In his celebrated Tutte l’Opere d’Architettura published over the period 1537–1575 Sebastiano Serlio introduced four techniques for constructing ovals which have thereafter been applied by many architects across Europe. Using various geometric forms (i.e. the triangle, square, and circle) as a basis they produced ovals made up from four circular arcs. This paper analyses both Serlio’s constructions and some of the many possible alternatives and evaluates their accuracy in terms of the ovals’ approximations to an ellipse.

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Quadrarcs, St. Peter's, and the Colosseum.

On serlio’s constructions of ovals

Several constructions for piecewise circular approximations to ellipses are examined. It is shown that a simple approach based on positioning the arc centres based on factors of the difference in major and minor axes lengths generates a family of tangent continuous solutions that can provide near optimal approximations for specific aspect ratios.

A family of constructions of approximate ellipses

When conic sections are introduced to mathematics classes, certain real-world examples are often cited. Favorites include lamp-shade shadows for hyperbolas, paths of baseballs for parabolas, and planetary orbits for ellipses. There is, however, another outstanding example of an ellipse. Known simply as the Ellipse, it is a gathering place for thousands of Americans every year, and it is probably the worlds largest noncircular ellipse. Situated just south of the White House in Presidents Park, the Ellipse has an interesting shape and an interesting history.

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/pdf/the-shape-and-history-of-the-ellipse-in-washington-d-c-1n65mctf9x.pdf

The Shape and History of The Ellipse in Washington, D.C.

The current deals with the determination of the ‘true’ geometrical shape of the Great theatre of Ephesus, which is the largest theatre in Asia Minor. To detect the geometrical form of the theatre a...

Quadrarcs, St. Peter's, and the Colosseum.

Citations

On serlio’s constructions of ovals

A family of constructions of approximate ellipses

The Shape and History of The Ellipse in Washington, D.C.

The determination of the true geometrical form of Great Ephesus theater, Turkey by using field surveys

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