history of mathematics - National STEM Centre

Activity 3.1
Activity 3.2
Drawing a perpendicular
3 An introduction to Euclid
Figure 3, la Figure 3.1b Figure 3. 7c
Figure 3.1 shows an example of the use of Euclid's rules to draw a line
perpendicular to the line / through the point A.
1 Use the following instructions to make your own copy of Figure 3.1c.
Take a point B on / and draw the circle with centre A and radius AB.
This circle intersects / in a second point C.
Draw circles of radius AB with centres B and C, and mark the point D where
these circles intersect.
Make the triangle BDC, a copy of the isosceles triangle BAG on the other side
of/.
Draw the line AD, and mark the point E where it intersects /.
2 Give reasons why AD is perpendicular to /.
3 Use your diagram so far to draw the circle centre A, which has / as a tangent.
4 Explain why, in Greek mathematics, you would not be allowed to draw the circle
in question 3 directly from Figure 3.la.
Some more constructions
If you can, work in a group for this activity. Discuss your answers to question 4 in
your group.
Two regularly used constructions are the perpendicular bisector of a line-segment,
and the bisector of an angle.
Figure 3.2
1 a Use the progressive drawings in Figure 3.2 to write a list of instructions,
similar to those in question 1 of Activity 3.1, for constructing the perpendicular
bisector of the line AB.
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