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A simple geometrical model describing shapes of soap films suspended on two rings

机译:描述悬挂在两个环上的肥皂膜形状的简单几何模型

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We measured and analysed the stability of two types of soap films suspended on two rings using the simple conical frusta-based model, where we use common definition of conical frustum as a portion of a cone that lies between two parallel planes cutting it. Using frusta-based we reproduced very wellknown results for catenoid surfaces with and without a central disk. We present for the first time a simple conical frusta based spreadsheet model of the soap surface. This very simple, elementary, geometrical model produces results surprisingly well matching the experimental data and known exact analytical solutions. The experiment and the spreadsheet model can be used as a powerful teaching tool for pre-calculus and geometry students.
机译:我们使用简单的基于视锥圆锥体的模型测量并分析了两种类型的肥皂膜的稳定性,该膜悬挂在两个环上,在该模型中,我们使用视锥圆锥体的普通定义作为位于两个平行平面之间的圆锥部分。使用基于视锥面的方法,我们可以得出带有或不带有中心盘的链状表面的非常著名的结果。我们首次展示了基于简单圆锥形视锥的肥皂表面电子表格模型。这个非常简单的基本几何模型产生的结果出奇地与实验数据和已知的精确分析解决方案完全匹配。实验和电子表格模型可以用作微积分和几何预科学生的强大教学工具。

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