithmetic operations applied to ratios of geometrical quantities, and contributed to the development of analytic geometry. Omar Khayyám found geometric solutions to cubic equations.
In the early 17th century, there were two important developments in geometry. The first was the creation of analytic geometry, or geometry with coordinates and equations, by René Descartes and Pierre de Fermat. This was a necessary precursor to the development of calculus and a precise quantitative science of physics. Two developments in geometry in the 19th century changed the way it had been studied previously. These were the discovery of non-Euclidean geometries by Nikolai Ivanovich Lobachevsky , János Bolyai and Carl Friedrich Gauss and of the formulation of symmetry as the central consideration in the Erlangen Programme of Felix Klein (which generalized the Euclidean and non-Euclidean geometries). Two of the master geometers of the time were Bernhard Riemann (1826–1866), working primarily with tools from mathematical analysis, and introducing the Riemann surface, and Henri Poincaré, the founder of algebraic topology and the geometric theory of dynamical systems. As a consequence of these major changes in the conception of geometry, the concept of "space" became something rich and varied, and the natural background for theories as different as complex analysis and classical mechanics.
Source: Wikipedia, the free encyclopedia
Skyscrapers blur upwards from hard geometry. Multiple exposure in infrared. Melbourne, Victoria, Australia.
Color eFex 4: bleach bypass.
Boys and Girls, see how many right triangles you can find in this picture.
Floyd Bennett Airfield, Brooklyn, USA
Silver Geometry Project print #14
Printed on albuminized paper salted with kosher salt. The blues and greens are cyanotype, while the oranges and browns are potassium dichromate. The red is a mixture of potassium dichromate and silver nitrate.
The CN Geometry train for testing track condition and gauge etc seen heading Eastbound (locomotive pushing train) towards the Waterloo yard for servicing (Fuel and sanitary dump etc) The back of the car the conductor is standing on, has LED ditch lighting and is very bright. Also there is a LED light bar above where the conductor is standing. Has to be a impressive sight at night
© 2008 All rights reserved by JulioC. (from my 2007 archives) Much better ::: On Black :::
Uploaded specially for the
40th Special Challenge - Theme: GEOMETRY (*Challenge You* group)
Pormenor do edifício do Centro de Ciência Viva (terraço) de Faro (Algarve - Portugal)
Detail of the Live Sciences Exhibit Center (terrace), in Faro (Algarve - Portugal)
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