DEFINITION: TILES AND TILING

Slides:



Advertisements
Similar presentations
TESSELLATIONS Oleh : Sulistyana SMP N 1 Wonosari.
Advertisements

Tantalising Tessellations
A tessellation or a tiling is a way to cover a floor with shapes so that there is no overlapping or gaps. Tessellation Remember the last jigsaw puzzle.
1. Prove that the sum of the interior angles of a polygon of n sides is 180 (n – 2). § 8.1 C B E D P F A Note that a polygon of n sides may be dissected.
Geometry 5 Level 1. Interior angles in a triangle.
Tessellations Warm Up Lesson Presentation Lesson Quiz
Chapter 20: Tilings Lesson Plan
Using Transformations to Create Fantastic Tessellations! Dr. Maria Mitchell 1.
Tessellations Confidential.
Students will name two dimensional figures (9-4).
10.3 Polygons, Perimeters, and Tessalatiolns.  Polygon- -Any closed shape in the plane formed by three or more line segments that intersect only at their.
© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 10 Geometry.
Tessellations 5.9 Pre-Algebra.
Tessellations 12-6 Warm Up Lesson Presentation Lesson Quiz
Geometry Review. What is a six sided polygon called?
CHAPTER 24 Polygons. Polygon Names A POLYGON is a shape made up of only STRAIGHT LINES.
Becca Stockford Lehman. Tessellate: to form or arrange small squares or blocks in a checkered or mosaic pattern Tessellate: to form or arrange small squares.
Tessellations *Regular polygon: all sides are the same length (equilateral) and all angles have the same measure (equiangular)
6.1 Polygons 6.2 Properties of Parallelograms Essential Question: How would you describe a polygon?
Polygons Lesson What is a polygon? A polygon is a simple, closed, two-dimensional figure formed by three or more line segments (sides). Closed?
7-9 Tessellations Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.
Chapter Congruence and Similarity with Transformations 13 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Here are the eight semi-regular tessellations:
G Stevenson What Are Tessellations? Basically, a tessellation is a way to tile a floor (that goes on forever) with shapes so that there is no overlapping.
Lesson 10-4: Tessellation
to summarize this presentation
POLYGONS & QUADRILATERALS
Plane figure A two dimensional figure. Chapter 10.
© T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not.
Tessellations.
Tessellations 1 G.10b Images from ygons/regular.1.html
5-9 Tessellations Warm Up Problem of the Day Lesson Presentation
© 2010 Pearson Education, Inc. All rights reserved Motion Geometry and Tessellations Chapter 14.
Tessellations with Regular Polygons.  Many regular polygons or combinations of regular polygons appear in nature and architecture.  Floor Designs 
Polygons and Area (Chapter 10). Polygons (10.1) polygon = a closed figure convex polygon = a polygon such that no line containing a side goes through.
A tessellation (or tiling) is a special type of pattern that consists of geometric figures that fit without gaps or overlaps to cover the plane.
Tessellations.
 Are patterns of shapes that fit together without any gaps  Way to tile a floor that goes on forever  Puzzles are irregular tessellations  Artists.
TESSELLATIONS A Tessellation (or Tiling) is a repeating pattern of figures that covers a plane without any gaps or overlaps.
10-7: Tessellations T ESSELLATION : A tiled pattern formed by repeating figures to fill a plane without gaps or overlaps. Regular Tessellation: When a.
Lesson 10-4: Tessellation
Transformations, Symmetries, and Tilings
A tessellation or a tiling is a way to cover a floor with shapes so that there is no overlapping or gaps. Tessellations Remember the last jigsaw puzzle.
11 Chapter Introductory Geometry
$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500.
Classifications Bowen’s Class. Quadrilateral Any four sided polygon Any four sided polygon.
Tessellations 9-6 Warm Up Lesson Presentation Lesson Quiz
Tessellations.
Tessellations A tessellation is made by reflecting, rotating or translating a shape. A shape will tessellate if it can be used to completely fill a space.
Polygons, Perimeters, and Tessellations
5-9 Tessellations Warm Up Problem of the Day Lesson Presentation
Investigation 12: Tessellation
Tessellations POD: What is the measure of each interior angle of each regular polygon? Equilateral triangle Pentagon Hexagon Octagon.
All sides have the same length and angles have the same measure.
Classifying Polygons.
Warm Up Classify each polygon. 1. a polygon with three congruent sides
Tessellations POD: What is the measure of each interior angle of each regular polygon? Equilateral triangle Pentagon Hexagon Octagon.
Lesson 10-4: Tessellation
Tessellations.
Tessellations.
12-6 Tessellations Lesson Presentation Holt Geometry.
13 Chapter Congruence and Similarity with Transformations
Tessellations 12-6 Warm Up Lesson Presentation Lesson Quiz
Shapes Polygons and Quadrilaterals
Tessellations of the Plane
Tessellations Warm Up Lesson Presentation Lesson Quiz
Tessellations Warm Up Lesson Presentation Lesson Quiz
Classifying Polygons.
CHAPTER 10 Geometry.
Tessellations Geometry Unit 2 Session 4.
Presentation transcript:

DEFINITION: TILES AND TILING 13.3 DEFINITION: TILES AND TILING A simple closed curve, together with its interior, is a tile. A set of tiles forms a tiling of a figure if the figure is completely covered by the tiles without overlapping any interior points of the tiles. In a tiling of a figure, there can be no gaps between tiles. Tilings are also known as tessellations. Copyright © 2008 Pearson Education, Inc.

TILING WITH REGULAR POLYGONS 13.3 TILING WITH REGULAR POLYGONS Any arrangement of nonoverlapping polygonal tiles surrounding a common vertex is called a vertex figure. Equilateral triangles form a regular tiling because the measures of the interior angles meeting at a vertex figure add to 360. Copyright © 2008 Pearson Education, Inc.

TILING WITH EQUILATERAL TRIANGLES 13.3 TILING WITH EQUILATERAL TRIANGLES One interior angle of an equilateral triangle has measure 60. At a vertex angle: Copyright © 2008 Pearson Education, Inc.

One interior angle of a square has measure 90. 13.3 TILING WITH SQUARES One interior angle of a square has measure 90. At a vertex angle: Copyright © 2008 Pearson Education, Inc.

TILING WITH REGULAR HEXAGONS 13.3 TILING WITH REGULAR HEXAGONS One interior angle of a regular hexagon has measure At a vertex angle: Copyright © 2008 Pearson Education, Inc.

TILING WITH REGULAR PENTAGONS? 13.3 TILING WITH REGULAR PENTAGONS? One interior angle of a regular pentagon has measure At a vertex angle: Copyright © 2008 Pearson Education, Inc.

THE REGULAR TILINGS OF THE PLANE 13.3 THE REGULAR TILINGS OF THE PLANE There are exactly three regular tilings of the plane: by equilateral triangles, by squares, and by regular hexagons. Copyright © 2008 Pearson Education, Inc.

TILING THE PLANE WITH CONGRUENT POLYGONAL TILES 13.3 TILING THE PLANE WITH CONGRUENT POLYGONAL TILES The plane can be tiled by: any triangular tile; any quadrilateral tile, convex or not; certain pentagonal tiles (for example, those with two parallel sides); certain hexagonal tiles (for example, those with two opposite parallel sides of the same length). Copyright © 2008 Pearson Education, Inc.

SEMIREGULAR TILINGS OF THE PLANE 13.3 SEMIREGULAR TILINGS OF THE PLANE An edge-to-edge tiling of the plane with more than one type of regular polygon and with identical vertex figures is called a semiregular tiling. Copyright © 2008 Pearson Education, Inc.

ITS GRID OF PARALLELOGRAMS 13.3 TILINGS OF ESCHER TYPE Dutch artist Escher created a large number of artistic tilings. ESCHER’S BIRDS ITS GRID OF PARALLELOGRAMS Copyright © 2008 Pearson Education, Inc.

MODIFYING A REGULAR HEXAGON WITH ROTATIONS 13.3 TILINGS OF ESCHER TYPE MODIFYING A REGULAR HEXAGON WITH ROTATIONS CREATES: Copyright © 2008 Pearson Education, Inc.