Although the head shape of a spade seems like the reverse shape of a heart curve, it is very difficult to find the equation expressing the head of a spade because the margin of the choice of a spade curve is much more narrow than that in the case of a heart curve.
    In this time, we find only a heart curve, which may be adopted as the shape of a spade after the top and the bottom of the heart curve were made reverse, among a lot of the obtained heart curves.
    By the way, the shape of a spade is indicated in this site.

    If the top and the bottom of the heart curve which is displayed in the third section of the page of Heart Curves III (here in ) are made inverse, relatively good shape of a spade yields.     Then, if only the sign of Eq.(6) in the page of heart curve III is changed while that of Eq.(5) is not changed, the following two equations are rewritten.

                     ,                        (1)
and

                     ,                        (2)
where .
    When the intermediate variable varies in the range of , two examples of curves displaying Eqs.(1) and (2) and these painted figures are shown in the followings.