5.4 棱柱交叉区-interactive
Section outline
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In This Lesson
::在本课程中Y ou will investigate 3-dimension al shapes . Recall that a 3- dimensional shape with polygon sides is a polyhedron . Prisms and pyramids are examples of . All the sides of a polyhedron lie on different planes (a plane is a 2- dimensional surface that extends infinitely in all directions) and intersect to form faces , edges and vertices . S pheres and cylinders are not considered polyhedrons because they have curved sides.
::您将调查三维形状。 请注意, 多边多边形的三维形状是一个多面形。 棱柱和金字塔就是例子 。 多面形的两侧都位于不同的平面上( 平面是两维表面, 无限延伸于所有方向) , 交叉形成面、 边缘和脊椎。 球体和圆柱体不被视为多面形, 因为它们的侧面已经弯曲 。The polyhedron above is a right square prism . The prism is "right" because all of the faces are perpendicular or parallel to each other. The two faces of the prism that are squares are called the bases , because they are parallel and the only two square faces. The other four faces are called lateral faces and are all . A right triangular prism would have two triangles as the bases instead of squares, but the lateral faces would still be rectangles.
::上面的一面形是右方形。 棱镜是“ 右方形 ” , 因为所有面孔都是垂直的或平行的。 方形的两面面面被称为基座, 因为它们是平行的, 只有两个平面。 其它四面面面面被称为横向面, 它们都是正方形 。 右三角棱镜将有两个三角形作为基座而不是正方形, 但横向面仍然是矩形 。In this lesson, you are going to be studying cross sections of prisms . A cross section is an intersection of a plane with a three-dimensional figure. They can also be referred to as a "slice" or "plane section."
::在此课中, 您将研究棱晶的交叉部分。 交叉部分是平面与三维图的交叉部分。 它们也可以被称为“ 切片 ” 或“ 平面 ” 。
Prism Slicing
::棱晶切片How many different ways could you intersect a plane with a rectangular prism ? Use this interactive to view the prism and slice it with the plane. Try to create the following cross sections: a rectangle , square, triangle , , pentagon (5 sided 2D figure), and hexagon (6 sided 2D figure).
::您可以用多少种不同的方式将平面与矩形棱柱相交叉? 使用此交互式方式查看棱柱, 并用平面将其切除。 尝试创建以下交叉区域: 矩形、 方形、 三角形、 边形、 五边形( 5 面 2D 图) 和 六边形( 6 面 2D 图) 。INTERACTIVEPrism Slicing-
Drag the slider to change the height of the plane.
::拖动滑块以改变平面的高度。 -
Drag the point to rotate the plane.
::拖动点旋转平面 。 -
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 。 -
Observe how slices from different angles can make different cross sections.
::观察不同角度的切片如何能形成不同的交叉区块。
+Do you want to reset the PLIX?Discussion Question
::讨论问题Would it be just as easy to answer these questions without the interactive? What physical tools could you use? What advantages do 3D computer models provide?
::如果没有互动,回答这些问题是否同样容易?你能使用哪些物理工具?3D计算机模型有什么好处?
Prism Slicing , Part 2
::棱晶切片,第2部分How many different ways could you intersect a plane with a triangular prism? Use this interactive to view the prism and slice it with the plane. Try to create the following cross sections: a rectangle, square, triangle, parallelogram, pentagon (5 sided 2D figure), and hexagon (6 sided 2D figure).
::您可以用多少种不同的方式将平面与三角棱镜相交叉? 使用此交互式方式查看棱镜, 并用平面切开它。 尝试创建以下交叉区域: 矩形、 方形、 三角形、 平行图、 五边形( 5 面 2D 图) 和 六边形( 6 面 2D 图) 。INTERACTIVEPrism Slicing Part 2-
Drag the slider to change the height of the plane.
::拖动滑块以改变平面的高度。 -
Drag the point to rotate the plane.
::拖动点旋转平面 。 -
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 。 -
Observe how slices from different angles can make different cross sections.
::观察不同角度的切片如何能形成不同的交叉区块。
+Do you want to reset the PLIX?You now know the different types of cross sections a prism can have. Next, you will explore the cross sections of a cylinder . A cylinder is similar to a prism, but with circles as bases. Therefore, there is only one lateral face that unfolds to a rectangle (like when you unwrap the label of a soup can).
::您现在知道棱柱可以有不同类型的交叉区块。 接下来, 您将探索圆柱体的交叉区块。 一个圆柱体与棱柱相似, 但圆圈是底部。 因此, 只有一张横向面孔可以显示为矩形( 比如您解开汤汤罐标签时) 。
Cylinder Slicing
::气瓶切碎What are the different types of cross sections that a cylinder can produce? Use this interactive to view the cylinder and slice it with the plane. Try to form a rectangle, circle , and oval cross section.
::圆柱体可以产生哪些不同类型的交叉部分? 使用此互动方式查看圆柱体, 并用平面切分。 尝试形成矩形、 圆形和 oval 交叉部分 。INTERACTIVECylinder Slicing-
Press the buttons to view the cross section made by intersection the plane and the cylinder.
::按下按钮查看平面和圆柱体交叉形成的横截段。 -
Drag the sliders to change the position of the plane.
::拖动滑动器以改变平面的位置。 -
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 。 -
Observe how slices from different angles can make different cross sections.
::观察不同角度的切片如何能形成不同的交叉区块。
+Do you want to reset the PLIX?Summary
::摘要-
A cross section is the intersection of a plane and a three dimensional figure.
::横截面是平面和三维图的交叉点。 -
A rectangular prism can have several different types of cross sections.
::矩形棱镜可以有几种不同类型的交叉区块。 -
If the cross section is perpendicular to the base, it will be the same as the lateral faces (for a rectangular prism).
::如果横截面与底部垂直,则与横向面(矩形棱柱)相同。 -
If the cross section is parallel to the base, it will be the same as the bases (for a rectangular prism).
::如果横段与基点平行,则与基点(矩形棱柱)相同。 -
A cylinder is not considered a prism because it has curved surfaces.
::圆柱体不被视为棱镜,因为它有弯曲的表面。
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Drag the slider to change the height of the plane.
