This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to Megan Urbanik, 29 November 2013, Created with GeoGebra Move the blue points to change the shape of the translated object. This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to Megan Urbanik, 4 December 2013, Created with GeoGebra Translation, respectively, to the boundary parts ED, FE, and AF (see Such that the boundary parts AB, BC, and CD are congruent by There are six consecutive points A, B, C, D, E, and F on the boundary (b) the boundary part from B to C is congruent by translation to theīoundary part from A to D (see Figure 20.12a) orĢ. (a) the boundary part from A to B is congruent by translation to the There are four consecutive points A, B, C, and D on the boundary such that "A tile can tile the plane by translations if eitherġ. Polygons "which displace every point by a specified vector" produce a tessellation by translation (Kaplan, 2009). Not all the shapes that can be tessellated can be a translated to form a tessellation. "Each tile is a translation of each other one, since we can move one to coincide with another without doing any rotation or reflection."(Campbell, 1996) Vertex rotation, midpoint rotation/ reflection, and glide-reflection/ half turn. Some of the others I want to point out are The most basic and well known tessellation is a translation tessellation. The different shapes can produce so many different tessellations on their own, but there are also many different ways to modify polygons to produce an endless Reinhardt came up with three cases for when irregular hexagons will tessellate. Triangles and quadrilaterals are awesomeīecause they can all be tessellated. Irregular triangles, quadrilaterals, and hexagons can be tiled and tessellated. Shapes don't have to be regular polygons to tessellate. This link shows the regular polygons that tessellate and also shows some examples. There are also polygons that can be put together with other polygons to produce tessellations as well, such as squares and triangles. Their angle measures can add up toģ60 degrees. If we think about the interior angle measures of theses polygons, it makes sense why they can tessellate. Shapes that can produce tessellations by themselves are triangles, For a polygon to tessellate the total of all the angles around a point must be 360 degrees. Regular tilingĪre tilings that use regular polygons. To better understand this, we should look at tiling. In a sense they have to fit together perfectly. Like a puzzle where there are no holes or overlap. For a tessellation to be produced, the geometric shape has to be able to fit together One thing to note is that not all geometric shapes will tessellate. Every tessellation starts out as a geometric shape that has been manipulated and then repeated The basic mathematics of tessellations are based on geometry.
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