Geometry: using only compasses and straightedge
How to divide a line equally in 3 - trisect a line.
Draw aline AB. Find its mid point C. (How?)
Now draw lots of circles! (5)
Draw a circle centre A width AC.
Keep the compasses at the same width and draw two more equal circles centred at C and B.
Draw a circle centre A width AB. Draw an equal circle with AB centred at B.
Draw a circle centre A width AC.
Keep the compasses at the same width and draw two more equal circles centred at C and B.
Draw a circle centre A width AB. Draw an equal circle with AB centred at B.
Draw lines from D to G and D to H. They cross AB at E and F. This divides AB in 3.
If you draw these figures on graph paper you can count the squares and see that it is true!
If you draw these figures on graph paper you can count the squares and see that it is true!