Construction sheets

Instruments, and a lesson reading over your shoulder.

• How tall is that building? A tape across the street, a home-made clinometer, and a triangle on a sheet of paper that turns one angle into 75 feet of wall.
• Build a clinometer A printable scale at true size, and how to make it measure buildings, trees and the height of the pole star.
• Eight things measured from where you are standing A flagpole, a wall, a tree by its shadow, and four students who cannot all be right.
• Triangles with the same angles Euclid VI.4 on a roof. Slide the upright anywhere along the rafter and one of the three numbers refuses to move.
• The cosine of fifteen degrees Build 15° out of 60° and 45° with one opening of the compass, then read cos 15° off the figure exactly.
• The angle at the centre Euclid III.20. The angle at the centre is twice the angle at the circumference, and the last three steps break the proof on purpose.
• The exterior angle Euclid I.32, cited by III.20 at step 8.
• A blank sheet The instruments, and four of Euclid’s constructions to aim at.