共查询到19条相似文献,搜索用时 46 毫秒
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通过有心二次曲线的性质,说明了文[1]中一些错误的结论.运用有心二次曲线切线的性质,以及有心二次曲面切面的性质,得到了有心二次曲线和有心二次曲面的包络形成法. 相似文献
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通过对二次曲面方程配方变形,根据直线与二次曲面相交时参数t的几何意义,以及仿射变换的性质,得到了二次曲面方程分类与化简的一种新方法,从而解决了利用坐标系的平移、旋转、不变量对二次曲面方程进行分类、化简时运算复杂或者无法确定图形具体位置等问题. 相似文献
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在一般解析几何课本中讨论和绘制二次曲面的图形,都是采用“平行截线法”,即是用平行于坐标平面的平面去截二次曲面,得到平截线,这样的平截线是二次曲线,画出一些这样的二次曲线及二次曲面的轮廓线,即得所要求作的二次曲面的近似形象的方法。但是为什么和怎样把它们画成那个样子?其作图原理是什么? 解析几何课本中的二次曲面,如中学立体几何课本中的直观图一样,都是根据轴测投影的原理来画的。在学习数学中,经常要画直观图。我们知道,正确的直观图能明显地表示出空间形体的几何关系。通过直观图的直观作用,对原有空间形体产生了清楚的观念,这样有助于对图形性质的理解,从而使我们在进行定理论证或习题解答时的逻辑推理导向正确的途径。在数学教学工作中,也经常要画黑板图和直观挂图。成功 相似文献
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针对平面与二次曲面相切的条件。根据二次曲面标准方程的五种分类.利用二次曲面上点的切平面的唯一性.给出任一平面与五类二次曲面相切的充要条件,得到一组相关推论,并给出一些应用实例. 相似文献
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在二次曲面中,唯有单叶双曲面和双曲抛物面是直纹面。这两种直纹面都有两族直母线(u族和v族),两族直母线有很多有益的性质,掌握这些有益的性质并运用这些性质便可在两个曲面上将这些直母线一条一条地作出来,这 相似文献
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《数学的实践与认识》2013,(9)
直纹二次曲面中有两种性质独特的曲面:单叶双曲面和双曲抛物面,它们在现实生活中多个领域都有特殊的用途.从理论角度对单叶双曲面和双曲抛物面在建筑、机械以及水利工程中的典型应用给予详细总结和分析,并结合它们自身的数学性质对其实际应用效果给予评析. 相似文献
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<正> 在工科“高等数学”教材中,二次曲面的形状一般都是用截痕法进行研究的,即用一系列平行平面截已知二次曲面所得的截线来确定二次曲面的形状,利用截痕法画二次曲面时, 相似文献
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Zane Kun Li 《Journal of Pure and Applied Algebra》2010,214(11):2078-2086
The intersection curve between two surfaces in three-dimensional real projective space RP3 is important in the study of computer graphics and solid modelling. However, much of the past work has been directed towards the intersection of two quadric surfaces. In this paper we study the intersection curve between a quadric and a cubic surface and its projection onto the plane at infinity. Formulas for the plane and space curves are given for the intersection of a quadric and a cubic surface. A family of cubic surfaces that give the same space curve when we intersect them with a quadric surface is found. By generalizing the methods in Wang et al. (2002) [6] that are used to parametrize the space curve between two quadric surfaces, we give a parametrization for the intersection curve between a quadric and a cubic surface when the intersection has a singularity of order 3. 相似文献
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E. N. Shananina 《Mathematical Notes》2000,67(3):382-388
Models similar to the tangent quadric are constructed for surfaces with one-dimensional complex tangent space. It is shown
that these models possess the main properties of the tangent quadric. Their groups and algebras of automorphisms are found.
Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 452–459, March, 2000. 相似文献
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在解析几何中有二次曲线与直线位置关系的讨论、二次曲面与直线位置关系的讨论,而二次曲面与平面相关位置关系的探讨较少.本文给出二次曲面a11x2+a22y2+a33z2+2a12xy+2a13xz+2a23yz+2a14x+2a24y+2a34z+a44=0(1)和平面Ax+By+Cz+D=0(2)的相对位置的判别式Δ=a11a12a13a14Aa21a22a23a24Ba31a32a33a34Ca41a42a43a44DA B C D0(aij=aji).(3)并证明了:若Δ>0,则二次曲面(1)与平面(2)相交;若Δ=0,则(1)和(2)相切;若Δ<0,则(1)和(2)相离. 相似文献
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In Hirschfeld and Thas [5] the most important
characterizations of quadric Veroneseans are surveyed. However a few
difficult cases were still open, in particular the even case. In [10, 11]
Thas and Van Maldeghem not only solve all open cases, but they also
generalize most of these characterizations in several ways: they do not
restrict themselves to the quadric Veronesean of the plane PG,
they allow ovals instead of conics, and they also characterize
projections of quadric Veroneseans. Further, Cooperstein, Thas and Van
Maldeghem [1] contains some properties of Hermitian Veroneseans over
finite fields and also these varieties and some of their projections are
characterized. All these results on Veroneseans will be surveyed here. 相似文献
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We give the parameters of any evaluation code on a smooth quadric surface. For hyperbolic quadrics the approach uses elementary results on product codes and the parameters of codes on elliptic quadrics are obtained by detecting a BCH structure on these codes and using the BCH bound. The elliptic quadric is a twist of the surface P 1 × P 1 and we detect a similar BCH structure on twists of the Segre embedding of a product of any d copies of the projective line. 相似文献
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The parity operator P and time reversal operator T are two important operators in the quantum theory, in particular, in the PT-symmetric quantum theory. By using the concrete forms of P and T, we discuss their geometrical properties in two dimensional spaces. It is showed that if T is given, then all P links with the quadric surfaces; if P is given, then all T links with the quadric curves. Moreover, we give out the generalized unbroken PT-symmetric condition of an operator. The unbroken PT-symmetry of a Hermitian operator is also showed in this way. 相似文献