transformations and tessellations edited by: k. stone
TRANSCRIPT
Transformationsand Tessellations
Edited By: K. Stone
Transformation•Movements of a figure in a plane
•May be a SLIDE, FLIP, or TURN
Translation
Another name for a SLIDE
A
BC
A’
C’ B’
A’, B’ and C’ are explained in the next slide...
Writing a Rule9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9
Right 4 (positive change in x)
Down 3 (negative change in y)
A
A’
B
B’
C
C’
Reflection
Another name for a FLIP
A A’
C C’B B’
Reflection
Used to create SYMMETRY on the coordinate
plane
Symmetry
When one side of a figure is a
MIRROR IMAGE of the other
Line of Reflection
The line you reflect a figure
acrossEx: X or Y axis
Rotation
Another name for a TURN
B
B’
C
C’
A
A’
Center of Rotation
The fixed point
(0,0)
AA’
C
C’
B
B’
Tessellation
A design that covers a plane with NO GAPS
and NO OVERLAPS
Tessellation
Formed by a combination of TRANSLATIONS, REFLECTIONS,
and ROTATIONS
Pure Tessellation
A tessellation that uses only
ONE shape
Pure Tessellation
Pure Tessellation
Semiregular Tessellation
A design that covers a plane
using more than one shape
Semiregular Tessellation
Semiregular Tessellation
Semiregular Tessellation
Semiregular Tessellation
What will tessellate?• In order to tessellate,
shapes must fit together to form 360○ at their vertex.
• To find out if a shape will tessellate a plane alone, divide the measure of one of its angles into 360. If it divides evenly, it will tessellate. If not, it won’t.
• For example, a square has 90 ○ angles. 90 goes into 360 exactly 4 times, so a square will tessellate by itself.
Tessellation
Used famously in artwork by M.C. Escher
LINKS
• Cool math Lessons - Geometry - What are Tessellations?
• Interactivate: Tessellate!