an interesting function on quadrilaterals
- Author:
- Judah L Schwartz
- Topic:
- Geometry, Quadrilaterals
Before exploring this applet please study the Circumcenter-finder applet here.
Here is function from the space of quadrilaterals to the space of quadrilaterals.
Consider the four points [Yellow dots] which form the quadrilateral ABCD [green]. Circumscribe circles around ABC [center will be at E], around BCD [center will be at F], around CDA [center will be at G] and around DAB [center will be at G].
The centers form the quadrilateral EFGH [blue].
If you carry out the same procedure on the blue quadrilateral you get the orange quadrilateral.
Drag the Yellow dots -
conjectures?
proofs?
extensions?
What questions could / would you put to your students based on this applet?
Now suppose we change the function so that it now reads -
Consider the four points [Yellow dots] which form the quadrilateral ABCD [green].
Inscribe circles in ABC [center will be at E], in BCD [center will be at F], in CDA [center will be at G] and in DAB [center will be at G].
The centers form a new quadrilateral EFGH.
If you carry out the same procedure on EFGH what will you get?