Serlio's Ovals
Serlio's Ovals
The oval was an essential pattern in baroque architecture and later periods. Well-known examples of architecture employing ovals are Saint Peter's Square in Rome and the Oval Office in the White House. In his famous work "Tutte l'Opere d'Archittetura", Sebastiano Serlio declared, "In diversi modi si possono fare delle forme ovali, ma in quattro modi ne darò la regola." [As a rough translation: "There are many ways to draw an oval, but I will give you four ways to do it."] In this Demonstration you can regulate not only four ovals but a huge variety of other shapes.
Two centers are marked by a red locator and a blue locator. The straight lines from the centers of the circles to the points of contact are radii and the dashed lines are the tangents. With the green locator you can change the radius of the blue circles. You have chosen good parameters if the tangents coincide. If the tangents are identical then the two circles join smoothly.