Tuesday February 7
Cutting and reassembling polygons.
Any two points in the figure
have a line segment connecting them. If that line segment is always inside the figure, then the
figure is called "convex".
Making Dissection Puzzles
[more links] :
Dissection of the
of the plane:
- Activity: Tile plane with playing
- FAPP watch Video: Possible tiles and
- One Regular Convex Polygon.
- Two or more Regular Convex Polygons.
- Other Polygon Tilings.
- Non polygonal tilings.
- One polygonal Tile: Quadrilateral Activity.
An on-line tool for making tilings of the plane
- Regular and semiregular Tilings of the plane. Some explorations - classification.
- A tiling is a regular tiling if (i)it has a single tile shape
that is a regular polygon and (ii) the vertices and edges of the tiles
coincide (no overlapping edges)
- A tiling is a semi-regular tiling if (ii) each tile shape is a
regular polygon, (ii) the vertices and edges of the tiles coincide (no
overlapping edges) and (iii) every vertex has the same polygon types
download! and demonstrate tesselations.
tilings (Math Forum)
- The numbers represent the number of sides in the poygons.
- The order indcates the order in which the poygons are arranged
about a vertex.
- Semiregular Tilings: global results!
Look at the results using wingeometry.
lesson (Math Forum) a place for further explorations on-line.
- Symmetry Ideas
- Reflective symmetry: BI LATERAL
T C O
0 I A
- Folding line: "axis of symmetry"
- The "flip."
- The "mirror."
- R(P) = P' : A Transformation. Before: P
.... After : P'
- If P is
on the line (axis), then R(P)=P. "P remains fixed by the reflection."
- If P is not on the axis, then the line PP' is
perpendicular to the axis and if Q is the point of intersection of PP'
the axis then m(PQ) = m(p'Q).
- Definition: We say F has a reflective symmetry wrt a line l if there is a
reflection R about the line l
R(P)=P' is still an element of F for every P in F....i.e.. R (F) =
F. l is called the axis of symmetry.
- Examples of reflective symmetry:
- Rotational Symmetry.
- Center of rotation. "rotational pole" (usually
O) and angle/direction of rotation.
- The "spin."
- R(P) = P' : A transformation
- If O is the center then R(O) = O.
- If the angle is 360 then R(P) = P for all
P.... called the identity transformation.
- If the angle is between 0 and 360 then
only the center remains fixed.
- For any point P the angle POP' is the
- Examples of rotational symmetry.
- Now... what about finding all the
and rotational symmetries of a single figure?
- Symmetries of playing card.... classify the cards
having same symmetries.
Notice symmetry of