grid geometry angles, using arc tan

using the tangent of the angle as a measure of the size of the angle
is better than a protractor!
convert an angle into a fraction (inv tan (rise / run), possibly by summing or subtracting) - so that it can be compared in size with other grid angles (i.e. as fractions)

a powerpoint is here

this presentation was part of a session in London, joint ATM/MA on march 16th 2019 and was intended to illustrate how a square grid might be helpful in geometry, an idea proposed by van Hiele in 1986 ('structure and insight') following the research of Dina and he from 1957 onwards