The Pythagorean Theorem - Educational Outreach

2.6) Leonardo da Vinci’s Magnificent SymmetryLeonardo da Vinci (1452-1519) was born inAnchiano, Italy. In his 67 years, Leonardo became anaccomplished painter, architect, designer, engineer, andmathematician. If alive today, the whole world wouldrecognize Leonardo as ‘world class’ in all theaforementioned fields. It would be as if Stephen Hawkingand Stephen Spielberg were both joined into one person.For this reason, Leonardo da Vinci is properly characterizedas the first and greatest Renaissance man. The world hasnot seen his broad-ranging intellectual equivalent since!Thus, it should come as no surprise that Leonardo da Vinci,the eclectic master of many disciplines, would havethoroughly studied and concocted an independent proof ofthe Pythagorean Theorem.Figure 2.22 is the diagram that Leonardo used todemonstrate his proof of the Pythagorean Proposition. Theadded dotted lines are used to show that the right angle ofthe fundamental right triangle is bisected by the solid linejoining the two opposite corners of the large dotted squareenclosing the lower half of the diagram. Alternately, the twodotted circles can also be used to show the same (readerexercise).Figure 2.22: Leonardo da Vinci’s Symmetry Diagram55