# oval and ellipse

Topic:
Ellipse

## epilogue of a conflict

We can't blame Serlio and his renaissance contemporaries. There wasn't an equation for an ellipse yet, since analytic geometry was introduced only in the 17th century. However despite what's known in mathematics the abiguity and confusion remains until now. In the article Ellipses and ovals in the physical space of St.Peter's square in Rome autors Alessandra Carlini and Paola Magrone write: "An ambiguity of use use between the terms ellipse and oval remains in some kind of literature, as toutistic literature and some school textbooks. For exemple, the Coliseum and the plan od St Peter's square are both described als elliptical shaped. Moreover, in thouristic guids (in the fout we consulted) St Peter's square is described al elliptical". The autors also quote the bestseller book 'Angels and Demons' by Dan Brown: "Two fountains flanked the obelisk in perfect symmetry. Art historians knew the fountains marked the exact geometric focal points of Bernini's elliptical piazza, but it was an architectural oddity Langdon had never really considered unti today. It seemed Rome was suddenly filled with ellipses, pyramids and startling geometry". Talking about ambiguity and confusion I can confirm what the autors write. In all kinds of touristic guides and even books on architecture ovals and ellipses are mixed together. In one the tourist is encouraged to place himself upon the round stones in St Peter's Square that indicate the centre of the colonnade and lok towards the colonnade. These stones mark the foci of the ellipsoid square, says the guide... In some books on architecture you read about ovals and on the next line about 'elliptic shapes'. In his artikel Ellissi e ovali, epilogo di un conflitto Riccardo Miglari focusses on this matter and with the word 'epilogue' in the title he makes clear that as far as he's concerned the discussion is finished. According to him the solutions is not to be found in measuring but in building traditions and literature, both of them very clear.

## an inevitable discussion

Migliari calls the discussion inevitable, referring to humanist autors, who were using both names wrongly and mixed together. Pietro Cataneo describes the construction of a curve using a rope and calls it 'figure ovale'. Vincenzo Scamozzi explains the construction of an curve 'the Greek call ellipse'... but draws an oval. Migliari continuous: "Therefore I'm inclined to accept the promiscuity of our two curves whitin this discussion. But in a contemporary technical-scientifical context the two names stand for curves that are far apart, not only by their origin, but also by their appearance, so you can't be an architect or ingeneer and not distinguish both." He continuous: "It's important for me to add that I'm not willing to award a primacy of intellectual nobility to the ellipse an oval wouldn't have. Yes, the ellipse is a cone, the planets follow an elliptical orbit , the ellipse was described throughout the ages from Apollonius to Dessargues. The ovaal has got a more modest origin. It's just a concatenation of circular arcs that's in its practical use more interessanting than mathematical theory. According to some because it's easier to construct than an ellips, especially in large dimensions. But on closer inspection in architecture in fact the oval is the most interesting option." But how can you draw these curves?

## an oval that looks almost an ellipse

• Construct two circles with equal radius as in the figure below.
• Draw a line starting from the intersection points of the two circles through the center of the circles and define the other intersection point with the circle.
• Now compose the oval out of two green circular arcs with the green centers and two red circular arcs with the red centers.
• Define r as half the long axis of the oval.

## an ellipse that looks almost an oval

Select the checkbox and show the ellipse with the same axes as the oval. Construct the ellipse as follows:
• Mark the intersection point of the vertical axis and the oval.
• Draw a circle with radius r and center this intersection point.
• Define the foci F1 and F2 as the intersection points of the circle and the long axis of the oval.
• Create the ellipse with foci F1 and F2 and long axis 2r.
Notie the minimal difference between oval and ellipse. Only at an angle of 45° from the centers of both small circles there's a little difference. For exemple the St-Peter's Square, with a log axis of 240 m the maximum difference is just 1,6 m and for the greatest part of both curves the difference is almost negligible. Of course the little difference doesn't help to dispel the misconception the square is elliptical.