![11.3 Curves, Polygons and Symmetry](http://s1.studyres.com/store/data/004457975_1-2efb968327a10af63f62b542b7bf99f7-300x300.png)
PERIMETER-MINIMIZING TILINGS BY CONVEX AND NON
... In this paper, we assume that all tilings by polygons are edge-to-edge; that is, if two tiles are adjacent they meet only along entire edges or at vertices. We say that a unit-area pentagon is efficient if it has a perimeter less than or equal to that of a Cairo pentagon’s, and that a tiling is effi ...
... In this paper, we assume that all tilings by polygons are edge-to-edge; that is, if two tiles are adjacent they meet only along entire edges or at vertices. We say that a unit-area pentagon is efficient if it has a perimeter less than or equal to that of a Cairo pentagon’s, and that a tiling is effi ...
7-5
... 3. A part of a line between two points is called a _________. segment 4. Two lines that intersect at 90° are ______________. perpendicular ...
... 3. A part of a line between two points is called a _________. segment 4. Two lines that intersect at 90° are ______________. perpendicular ...
15.2 Draw Quadrilaterals
... Connect You have learned to classify quadrilaterals by the number of pairs of opposite sides that are parallel, by the number of pairs of sides of equal length, and by the number of right angles. How can you draw quadrilaterals? ...
... Connect You have learned to classify quadrilaterals by the number of pairs of opposite sides that are parallel, by the number of pairs of sides of equal length, and by the number of right angles. How can you draw quadrilaterals? ...
Chapter 8 Sample Unit
... Process: Cut out the polygon cards. Sort them into regular or irregular. Quiz a partner by showing a card and having him identify the type of polygon and whether it is regular or not. Play memory trying to match up the words and the pictures. ...
... Process: Cut out the polygon cards. Sort them into regular or irregular. Quiz a partner by showing a card and having him identify the type of polygon and whether it is regular or not. Play memory trying to match up the words and the pictures. ...
Word
... Name: _____________________________ Geometry Chapter 4.3: Congruent Triangles We learned about congruent angles in chapter 4.2 and we will now work on applying congruence of angles and sides to proving that certain triangles are congruent to each other. Key Concept: Definition of Congruent Polygons ...
... Name: _____________________________ Geometry Chapter 4.3: Congruent Triangles We learned about congruent angles in chapter 4.2 and we will now work on applying congruence of angles and sides to proving that certain triangles are congruent to each other. Key Concept: Definition of Congruent Polygons ...
This is an activity worksheet
... interior angles of more sided figures, such as the rectangle or the hexagon? Furthermore, can we find the individual interior angles of a regular polygon? In case we forgot, a regular polygon is a polygon where all the angles are the same measure and all the sides are the same length. Opening up a n ...
... interior angles of more sided figures, such as the rectangle or the hexagon? Furthermore, can we find the individual interior angles of a regular polygon? In case we forgot, a regular polygon is a polygon where all the angles are the same measure and all the sides are the same length. Opening up a n ...
Isosceles Triangle Investigation Name(s): DIRECTIONS: Use any
... 3) The two equal sides of an isosceles triangle are called ________________ 4) The non-equal side of an isosceles triangle is called the ________________ 5) The two equal angles in an isosceles triangle are called ________________ 6) The non-equal angle of an isosceles triangle is called the _______ ...
... 3) The two equal sides of an isosceles triangle are called ________________ 4) The non-equal side of an isosceles triangle is called the ________________ 5) The two equal angles in an isosceles triangle are called ________________ 6) The non-equal angle of an isosceles triangle is called the _______ ...
Tessellation
![](https://commons.wikimedia.org/wiki/Special:FilePath/Ceramic_Tile_Tessellations_in_Marrakech.jpg?width=300)
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.