“Five-Squares-to-One Dissection” from the Wolfram Demonstrations Project
The applet above is an example of a dissection puzzle. A dissection puzzle, also called a transformation puzzle tiling puzzle where a set of pieces can be assembled in different ways to produce two or more distinct geometric shapes (Wikipedia).
Paper Folding Activity
1. Draw a circle and draw a point in its interior.
2. Mark a point anywhere on the circle.
3. Fold such that the two points coincide and crease well.
4. Repeat steps 2-3 as many times as you can.
What do you observer about the creases?Note: The green lines represents the folds on the circle.
In any triangle, a circle called circumcircle maybe drawn that passes through its vertices. The center of the circumcircle is called the circumcenter. The perpendicular bisector of the three sides of any triangle passes through its circumcenter.
1) What do you observe about the figure?
2) Move points A, B, and C. Are your observations still the same?
The Napoleon theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, the centers of those triangles themselves form an equilateral triangle.