A skew apeirogon is an infinite sequence of sides and angles that do not lie in a flat plane. A polygon is a closed plane figure bounded by three or more line segments that only meet at their endpoints.
Students will likely not have been so succinct in their description, so encourage them to use this definition. For example, ask them to identify three quadrilaterals in the classroom.
Continue to emphasize that a circle is not a polygon, as this is a common misconception. A spherical polygon is a circuit of arcs of great circles sides and vertices on the surface of a sphere.
A quadrilateral is a polygon with exactly four sides. Generalizations of polygons[ edit ] The idea of a polygon has been generalized in various ways. Depending on the mapping, all the generalizations described here can be realized. Create a set of index cards that includes examples and nonexamples of each term, including polygons, quadrilaterals, concave and convex polygons.
The other students must decide why they agree or disagree about the placement of the card.
It is important that students realize a polygon is closed, all sides are line segments and not curves, and the sides only meet at the endpoints and do not intersect elsewhere. The two triangular regions of a cross-quadrilateral like a figure 8 have opposite-signed densities, and adding their areas together can give a total area of zero for the whole figure.
A real geometric polygon is said to be a realization of the associated abstract polygon. This is a formal definition of a quadrilateral that is very accessible to third grade students: The Petrie polygons of the regular polytopes are well known examples.
Observe students as they are drawing these examples, and help any struggling students by reviewing the characteristics of a polygon as listed in the table.
Continue this until all shapes have been sorted into the groups. Be sure to ask them to explain their reasoning, using specific terms about the attributes of the shape. Students who are ready for a challenge beyond the requirements of the standard should be introduced to new terms and additional properties of polygons.
An apeirogon is an infinite sequence of sides and angles, which is not closed but has no ends because it extends indefinitely in both directions. Explain that both a set of quadrilaterals and a set of nonquadrilaterals are shown.
Students will likely use informal language to describe characteristics of the convex and concave polygons. A complex polygon is a configuration analogous to an ordinary polygon, which exists in the complex plane of two real and two imaginary dimensions.
Considering the enclosed regions as point sets, we can find the area of the enclosed point set. After this discussion, ask students to draw an example of a polygon and a nonpolygon in the space provided.They can have 4 sides, 44 sides, or even sides.
The names would be 4-gon, or quadrilateral, gon, and gon, respectively. However many sides a polygon has is the same number of. Find an answer to your question describe a polygon by as many names as possible.
Each corner of a polygon, where two sides meet, is called a vertex. vertices in order as you move around it in either direction. One name for the shaded triangle is Triangle ABC.
Other names are possible, including BCA and ACB. DCBA, or DABC. All of these names list the vertices in order as you move around the quadrilateral.
The name. A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than °. More precisely, no internal angle can be more than °. If any internal angle is greater than ° then the polygon is concave.
Constructing higher names. To construct the name of a polygon with more than 20 and less than edges, combine the prefixes as follows. The "kai" term applies to gons and higher and was used by Kepler, and advocated by John H. Conway for clarity to concatenated prefix numbers in the naming of quasiregular polyhedra.
Use a document camera, if possible, to project the worksheet so students can point out characteristics of a shape as they are discussing whether a polygon is concave or convex.
After all six examples have been discussed, ask students to draw an example of a convex and a concave polygon in the space provided, and ask students to write sentences.Download