I have an idea of a quadrilateral / square game, and am looking for help.
For the moment lets call it the "Square or Not " game.
Imagine we have a big stack of cards with on each card some property of a square.
The properties have the following limitations:
- The property is valid for square.
- The property is valid for some quadrilateral that is not a square (so the property doesn't define the quadrilateral as a square)
- The property is expressable in a short sentence, and understandable for a twelf year old.(except maybe some geometrical terms, that can be explained in a booklet)
Examples of valid properties:
- the quadrilateral is a rectangle.
- the quadrilateral has a line of symmetry.
- a diagonal cuts the quadrilateral in two similar triangles.
- a bimedian cuts the quadrilateral in half (by area).
- the quadrilateral has at least one right angle.
- two adjecent sides have the same length.
- the two diagonals have the same length.
- the quadrilateral is convex.
Examples of invalid properties:
- a diagonal lies outside the quadrilateral (not valid for a square).
- the area of the circumscribed circle is twice the area of the inscribed circle (this implies the quadrilateral is a square).
the game (solitaire version)
The player picks at random a dozen property cards and must decide if a quadrilateral with all these properties is nescesarily a square or not.
If it is a square: (Probably it is) - what is the minimal number of properties that needs to be removed so that the quadrilateral is not necesary a square?
What help I need:
more properties of a square, (will later add my own list of properties)
who could help me making this game (or a software version of it)