Geometry - macgeometrystudent
... What observations can you make? Using these examples, can you form a good definition of each? Concave: ...
... What observations can you make? Using these examples, can you form a good definition of each? Concave: ...
360 a b c d e + + + + = ( 2) 180 N Θ =
... Regular polygons inscribed and circumscribed by circles. As N becomes large, the polygon will tend to a circle and hence all three shapes will coalesce. ...
... Regular polygons inscribed and circumscribed by circles. As N becomes large, the polygon will tend to a circle and hence all three shapes will coalesce. ...
equiangular polygon
... A polygon is equiangular if all of its interior angles are congruent. Common examples of equiangular polygons are rectangles and regular polygons such as equilateral triangles and squares. Let T be a triangle in Euclidean geometry, hyperbolic geometry, or spherical geometry. Then the following are e ...
... A polygon is equiangular if all of its interior angles are congruent. Common examples of equiangular polygons are rectangles and regular polygons such as equilateral triangles and squares. Let T be a triangle in Euclidean geometry, hyperbolic geometry, or spherical geometry. Then the following are e ...
MA.912.G.2.1 - Identify and describe convex, concave, regular, and
... Standard: Polygons - Identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. Find measures of angles, sides, perimeters, and areas of polygons, justifying the methods used. Apply transformations to polygons. Relate geom ...
... Standard: Polygons - Identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. Find measures of angles, sides, perimeters, and areas of polygons, justifying the methods used. Apply transformations to polygons. Relate geom ...
Homework
... 1. Recognize (see and name) transformations including rigid and size transformations. 2. Define (both conceptually and abstractly) and use the four rigid motions: translation, rotation, reflection, and glide reflection. 3. Given one transformation find a combination of two others that is equivalent ...
... 1. Recognize (see and name) transformations including rigid and size transformations. 2. Define (both conceptually and abstractly) and use the four rigid motions: translation, rotation, reflection, and glide reflection. 3. Given one transformation find a combination of two others that is equivalent ...
Exemplar 15: Tessellation in a Plane
... Tessellation comes from the Latin word tessella, which was the small, square stone or tile used in ancient Roman mosaics. Tiling and mosaics are common synonyms for tessellation. A plane tessellation is a pattern made up of one or more shapes, completely covering a surface without any gaps or overla ...
... Tessellation comes from the Latin word tessella, which was the small, square stone or tile used in ancient Roman mosaics. Tiling and mosaics are common synonyms for tessellation. A plane tessellation is a pattern made up of one or more shapes, completely covering a surface without any gaps or overla ...
Tessellation
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries.A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semi-regular tilings with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called ""non-periodic"". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern. In the geometry of higher dimensions, a space-filling or honeycomb is also called a tessellation of space.A real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons. Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor or wall coverings. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the decorative tiling of the Alhambra palace. In the twentieth century, the work of M. C. Escher often made use of tessellations, both in ordinary Euclidean geometry and in hyperbolic geometry, for artistic effect. Tessellations are sometimes employed for decorative effect in quilting. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.