These two complementary ideas are now well established. Being able to see, draw diagrams, make models, feel and touch models are all pedagogical tools for understanding mathematics. For instance the three triangles shown below are similar, so their areas are in proportion to their hypotenuses and this gives, with unexpected simplicity, a 'proof' of Pythagoras' theorem - the 'proof' can be 'seen'. Visual perception in 2 and 3 dimensions is the source of so much mathematics that it needs a high prof ite if students are to develop properly as mathematicians, appreciating the interaction of intuition and rigour and understanding the nature of mathematics. Vector geometry provides elegant solutions to a variety of geometrical problems.
Geometry is important in other branches of mathematics.
Both Newtonian and relativistic mechanics depend on geometrical notions. At a more practical level, geometry offers a range of interesting problems which can be explored visually and logically, and gives students access to the need for proof. Today with modern computers and flexible software packages, we have opportunities to enhance teaching and the quality of students' learning, and to take advantage of the investigational environment and attitudes which are now current in schools. Let us look at just one example, Cabri Geometre. Cabri Geometre is a computer package that allows the creation of points, lines and circles on the screen.