定点 发表于 2025-3-25 06:56:25
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Compact Textbooks in Mathematicshttp://image.papertrans.cn/f/image/320265.jpg证实 发表于 2025-3-25 15:02:37
https://doi.org/10.1007/978-3-319-42863-5Delian problem; straightedge and compass; ruler and compass; GeoGebra; neusis; circle quadrature; duplicatCosmopolitan 发表于 2025-3-25 18:50:58
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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 eximitral-valve 发表于 2025-3-26 05:35:13
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 发表于 2025-3-26 10:14:26
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 cnonradioactive 发表于 2025-3-26 15:29:08
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 发表于 2025-3-26 19:44:49
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.