The heart and arterial system are matched in the sense that the heart pumps at maximal external power. Why external power is optimized and what regulatory mechanisms are responsible for this optimization are not known. In the present report we will suggest a mechanism of matching on the basis of the following arguments. 1) Mean aortic pressure, the perfusion pressure for most organs, most notably the cerebral circulation, is similar in mammals. 2) Heart period (T), a cardiac parameter, is related to body mass in a similar way as the decay time (tau = R(p)C, where R is peripheral resistance and C is total arterial compliance) of aortic pressure in diastole, a vascular parameter. In other words, the ratio of T/tau is similar in all mammals and assures a similar aortic pressure in diastole so that coronary perfusion, which mainly takes place in diastole, is guaranteed. 3) Assuming given mechanical properties of mammalian cardiac muscle, optimal power delivery relates to a minimal cardiac size; in other words, during evolution total cardiac volume was minimized, resulting in a heart that pumps at maximal power.