To be a mathematicus in 15th- and 16th-century Europe often meant practising as an astrologer. Far from being an unwelcome obligation, or simply a means of paying the rent, astrology frequently represented a genuine form of mathematical engagement. This is most clearly seen by examining changing definitions of one of the key elements of horoscope construction: the astrological houses. These twelve houses are divisions of the zodiac circle and their character fundamentally affects the significance of the planets which occupy them at any particular moment in time. While there were a number of competing systems for defining the houses, one system was standard throughout medieval Europe. However, the 16th-century witnessed what John North referred to as a “minor revolution”, as a different technique first developed in the Islamic world but adopted and promoted by Johannes Regiomontanus became increasingly prevalent. My paper reviews this shift in astrological practice and investigates the mathematical values it represents – from aesthetics and geometrical representation to efficiency and computational convenience.