Squares

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

A Short introduction to using Logo. This is the first in a twelve part series.

What fractions can you divide the diagonal of a square into by simple folding?

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

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

Can you work out the area of the inner square and give an explanation of how you did it?

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

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.

What is the minimum number of squares a 13 by 13 square can be dissected into?

What is the perimeter of this unusually shaped polygon...