In geometry, a torus (pl.: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle. …

A toric section is an intersection of a plane with a torus, just as a conic section is the intersection of a plane with a cone. Special cases have been known since antiquity, and the general case …

1 天前 · The torus surface is implemented in the Wolfram Language as Torus[x, y, z, c-a, c+a], and the solid torus as FilledTorus[x, y, z, c-a, c+a]. The three standard tori are illustrated …

1999年5月26日 · A torus is a surface having Genus 1, and therefore possessing a single ``Hole.'' The usual torus in 3-D space is shaped like a donut, but the concept of the torus is extremely …

In this article we'll present some types of toric sections, including Villarceau's circles, Cassini's ovals, Bernoulli's lemniscates and the Hippopedes of Proclus. We'll then discuss some …

A torus is a fascinating 3D shape that looks like a donut or swim ring. It is created by revolving a smaller circle around a larger one.

对于下图所示的 环面 结构，本文给出其一些常见的几何性质. 首先，我们知道，环面的 参数方程 为： \begin {cases} x\left (u, v\right) = (R_1 + R_2\cos v) \cos u \\ y\left (u, v\right) = (R_1 + …

The torus, a shape as familiar as a donut yet as rich in complexity as the most intricate mathematical concepts, holds a unique place in the study of mathematics. It’s a shape that …

5 天之前 · A toric section is a curve obtained by slicing a torus (generally a horn torus) with a plane. A spiric section is a special case of a toric section in which the slicing plane is …

2020年5月4日 · In this article I’ll discuss some properties of this curve, investigate its differences with the most renowned conic section, show how to build its general quartic equation, explore …