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1. 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 The earliest known texts on
geometry and various crafts. in surveying, construction, astronomy,
are the Egyptian Rhind Papyrus (20001800 BC) and Moscow Papyrus (c.
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.
2. The theme of symmetry in geometry is nearly as old as the
science of geometry itself. Symmetric shapes such as the circle,
regular polygons and platonic solids held deep significance for
many ancient philosophers and were investigated in detail before
the time of Euclid. Symmetric patterns occur in nature and were
artistically rendered in a multitude of forms, including the
graphics of M. C. Escher. Nonetheless, it was not until the second
half of 19th century that the unifying role of symmetry in
foundations of geometry was recognized. Felix Klein's Erlangen
program proclaimed that, in a very precise sense, symmetry,
expressed via the notion of a transformation group, determines what
geometry is. Symmetry in classical Euclidean geometry is
represented by congruences and rigid motions, whereas in projective
geometry an analogous role is played by collineations, geometric
transformations that take straight lines into straight lines.
3. Geometry is a branch of mathematics concerned with questions
of shape, size, relative position of figures, and the properties of
space. A mathematician who works in the field of geometry is called
a geometer.
4. Arches are used to withstand maximum weight . Structural
designs use to withstand force of nature