The Babylonian theorem : the mathematical journey to Pythagoras and Euclid / Peter S. Rudman.

Sequel to: How mathematics happened, the first 50,000 years. 2007.

Includes bibliographical references (p. 233-243) and index.

Number system basics -- Egyptian numbers and arithmetic -- Babylonian numbers and arithmetic -- Old Babylonian "quadratic algebra" problem texts. YBC 6967 ; AO 8862 ; Db₂ 146 ; VAT 8512 -- Pythagorean triples. OB problem text BM 85196 #9 ; Berlin Papyrus 6610 #1 ; Proto-Plimpton 322 ; Plimpton 322 -- Square root calculations. Egyptian calculation ; OB problem text YBC 7289 ; OB squaring-the-rectangle (Heron's method) ; OB cut-and-paste square root (Newton's method) ; Pythagoras calculates square roots ; Archimedes calculates square roots ; Ptolemy calculates square roots --PI [mathematical symbol for Pi]. RMP problems 48 and 50 ; OB problem text YBC 7302 ; A scribe from Susa calculates [Pi] (ca. 2000 BCE) ; Archimedes calculates [Pi] (ca. 200 BCE) ; Kepler calculates the area of a circle (ca. 1600) ; Everybody calculates the area of a circle (ca. 2000) -- Similar triangles (Proportionality). RMP problem 53 ; OB problem text MLC 1950 ; OB problem text IM 55357 -- Sequences and series. Arithmetic sequences and series ; OB problem text YBC 4608 #5 ; TMP problem 64 ; RMP problem 40 ; Geometric sequences and series ; OB problem text IM 55357-- revisited -- Old Babylonian algebra : simultaneous linear equations. A modern elementary algebra problem ; OB problem test VAT 8389 -- Pyramid volume. How they knew V (pyramid) / V (prism) = 1/3 ; Euclid proves V (pyramid) / V (prism) = 1/3 ; Truncated pyramid (frustum) volume -- From Old Babylonian scribe to Late Babylonian scribe to Pythagoras to Plato. Late Babylonian (LB) mathematics ; Pythagoras (ca. 580-500 BCE) ; Plato (427-347 BCE) -- Euclid. Who was Euclid? ; Euclid I-1 ; Euclid I-22 ; Euclid I-37 ; Euclid I-47 : the Pythagorean Theorem ; Euclid II-22 ; Euclid II-14 : the Babylonian Theorem.