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The definition of figure needs to be fleshed out. In order to be a figure, a region must be bounded, that is, held in by a boundary. For instance, an infinite plane is unbounded, so it is not intended to be a figure. Neither is the region between two parallel lines even though that region has the two parallel lines as its extremities.
Other figures may be considered if other ambient spaces are allowed, although Euclid only uses plane and solid figures. online math forum; For a one-dimensional example, a line segment could be considered to be a figure in an infinite line with its endpoints as its boundary. Also, a hemisphere could be considered to be a figure on the surface of a sphere with the equator as its boundary. read more on math forum.
The definition of figure needs to be fleshed out. In order to be a figure, a region must be bounded, that is, held in by a boundary. For instance, an infinite plane is unbounded, so it is not intended to be a figure. Neither is the region between two parallel lines even though that region has the two parallel lines as its extremities.
Other figures may be considered if other ambient spaces are allowed, although Euclid only uses plane and solid figures. online math forum; For a one-dimensional example, a line segment could be considered to be a figure in an infinite line with its endpoints as its boundary. Also, a hemisphere could be considered to be a figure on the surface of a sphere with the equator as its boundary. read more on math forum.
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