qual and an angle inscribed in a semicircle being a right angle. 572 BC - Pythagoras of Samos produces all those useful equations for triangles and circles and shows how complex shapes can be described in terms of simple straight lines and circles, an early example of a transform. 427-347 BC - Plato founds his academy in Athens (387 BC) and encourages mathematicians such as Theaetetus and Eudoxus, the exhaustion man, to work on geometry and proportional theory. 300 BC - Euclid produces 'the bible of mathematics', 13 books and 456 proposi- tions on plane and solid geometry and number theory including prime numbers, the infinitude of the primes. Euclid's axioms include the concept of Euclidean dis- tance, the straight-line distance between two signal vectors that still serves today as a starting point for many mathematicians. Note that 'distance' can be related to many performance metrics in present communication systems including system sensitivity and selectivity. 287-212 BC - Archimedes equates the area of a circle with a triangle and works out the value of Pi using inscribed and circumscribed polygons as well as that business with the bath. Physical Layer Connectivity A bit of a gap due to the Romans being more interested in building roads than maths. 430-501 AD - Tsu Ch'ung-chih - the famous Chinese mathematician defines Pi more accurately. 529 AD - the closing of the Alexandrian library marks a shift towards Arabia in terms of mathematical innovation, including the evolution of algebra, the art of calculating with unknown quantities represented by letters after the arabic al gebr/al jabr meaning to equalise. 900 AD - Al Khumar Rizmi works on algorithmic approaches to problem solving. The word algorithm is named after him and is used to describe the step-by-step iterative process for solving problems using a predetermined set of rules within a finite number of steps. 1452-1519 - Leonardo Da Vinci and the arrival of Renaissance man including; 1501-1576 - Gerolamo Cardamo of Milan works on the mathematics of pro