章节大纲

  • In T his Lesson
    ::在本课程中

    You will  learn about pyramids and their cross sections.  A   pyramid  is a polyhedron that only has one base. All of the lateral faces meet at a vertex at the top of the pyramid. The height of a pyramid is the   line segment from  the top vertex to the base such that  it is   perpendicular to the base.   Pyramids also have a  slant height ,  which is the height of any of the lateral faces. Depending on the base, the  lateral  faces may or may not all be congruent .
    ::您将了解金字塔及其交叉区块。 金字塔是一个只有一个基数的多面体。 所有平面面面面部都聚集在金字塔顶部的顶端的顶端。 金字塔的高度是从顶端的顶端到底部的线段,因此与底部垂直。金字塔也有倾斜高度,即横向面部的高度。根据底部,横向面面部可能或不可能完全吻合。

    A right rectangular pyramid with labels for slant height and height.
    Slant height vs. height

    The pyramid  above is a   right rectangular pyramid   because the base is a rectangle . Pyramids are always named after their bases. For the pyramid to be considered "right," the height must hit the center of the base.
    ::上方的金字塔是一个右方矩形金字塔, 因为基座是一个矩形。 金字塔总是以其底座命名。 要将金字塔视为“ 正确 ” , 高度必须击中基座的中心 。

     

    Pyramid Ninja
    ::金字塔宁加

    How many different ways could you intersect a plane with a rectangular pyramid ? Use this interactive to view the prism and slice it with planes that are perpendicular and parallel to the base. Try to form a square , triangle , and trapezoid cross section .
    ::您可以用多少种不同的方式将平面与矩形金字塔相交叉? 使用此互动来查看棱镜, 并用垂直和与底部平行的平面将其切除。 尝试形成一个正方形、 三角形和三角形交叉段 。

     

     

    INTERACTIVE
    Cross Section of Pyramids
    minimize icon
    • Move the sliders to see how the shape within the pyramid changes.
      ::移动滑动器以查看金字塔内的形状如何变化 。
    • Drag the screen to change the view.
      ::拖曳屏幕以更改视图。
    Your device seems to be offline.
    Please check your internet connection and try again.
    +
    Do you want to reset the PLIX?
    Yes
    No

     

     

     

     

     

     

     

    Pyramid Ninja, P art 2
    ::金字塔宁贾,第2部分

    How many different ways could you intersect a plane with a triangular pyramid? Use this interactive to view the prism and slice it with the plane. Try to form a rectangle, trapezoid, triangle, and cross section.
    ::您可以用多少种不同的方式将平面与三角金字塔相交叉? 使用此互动方式查看棱镜, 并用平面切开。 尝试形成矩形、 三角形、 三角形和横截段 。

     

     

    INTERACTIVE
    Cross Sections of Pyramids Part 2
    minimize icon
    • Move the first two sliders on the left to move the plane around.
      ::左侧前两个滑动滑动器 将平面转动
    • Move the rotation sliders to rotate the plane around the two axes.
      ::移动旋转滑动滑动器,在两个轴周围旋转平面。
    • Move the opacity slider to change the opacity of the pyramid faces.
      ::移动不透明滑块以改变金字塔面孔的不透明性 。
    • Drag the screen to change your point of view. 
      ::拖曳屏幕以改变您的观点 。
    • Observe how many different types of cross sections can be made.
      ::观察可以作出多少不同类型的跨节。
    Your device seems to be offline.
    Please check your internet connection and try again.
    +
    Do you want to reset the PLIX?
    Yes
    No

     

     

     

     

     

     

    You now  know the  different types of cross sections that a pyramid can have. Next, you will explore the cross sections  of a cone. A cone is like a pyramid but with a circle as the base. Therefore, there is only one lateral face that that unfolds  to a sector (a section of a circle). 
    ::您现在知道金字塔可以拥有不同种类的交叉区块。 接下来, 您将探索锥体的交叉区块。 锥体就像金字塔, 但以圆为基点。 因此, 只有一张横向面孔可以显示到一个区块( 圆的一个区块 ) 。

     

    Cone Ninja
    ::中忍者

    What are the different types of cross sections that a cone  can produce?  Use this interactive to view the   cone  and slice it with the plane. Try to form a  triangle,  circle, and oval cross section.
    ::锥体能够生成的交叉区块的不同类型是什么? 使用此互动方式查看锥体, 并用平面切分。 尝试形成三角形、 圆形和 oval 交叉区块 。

     

     

    INTERACTIVE
    Cone Ninja
    minimize icon
    • Move the first two sliders on the left to move the plane around.
      ::左侧前两个滑动滑动器 将平面转动
    • Move the rotation sliders to rotate the plane around the two axes.
      ::移动旋转滑动滑动器,在两个轴周围旋转平面。
    • Move the opacity slider to change the opacity of the cone.
      ::移动不透明滑动器以改变锥体的不透明性。
    • Use the dropdown menu to see different views.
      ::使用下拉菜单查看不同的视图 。
    • Drag the screen to change your point of view. Use two fingers on your trackpad or touch screen or scroll the mouse wheel to zoom.
      ::拖曳屏幕以改变您的视图点。 在您的跟踪板上使用两根手指或触摸屏幕或滚动鼠标方向盘以缩放 。
    Your device seems to be offline.
    Please check your internet connection and try again.
    +
    Do you want to reset the PLIX?
    Yes
    No

     

     

     

     

     

     

       Summary
    ::摘要

    A pyramid is a polyhedron where the lateral faces are triangles that meet at a point and the base is a polygon. They are always named after the base. 
    ::金字塔是多面形,横向面是在一个点相交的三角形,基是多边形。这些三角形总是以基数命名。

    • A rectangular pyramid can have several different types of cross sections.
      ::矩形金字塔可以有几种不同类型的交叉区块。
    • The cross section  of a pyramid that is perpendicular to the base will be a triangle.
      ::金字塔的横截面与基底垂直,将是一个三角形。
    • T he cross section of a pyramid that is parallel to the base will be a smaller version of the base. 
      ::金字塔的横截面与基底平行,将是基底的较小版本。

    A cone is not considered a pyramid because it has a curved surfaces.
    ::锥体不是金字塔,因为它有弯曲的表面。