Archimedes' principle and density measurements are highlighted as the most accurate methods for determining body fat percentage, although they are complex and often require specialized equipment, such as airtight boxes for body volume measurement. Water dunk tests remain the accepted standard in the field, as noted by an exercise physiologist. The discussion also touches on the potential of electrical impedance as a newer technique, though there is a lack of studies correlating its effectiveness with traditional methods. The idea of using mechanical resonance to measure body fat is proposed, raising questions about the resonant frequencies of different fat types. Vernier calipers are mentioned as a practical tool, but their effectiveness compared to other methods is questioned. Overall, the conversation emphasizes the ongoing exploration of various techniques for accurately measuring body fat.