Titlebook: All Sides to an Oval; Properties, Paramete Angelo Alessandro Mazzotti Book 20171st edition Springer International Publishing AG 2017 51E21,

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Introduction,ered not convenient or simply uninteresting. The ellipse is nature, it is how the planets move, while the oval is human, it is imperfect. It has often been an artist’s attempt to approximate the ellipse, to come close to perfection. But the oval allows for freedom, because choices of properties and

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Remarkable Four-Centre Oval Shapes,[13]), the oval shape families by Gridgeman and Franchi (used to fit a given ellipse—see [9] for references and comments), those by Bianchi, Kitao and the third study by Hewitt (see [10] for references and comments) as well as studies by Zerlenga (in [16]) of variations of single parameters and bord

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Introduction, in technical language, an ambiguous meaning. It may be any shape resembling a circle stretched from two opposite sides, sometimes even more to one side than to the other. When it comes to mathematics you have to be precise if you don’t want to talk about ellipses, or about non-convex shapes, or abo

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Properties of a Polycentric Oval,in Chap. . and for the formulas linking the different parameters, derived in Chap. .. All properties are derived by means of mathematical proofs based on elementary geometry and illustrated with drawings.

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Ruler/Compass Constructions of Simple Ovals,ady to tackle more complicated problems, such as the two . or the ., which we will discuss in the second part of this chapter. All the following constructions have been made with freeware Geogebra and most of them are linked through the website www.mazzottiangelo.eu/en/pcc.asp, as described further.

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Parameter Formulas for Simple Ovals and Applications,formulas which on the other hand allow to calculate all important parameters when the value of three independent ones is known, as well as the limitations the given parameters are subject to. These formulas allow for a deeper insight in the properties of any oval, as will be shown on the chosen form

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Ovals with 4n Centres and the Ground Plan of the Colosseum,g and/or to make the oval look more like an ellipse. In this chapter we will extend a property presented in Chap. 2 which allows solving some construction problems for ovals with more than four centres, and illustrate a procedure to draw eight-centre ovals once two of the three radii are known. We w