I wrote this after the excellent book Yagyu Shinkage Ryu Kyohon came out in 2004, this is a rough translation...
1. Sanma – This first design is familiar to all and one that is often copied. A triangle of equal sides within a circle and three small circles at the point of each angle. In the beginning of the book Yagyu Heiho Kaden-sho, there is mention of “Sanma no kurai”, this design harkens to this teaching and the three principles of Narai, Keiko and Kufu. Narai means teaching, instruction and represents your learning, and all the teachings of those before you. In order to make these teachings a part of your blood and bones you need Keiko. Keiko is practice, you need practice in order to remake yourself. There is the saying “Sentan Senren” or 1000 forgings, 1000 practices. Tanren means to forge, we use this as a term in discussing the forging of swords but it also means to forge or to harden oneself through discipline and hard practice, but the discipline in Yagyu swordsmanship is no ordinary discipline so we say “Sentan Senren!” What then is the result of this practice? It is a study that you pursue with your whole body and soul. Further you call upon your creativity and ingenuity to help get you to your goal. Thus the third principle is Kufu or shugyo, in which you seek within yourself to create a true spirit of independence, a true self. Within the circle keep seeking a state where all three are in balance, all three are one. This is described in the motto “to win today over yourself of yesterday.” Sanma is thus a symbol of lifelong practice, lifelong shugyo. (Note this design is also known as Sankaku Sansei, “three sides and three stars”.)