Thought of as a right triangle, the calculation of these triangles is easy and can be done using the two known sides (the two-by-one or the one-by-two multiplied by the price relationship) and a known angle within the right triangle (the 90-degree angle that every right triangle has).
“Gann angles” (below) shows triangles manually drawn on price charts. The first chart is a one-by-one angle so both side B (time) and side C (price) equal one unit, with angle X being equal to 45 degrees. The second chart demonstrates the same concept, and uses the same equation, except that it has a two-by-one angle and side B (time) is equal to two, side C (price) is equal to one and angle Y is equal to 26.25 degrees. The third chart has an inverse relationship — it is a one-by-two angle instead of a two-by-one angle — so side C (price) is equal to one, side B (time) is equal to two and angle Z is equal to 63.75 degrees.
In “Multi-view” (below), the triangles from each figure are combined and, to clean things up a bit, everything is removed but the trendlines. This figure is the Gann fan in its most basic form. The second chart in this graphic shows the Gann fan as drawn by technical analysis software, in this case Track ‘n Trade.