The objective of this monograph is to describe and explain the meanings underlying some otherwise anomalous archaeological data drawn from the study of Ancient Egypt. An explanation for the phenomena observed has hitherto proved elusive. The data is principally concerned with royal funerary architecture from the Old Kingdom, and the underlying systems of measurement and geometry that were employed therein. As well as providing a description and explanation for the data, this work also has the objective of providing the first synthesis of related cultural information drawn from several different textual and archaeological resources. The general subject matter is pharaonic funerary architecture from Old Kingdom Egypt, and the work focuses specifically on the circular proportions deliberately incorporated into the tomb designs by the architects. Contents: Introduction; 1) Fundamentals of Ancient Egyptian mathematics and architecture; 2) The Evidence and facts of Egyptian circular proportions; 3) The symbolism; 4) Methodology, analysis and discussion of mathematics; 5) Arguments from authorities; 6) Archaeology and philology; fieldwork and deskwork; 7) Conclusions; Appendix 1: Secondary Issues; Appendix 2: Social Context of early Egyptology; Appendix 3: Egyptian and Greek Mathematics; Appendix 4: Quotes from the Greeks.