Squares

Weekly Problem 8 - 2008
In how many ways can a square be cut in half using a single straight line cut?

What fraction of this square is shaded?

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.

This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles.

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.