章节大纲

  • How Translations Make Life Easier
    ::翻译如何让生活更加容易

    Translations are used by professionals across a wide range of fields. This type of rigid motion is often used in computer programs to complete tasks more efficiently, thereby save memory and allow computers to run faster. It takes less work for a computer to translate an existing shape to new locations than to create different shapes for each location.
    ::翻译被专业人员在广泛的领域使用。这种僵硬运动常常用于计算机程序,以便更有效地完成任务,从而保存记忆并使计算机运行速度更快。计算机将现有形状翻译到新地点比为每个地点创建不同的形状要少。

    An example of  using translations is in crowd design for video games.  It can be a true challenge for  a gaming system to display a crowd of perhaps  thousands of people in a realistic-looking way for a sports game, without running too slowly.  To solve this problem, many games use a smaller set of characters who have been translated to many different locations at once (sometimes they are altered slightly to make the duplicates less obvious). This allows the player to enjoy a realistic looking crowd without experiencing delays in performance.
    ::使用翻译的一个例子是视频游戏的人群设计。游戏系统要以现实的、看得见的方式展示成千上万人,以现实的方式展示一场体育比赛,而不会太慢,这可能是个真正的挑战。为了解决这个问题,许多游戏使用的是一组较小的字符,这些字符一次被翻译到许多不同的地点(有时会稍作改动,使复制的变得不那么明显 ) 。 这让玩家能够享受到一个现实的、看得见的人群,而不会在表现上出现延误。

    Scene from computer football game showing repeated pictures of the same person throughout the crowd
    Translated and repeated crowd members in Football video game.

     

    Corresponding  Sides and Angles
    ::对应的侧边和角

    When you investigate   a rigid motion   transformation, it is important to be able to identify corresponding sides and .   Corresponding sides are matching sides of two different shapes.  When dealing with rigid motion transformations, think of corresponding sides as a side on the original shape and the same side on the translated, reflected, or rotated shape. Similar to corresponding sides,  corresponding  angles are matching angles in two different shapes.
    ::当您调查僵硬的动作变换时,必须能够辨别对应的侧面和。对应的侧面是两种不同形状的对齐面。在处理僵硬的动作变换时,将对应的侧面视为原始形状的侧面,翻译、反射或旋转形状的同一侧。与对应的侧面相似,对应的角度是两种不同形状的对齐角度。

    Use the interactive below to match   corresponding   sides and corresponding angles.
    ::使用下面的交互效果来匹配相应的边和相应的角度。

     

     

    Discussion Question
    ::讨论问题

    If two sides are corresponding (like  B A ¯  on the purple triangle corresponds to the left side of the orange triangle), does that mean that  B A ¯  is not the same length as the right side or the base of the orange triangle?
    ::如果两边是对应的(紫色三角的BA和橙色三角的左侧是对应的),这是否意味着BA与右侧或橙色三角的底部的长度不同?

    Practice identifying corresponding sides and angles in the interactive below:
    ::确定以下互动互动中相应侧面和角度的做法:

     

     

     

    Trapezoidal  Translation
    ::剖形翻译

    Previously, you have learned that  translations  move an image a certain distance in a specific direction without changing the size or shape of the image. Every point of the image is moved the same distance and in the same direction. How can  you be sure that the size or shape of the image hasn't been changed? Use   the interactive below to examine whether the corresponding side lengths and angles of both shapes are equal .
    ::之前, 您已经学会了翻译将图像移动到特定方向而不改变图像的大小或形状。 图像的每个点都移动同样的距离和方向。 您如何确定图像的大小或形状没有改变 ? 使用下面的交互功能来检查两种形状的对应侧边长度和角度是否相等 。

     

     

     

     

    Discussion Questions
    ::讨论问题 讨论问题

    1. Is it possible two pictures could look the same size but not be the same size?
      ::可能两张相片看起来一样大小 却不一样大小吗?
    2. What tools could you use to measure the side lengths and angles of a shape? Which one(s) would you prefer to use and why?
      ::您可使用什么工具来测量形状的侧边长度和角度? 您希望使用哪种工具, 为什么使用 ?

    Deeper Exploration: Vectors
    ::深海勘探:矢量

    Do you think that it is possible to translate an object a negative direction ? How do you think it would affect the movement of the image?
    ::您是否认为可以将对象转换为负面方向? 您认为它会如何影响图像移动 ?

    A negative  direction would move the image the same distance in the opposite direction. This is common in robotics and animations where  an object needs to move backward without changing directions . This ties into vectors, which are a fascinating subject you can explore using the robot-based CK-12 Simulation below.
    ::负方向会将图像向相反方向移动相同的距离。 在机器人和动画中, 物体需要向后移动而不改变方向, 这一点很常见 。 此连接到矢量中, 您可以在下面使用基于机器人的 CK-12 模拟来探索 。

     

     

     

    T-Shirt Tessellation
    ::T-Shirt 发射

    is a form of pattern art which uses translations to create complicated designs. A tessellation is created within a grid of shapes, called tiles, which leave no empty space between them. When a change is made to one side of a shape it is translated across all the other shapes , this  ensures that there will be no empty space in the design. Tessellation art dates back to as far as 4,000 BCE, whe n ancient Sumerians would make these designs on cave walls.  This style of  art has appeared across cultures and more recently has been popularized by artists like M.C. Escher. You can likely even  find examples of tessellation art in your house! In addition to being used in graphic design, tessellations are used across many professions including fashion design, interior decorating, product design, and much more.
    ::是一种模式艺术形式, 它使用翻译来创造复杂的设计。 一种通缩艺术是在一个形状网格内创建的, 叫做瓷砖, 它在它们之间没有空空的空间。 当一个形状的一面被改变到一个形状的一面时, 它会被翻译到所有其他形状, 这样可以确保设计中没有空空间。 催泪艺术可以追溯到4000个 BCE, 当古代苏美人可以在洞穴墙上做这些设计的时候。 这种艺术风格已经出现在各种文化中, 最近被像 M. C. Esher 这样的艺术家所欢迎。 您甚至可以在家中找到熔化艺术的例子 。 除了在图形设计中使用外, 其它许多行业都使用星系, 包括时装设计、 内部装饰、 产品设计等等。

    lesson content
    Tessellation by M. C. Escher (left) and from an ancient temple (right)

    You have been tasked with creating a new design to go on dresses, shirts, and backpacks. Use the interactive below to create your own unique tessellation.  
    ::您已被赋予创建新设计的任务, 设计您可以上衣、 衬衫和背包。 使用下面的交互操作来创建您自己独特的套接层 。

     

     

     

    Tessellated Drawings
    ::蒸发绘图

    Until the 1990's,  tessellations  had to be drawn by hand. What are some strategies you could you use draw these patterns without electronics ?
    ::20世纪90年代之前,必须用手来绘制星系。您可以用什么策略来绘制这些图案,而不用电子仪器?

    • Can you duplicate by hand the tessellation you created with the interactive?
      ::您能亲手复制您用交互程序创建的熔融吗 ?
    • Start with a square and redraw the sides similarly to the way they were changed in the interactive. Then cut out the modified shape and trace the image repeatedly in all directions on a piece of paper.
      ::以一个正方形开始, 重新绘制两边, 和互动中改变它们的方式相似。 然后切除修改后的形状, 在一张纸上从各个方向反复追踪图像 。
    • Are there advantages to doing this by hand? What are the disadvantages?
      ::手工这样做是否有好处? 缺点是什么?
    lesson content
    Tessellations

    Discussion Question
    ::讨论问题

    Which shape is being tessellated, the fish or the bird? How do you think the artist was able to tessellate something as complex as two different animals?
    ::哪种形状是连接的, 鱼还是鸟?你认为艺术家是如何 将像两种不同的动物一样复杂的东西 捆绑起来的?

      Summary
    • Translations move an image a certain distance in a specific direction without changing the size or shape of the image
      ::翻译在特定方向移动一定距离的图像,而不改变图像的大小或形状
    • If a shape has gone through a rigid transformation the corresponding sides will be equal and the corresponding angles will be equal. 
      ::如果一个形状经历了僵硬的转变,对应的两面将是相等的,相应的角度将是相等的。
    • A tessellation is a design with shapes/polygons in a repeated pattern without gaps or overlaps.
      ::系合物是一种设计,其形状/多边形的形状/多边形反复出现,没有空白或重叠。