Surfaces that locally minimize area have been extensively used to model physical phenomena, including soap films, black holes, compound polymers, protein folding, etc. The mathematical field dates to the 1740s but has recently become an area of intense mathematical and scientific study, specifically in the areas of molecular engineering, materials science, and nanotechnology because of their many anticipated applications. In this work, we show that all minimal surfaces are built out of pieces of the surfaces in and .The helicoid is a double spiral staircase given by sweeping out a horizontal line rotating at a constant rate as it moves up a vertical axis at a constant rate. Each half-line traces out a spiral staircase, and together the two half-lines trace out (up to scaling) the double spiral staircase
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机译：局部最小化的表面已被广泛用于模拟物理现象，包括肥皂膜，黑洞，复合聚合物，蛋白质折叠等。数学领域可追溯至1740年代，但最近已成为广泛的数学和科学研究领域，特别是在分子工程，材料科学和纳米技术领域具有广泛的应用前景。在这项工作中，我们证明了所有最小曲面都是由。和..fig ft0-> <！-fig mode = art f1-> <！-标题a7->螺旋线是双螺旋楼梯，它是通过扫掠以恒定速率沿垂直轴移动的恒定速率旋转的水平线而得到的。每条半线画出一个螺旋形楼梯，而两条半线一起画出（最大缩放）双螺旋形楼梯
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