Euclid
Summary
- Ancient Greek mathematician, around 300BC
- Not much is known about his personal life
- He is considered one of the greatest mathematicians of antiquity
Details
- He edited a history of concepts into 13 books named 'Elements of Geometry', complete with diagrams
- Starting with simple concepts he gets more and more detail, covering much of the framework for modern mathematics
References
Quotes
Biographical details on Euclid are less than scanty, but he bridged the fourth and third centuries BCE and penned one of the most influential mathematical books in history. Having inherited a jumble of geometrical concepts, Euclid painstakingly edited them into four hundred propositions, sorted into thirteen books (what we’d call chapters), totaling twenty thousand lines of Greek, complete with diagrams.
Euclid’s Elements of Geometry starts with the basics and progresses through layers of ascending conceptual complexity. Beginning with Book 1, readers first encounter points, lines, angles, triangles, and the Pythagorean theorem. By the time Book 13 rolls around, they’re ready to tackle the Platonic solids—not only the standard cube and the hexahedron but also
• the tetrahedron, with its four triangular faces;
• the octahedron, with its eight triangular faces;
• the dodecahedron, with its twelve pentagonal faces; and
• the icosahedron, with its twenty triangular faces.
Along the way, they pick up a framework for parallel lines; the geometry of circles; the volume of pyramids, cones, cylinders, and spheres; number theory; and more.
While modern high school students might cringe at the work such exercises suggest (I certainly did) and encounter the Platonic solids only in the form of many-sided dice while playing Dungeons & Dragons, the ancients devoured Euclid’s work and applied it to every discipline of thought imaginable. The mathematician, said historian Benjamin Wardhaugh, “arranged and exemplified a toolbox of the basic techniques and results that he had inherited: ways of arguing, ways of proving; facts that geometers commonly assumed or used, but seldom proved in full.” Students, scholars, and practitioners alike could consult the Elements and employ its axioms, formulas, logic, and methods to yield reliable answers to their own quandaries.
Fragment from a first- or second-century copy of Euclid’s Elements, including one of the earliest diagrams from the work. SOURCE: PAPYRUS OXYRHYNCHUS 29. FINE ART IMAGES/HERITAGE IMAGE PARTNERSHIP LTD, ALAMY.
To stress an earlier point, Euclid’s Elements was not simply a conveyor of information; it was also a partner in novel thinking, fresh problem-solving, and the development of new models. The simple fact that the book survived all those centuries is remarkable, but that it continued to underwrite the imaginative powers of mathematicians is phenomenal—and that, of course, also explains why it survived, pushing its way along the z-axis century after century. Euclid’s book applied to everything from astronomy to architecture, and manuscript evidence shows its readers engaged energetically with its concepts, scribbling in the margins as they commented on the axioms or worked them out for themselves.