Regular Polyhedra – 3-D figure made from the same regular polygon.Digon – 2 sides (degenerate in Euclidean geometry).Monogon – 1 side (degenerate in Euclidean geometry).List of Geometric Shapes And Names Polygons like polygons, polyhedra are further divided by the number of faces. Convex shapes made out of curved lines are typically called ellipsoids but there are many other shapes that do not clearly fall into any one category. A 3-D shape composed out of straight lines and flat 2-D surfaces is called polyhedra. Some systems of geometry allow for 1-sided or 2-sided shapes but not traditional Euclidean geometry. Since a shape must enclose a space, the smallest possible polygon in Euclidean geometry is a triangle with 3 sides. A 2-D shape that is composed of straight lines is called a polygon. Polygons can be further divided by their number of sides. Shapes are often categorized according to their dimensions, their number of sides, and whether they are constructed out of straight or curved lines. The mathematical machinery of algebra allows us to encode the properties of a geometric object into a single mathematical expression, which makes analysis much easier. For example, the equation that defines a circle is (x – h) 2 + (y – k) 2 = r 2, where (h,k) represents the center point of the circle, and r represents the radius of the circle. Lastly, for any given shape, there is at least one (in many cases more than one) mathematical representation of that shape in terms of an algebraic function relating at least two values of an ordered pair on a coordinate plane. “The right angle is one of the world’s basic shapes.” - Claes Oldenburg A sphere is a 3-D analog of a 2-D circle and a tetrahedron is a 3-D analog of a 2-D triangle. The construction of shapes gives them a unique hierarchy, where particular shapes have analogs at different dimensions. Similarly, a 3-dimensional cube is composed of 2-dimensional squares, a 4-dimensional hypercube is composed of 3-dimensional cubes, etc. For example, a 2-dimensional square is made out of 1-dimensional lines. Second, all shapes of N dimension are composed out of elements of N−1 dimensions. Things like 1-dimensional lines or 0-dimensional points do not have an area and do not count as shapes. First, all shapes are at least 2-dimensional. There are many different kinds of shapes but all shapes share a few properties. Shapes are one of the first things that human babies learn to recognize and according to many philosophers and scientists throughout history, the study of shape, and geometry more broadly, is one of the few instances where the human mind can come into direct contact with ultimate reality. Isaac Newton appealed primarily to geometric laws and shapes to construct his system of mechanics and Einstein’s greatest work involved describing the large-scale geometric shape of the universe. Ancient Egyptians understood the unique properties of different shapes and incorporated those insights into their monumental constructions like the pyramids, and the Greeks considered abstract geometric shapes to be among the most fundamental constituents of existence perfect idealizations of their imperfect material counterparts. Shapes have been studied by people since before recorded civilization. In more mathematical terms, one can think of the shape of an object as the mathematical description that remains when information about the location, scale, and orientation, and material properties of an object are abstracted away from. According to this intuitive understanding, the shape of an object is the external form or appearance of an object in space that can be represented by a set of lines oriented in some way. Intuitively, one can think of shape as a set of lines that enclose a space. The geometric shapes and their names below give you a general sense of what you will find in any given geometry classroom. One of the properties of objects that geometry studies is their shape.
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