Titlebook: Exploring Classical Greek Construction Problems with Interactive Geometry Software; Ad Meskens,Paul Tytgat Book 2017 Springer Internationa

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https://doi.org/10.1007/978-3-319-42863-5Delian problem; straightedge and compass; ruler and compass; GeoGebra; neusis; circle quadrature; duplicat

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The Delian Problem,o stop the epidemic. The oracle answered that they should build a new cubic altar, with a size (= volume) double that of the existing one. The length of the edge should be determined by compass and straightedge methods only..Plato gave a solution with mechanical aids, for which numerous variants exi

mitral-valve

Trisecting an angle, equal parts, by compass and straightedge methods then comes naturally..The question is simple enough and seems to suggest a simple solution. Here too, appearances are deceptive. It turns out that, like the duplication of the cube, the construction with compass and straightedge is impossible. We can

中止

Squaring the circle,same area as a given figure. We still refer to the square root of a number, meaning we are looking for the length of the edge of a square with the given number as area..‘‘Squaring the circle’’ has become more or less a catch line for something which is impossible or unsolvable. Indeed, the problem c

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Constructible numbers,e a consequence of Euclid’s first three postulates:.We will call a number . constructible if we can construct a line segment with length . in a finite number of steps..The axiom tells us that if we choose two different points . and ., then we actually turn the straight line into a ruler with . as un

苦笑

The Cinderella of regular polygons, is not constructible using compass and straightedge methods. In what follows, we will guide you through the proof of this non-constructibility..We call this configuration Viète’s ladder. Viète used this configuration to calculate the edge of a regular heptagon.