Now that you have navigated your way through this lesson, you are able to identify and describe three undefined terms (point, line, and plane) that form the foundation of Euclidean geometry. The order does not matter, but the set might be easier to work with in order from least to greatest: Mentally (or, better, jot down) a set of Saturday and Sunday dates. In geometry, we use sets to group numbers or items together to form a single unit, like all the triangles on a plane or all the straight angles on a coordinate grid. Other sets, like the set of all even numbers and the set of all multiples of five the set of all acute angles and the set of all angles less than 15°.Numbers, like all positive even integers proper fractions or decimals smaller than 0.001.Physical objects like angles, rays, triangles, or circles.SetĪ set can be described as a collection of objects, in no particular order, that you are studying or mathematically manipulating. Planes do not end, and they have no thickness. Also, all of these objects end abruptly at their edges. Nothing will accurately substitute for a plane, because even the thinnest piece of paper, cookie sheet, or playing card still has some thickness. Modeling a plane in everyday life is tricky. A single capital letter, or it can be named by three points drawn on it. For every three points in space, a unique plane exists.Ī symbol of a plane in geometry is usually a trapezoid, to appear three-dimensional and understood to be infinitely wide and long. PlaneĪ plane is described as a flat surface with infinite length and width, but no thickness. With only three points, you can create three different lines, and you can also describe a plane. They tell you where a spot is, but are not the spot itself (even though we show them with a dot). Points in geometry are more like signal buoys on the vast, infinite ocean of geometric space than they are actual things. It is named with a capital letter: Point A Point B and so on. A point has no width, depth, length, thickness - no dimension at all. PointĪ point in geometry is described (but not defined) as a dimensionless location in space. These four undefined terms are used extensively in theorems, proofs, and defining other words. Simply because these terms are formally undefined does not mean they are any less useful or valid than other terms that emerge from them. Mathematicians use descriptions of these four terms and work up from them, creating entire worlds of ideas like angles, polygons, Platonic solids, Cartesian graphs, and more. In geometry, three undefined terms are the underpinnings of Euclidean geometry:Ī fourth undefined term, set, is used in both geometry and set theory.Įven though these four terms are undefined, they can still be described.
In all branches of mathematics, some fundamental pieces cannot be defined, because they are used to define other, more complex pieces. Identify and describe the undefined term, set, used in geometry and set theory.Identify and describe the three undefined terms - point, line, plane - of Euclidean geometry.After working your way through this lesson and video, you will be able to:
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