Hi, Frans > > We all know that we need just two points to draw a stright line (like the > > solar time ones), five points to draw an hyperbola (like the datelines) > > but... > > Theoretically speaking, the hyperbola is a second-degree curve. > Therefore three points should completely define its shape.
Not to determine it completely... there can be infinitely many hyperbolae that pass through three points: just imagine the degenerate cases, ie., a couple of straight lines. It happens the same with ellipses (we might as well consider that an ellipse is an imaginary hyperbola). > The equation-of-time curve is (in good approximation, that is, within > one minute) the sum of two sine waves, with frequencies of 1/year > and 2/year. Knowing that, two parameters are necessary to > describe each sine wave; for instance, amplitude and phase angle. > So, four points should define the EoT curve. Yes, I know that four are enough, but... could we get the same result with three *carefully chosen* points. > You didn't ask a recipe to actually construct the EoT curve for an > arbitrary case, did you? Nee, Ik heb er niet gevragen. Anselmo
