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September 30, 2019 08:26
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merge_101.ipynb
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| { | |
| "nbformat": 4, | |
| "nbformat_minor": 0, | |
| "metadata": { | |
| "colab": { | |
| "name": "merge_101.ipynb", | |
| "provenance": [], | |
| "collapsed_sections": [], | |
| "include_colab_link": true | |
| }, | |
| "kernelspec": { | |
| "name": "python3", | |
| "display_name": "Python 3" | |
| } | |
| }, | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "view-in-github", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "<a href=\"https://colab.research.google.com/gist/ronfe/5b3de05d938caf247c8f2ed06484362d/merge_101.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "-tz0eePYL8mx", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "# 初中数学与计算机融合课程示例\n", | |
| "\n", | |
| "写给教师：\n", | |
| "\n", | |
| "这门课程试图为初中学生提供数学和编程思想。课程基本以初中数学教学序列为序，将数学思想和方法和算法思维融合在编程教育中。加深学生对自己所学数学知识的理解，同时培养学生的编程技能。\n", | |
| "\n", | |
| "这门课程以 Python Notebook 为主要呈现形式，单个 Notebook 设置了讲解和练习环节，讲解环节注重启发式教学，重视激发学生学习兴趣和思考，同时将编程知识和基本编程思想有机结合到讲解环节中。练习环节提供了必要的练习，本课程认为数学和编程均需要通过练习而达到精熟掌握，因此教师需要确保学生能够高质量完成 Notebook 中的练习，同时我们鼓励教师根据学生情况设置难度合理又有启发性的练习方式。\n", | |
| "\n", | |
| "我们推荐一个 Notebook 的完成时间在 45-60 分钟，尽管教材内容已经考虑到学生自学需求，每一个 Notebook 都可以由学生自学完成，但是我们仍建议教师进行必要的讲解，以及及时对学生给予反馈，同时对学生遇到的困难提供帮助。\n", | |
| "\n", | |
| "本课题目为 “加法的意义”。主要面向已经学习过如下内容的七年级学生：\n", | |
| "* 正数和负数\n", | |
| "* 有理数的加法\n", | |
| "\n", | |
| "在本课中，我们着力向学生展示**应将加法理解成一个动态过程**，而不是静态的求总加和。这个思路对之后学生学习如函数、方程乃至在解析几何中计算向量的和差时非常有用。教师在教学过程中应着重强调这一点。\n", | |
| "\n", | |
| "此外，由于七年级学生抽象思维较弱，我们在展示时使用了数轴进行形象化，通过“小圆点的旅程”将动态过程具体展现出来，一方面有利于学生理解加法的实质，另一方面也帮助学生复习数轴及其要素等内容。\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "vAHijafCRVrL", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "\n", | |
| "## 1-1 加法的意义\n", | |
| "\n", | |
| "\n", | |
| "小学一年级时我们就学过加法，两个数“相加”的意义似乎是把这两个数“合并”起来——一个苹果“加”一个苹果是两个苹果，三只松鼠“加”五只松鼠等于八只松鼠。然而，在我们学习过《正数与负数》后，“加法”这个看似最简单的数学概念，悄悄发生了变化。" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "7emZ6BFAM29j", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "### 让我们从小时候学到的加法说起，看看怎样让电脑计算加法！\n", | |
| "\n", | |
| "你可能听说过电脑有一个学名叫做“计算机”，这个名字恰如其分地展示了电脑的功能：计算。毕竟“计算机”就是用来计算的机器嘛！ \n", | |
| "\n", | |
| "不错！计算机的主要功能就是“计算”。从这个意义上看电脑只不过比平常使用的计算器更高级一些，复杂一些，但它们本质上是同类的工具。其实我们平时用电脑听音乐、看视频、玩游戏，实际上无一不充满着数字和计算。当你看到这段文字时，就已经身处计算世界之中了！\n", | |
| "\n", | |
| "既然名为计算机，那么加法这么基础和简单的计算当不在话下喽？是的！我们来看看下面的代码：\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "r1ImAf-JMy0v", | |
| "colab_type": "code", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| }, | |
| "outputId": "d7853ac9-30fe-4dce-d2df-30eea7fa1a8d" | |
| }, | |
| "source": [ | |
| "1+1, 3+5, 62+34" | |
| ], | |
| "execution_count": 2, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "(2, 8, 96)" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 2 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "ru5h7JwsPXHn", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "看，让电脑完成加法就是这么简单，只需要**在英文输入法状态下**直接输入想要计算的加法算式，轻敲回车，就可以得到结果了！" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "jV0rfesmRNRk", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "> 有关“括号” \n", | |
| "> 你可能已经注意到了，在上面得到的结果中，电脑为我们添上了一对小括号。在 Python 以及其他编程语言里，各种类型的括号会经常使用到。这里的小括号表示我们的代码输出了一个“元组”类型的数据。你现在可不求甚解，直接忽略它。在之后的课程里，我们会渐渐领略到这些括号的价值。" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "6gxGum2RSgW7", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "那么在下面的代码方框里亲自试试吧！请尝试用 Python 算出\n", | |
| "1. 4+6 \n", | |
| "2. 168+65\n", | |
| "3. 666+666666\n", | |
| "4. 0.1+0.925\n", | |
| "5. 12+123+1234" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "_rzTAib-SefV", | |
| "colab_type": "code", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| }, | |
| "outputId": "3883be91-9737-4442-d248-b98c2677c763" | |
| }, | |
| "source": [ | |
| "## 这里给出了第一题的例子\n", | |
| "4+6" | |
| ], | |
| "execution_count": 3, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "10" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 3 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "qCHw0BRUTpxm", | |
| "colab_type": "code", | |
| "colab": {} | |
| }, | |
| "source": [ | |
| "## 在这里把其他的算式计算出来吧！按 Shift + 回车提交" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "XwlxBHZcT7cM", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "### 两个数相加的和一定比这两个加数都大吗？\n", | |
| "\n", | |
| "在小学课堂上，我们学到的加法似乎有这样一个规律：两个数相加得到的和一定比这两个数都大。例如 1+2=3，3>1 并且 3>2；3+5=8，8>3 并且 8>5。可是，这个规律是否真的成立呢？加法的结果一定比加数还大吗？\n", | |
| "\n", | |
| "或许你已经想到了，这个规律并不一定真的成立，比如当一个数加上零时，得到的结果并不一定比这两个加数都大。来看下面的代码：" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "LY8_-nmrT1bc", | |
| "colab_type": "code", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| }, | |
| "outputId": "1b4381df-637f-4ec1-a760-cadb3dd3a731" | |
| }, | |
| "source": [ | |
| "a = 2+0\n", | |
| "a > 2" | |
| ], | |
| "execution_count": 11, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "False" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 11 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "CYcI0YHFVimp", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "这里我们使用了字母 \"a\" 来表示 2+0 的和，所以 a 的值就是 2 了。在编程语言中，我们曾学过的“用字母表示数” 就可以通过类似第一行的方式来完成，把一个字母放在等号的左边，再把这个字母要表示的数放到等号的右边即可。\n", | |
| "\n", | |
| "请注意哦，这里的“等号”并不表示相等的意思，它表示的是 “a” 这个字母 ***代表*** 了 2+0 的和。大多数编程语言使用 “==” （ ***两个等号*** ）表示相等的概念。" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "NApy7WZ6Y1l5", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "按照刚刚的规律，这里的 a 就应比 2 和 0 都大。果真如此吗？我们可以验证一下。\n", | |
| "\n", | |
| "在第 2 行中，我们用 `a > 2` 来验证，这一行的意思相当于 “`a>2?`“。用人话说，就是“魔镜魔镜告诉我，a>2 是真的吗？”，这时“魔镜”返回了一个 `False`。你可以查一查英语词典，或者搜一搜，False 是什么意思呢？\n", | |
| "\n", | |
| "不错， \"False\" 的意思就是 “假”，a 并不大于 2。但如果如果答案是“真”，魔镜又会返回什么呢？这个简单，我们可以用 a>0 来验证一下：" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "TId-yymdVaIZ", | |
| "colab_type": "code", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| }, | |
| "outputId": "95aa32fe-e501-43e7-c605-aee3caff72e1" | |
| }, | |
| "source": [ | |
| "a > 0" | |
| ], | |
| "execution_count": 12, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "True" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 12 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "8LTkFthYY8oX", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "这一次“魔镜”返回了另一个英文单词 —— True，也就是说，当一句话或一句描述是正确时，魔镜就会输出 True；如果这句话是错误的，就会输出 False。\n", | |
| "\n", | |
| "所以，我们可以让电脑去做判断题，做法很简单，只需要把要电脑判断的问题写出来即可，不需要加语言描述和问号。因为心照，所以不宣。" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "xQCANTCDZybr", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "同时，我们也证明了小学时得到的 “加法的和一定大于两个加数” 这个结论是 False 的。既然加法的和不一定大于两个加数，那么加法到底是怎样的一种运算呢？别着急，接下来就告诉你！" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "vVxu7dhmbbQM", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "### “加法”是一次旅程\n", | |
| "\n", | |
| "加法是一个“点”的旅程记录，而数轴就是这旅程的地图。让我们就从这张地图开始讲起。\n", | |
| "\n", | |
| "下面是一个包含 -9 到 9 的数轴。加法可以看作是一个点从原点出发的旅程。在正方向是右的情况下，加一个正数可以看成这个点向右边走，加一个负数当然可以看成这个点向左边走。" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "AIsWC68_Y6Kh", | |
| "colab_type": "code", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 211 | |
| }, | |
| "outputId": "7157fc27-b2ab-4c08-d6e8-2dc42f44ab94" | |
| }, | |
| "source": [ | |
| "### TODO: 将这些功能代码移动到脚本里，这里只 import 对应方法\n", | |
| "from matplotlib import pyplot as plt\n", | |
| "import numpy as np\n", | |
| "\n", | |
| "plt.figure(figsize=(10,3))\n", | |
| "a = [1,2,5,6,9,11,15,17,18]\n", | |
| "\n", | |
| "# plt.hlines(1,1,21) # Draw a horizontal line\n", | |
| "plt.arrow(0,1,20,0, fc='k', ec='k', length_includes_head=True, head_length=0.5, head_width=0.1)\n", | |
| "\n", | |
| "plt.eventplot(a, orientation='horizontal', colors='black', linelength=0)\n", | |
| "plt.scatter(10, 1, s=30, color='black', marker=2)\n", | |
| "for i in range(-9,10):\n", | |
| " xi = i+10\n", | |
| " plt.scatter(xi, 1, s=30, color='black', marker=2)\n", | |
| " plt.annotate(str(i), (xi-0.15,0.85))\n", | |
| "\n", | |
| "plt.axis('off')\n", | |
| "plt.show()" | |
| ], | |
| "execution_count": 125, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
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| "text/plain": [ | |
| "<Figure size 720x216 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "mWMQlItY4a5m", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "例如 “3+5”，就是一个点第一天从原点出发，向右边走了3个单位，到达了第3点的位置；第二天再从第3点出发，向右边走了5个单位。如下图所示：" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "ffU6slu8cWj-", | |
| "colab_type": "code", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 211 | |
| }, | |
| "outputId": "f3e5e5fc-3025-4b0f-bc5b-a74cc987bb82" | |
| }, | |
| "source": [ | |
| "from matplotlib.font_manager import FontProperties\n", | |
| "\n", | |
| "font_path = '/usr/share/fonts/truetype/NotoSansCJKsc-Medium.otf'\n", | |
| "ChineseFont = FontProperties(fname=font_path)\n", | |
| "\n", | |
| "plt.figure(figsize=(10,3))\n", | |
| "a = [1,2,5,6,9,11,15,17,18]\n", | |
| "\n", | |
| "# plt.hlines(1,1,21) # Draw a horizontal line\n", | |
| "plt.arrow(0,1,20,0, fc='k', ec='k', length_includes_head=True, head_length=0.5, head_width=0.1)\n", | |
| "\n", | |
| "## TODO: 箭头形状\n", | |
| "plt.eventplot(a, orientation='horizontal', colors='black', linelength=0)\n", | |
| "plt.scatter(10, 1, s=30, color='black', marker=2)\n", | |
| "for i in range(-9,10):\n", | |
| " xi = i+10\n", | |
| " plt.scatter(xi, 1, s=30, color='black', marker=2)\n", | |
| " plt.annotate(str(i), (xi-0.15,0.85))\n", | |
| "\n", | |
| "plt.scatter(10,1,s=80,color='red')\n", | |
| "plt.arrow(10,1,3,0, fc='b', ec='b', length_includes_head=True, head_width=0.1)\n", | |
| "plt.annotate('向右移动3个单位，\\n 到达3。', (10,0.5), fontproperties=ChineseFont)\n", | |
| "\n", | |
| "plt.scatter(13,1,s=80,color='red')\n", | |
| "plt.arrow(13,1,5,0, fc='orange', ec='orange', length_includes_head=True, head_width=0.1)\n", | |
| "plt.annotate('再向右移动5个单位，\\n 到达8。', (13.5,0.5), fontproperties=ChineseFont)\n", | |
| "\n", | |
| "plt.scatter(18,1,s=80,color='red')\n", | |
| "\n", | |
| "plt.axis('off')\n", | |
| "plt.show()" | |
| ], | |
| "execution_count": 143, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "image/png": 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| |
| "text/plain": [ | |
| "<Figure size 720x216 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "QEeh3o5f8qkg", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "类似地，“3+(-5)” 就可以看成是这个点第一天从原点出发，向右进发 3 个单位，到达位置 3；第二天再从位置 3 出发，向左走了 5 个单位，到达位置 -5。如下图：" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "QK1-3bp57kFu", | |
| "colab_type": "code", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 211 | |
| }, | |
| "outputId": "157e5f6b-1601-47ea-c6fa-e8e0e9c74ebd" | |
| }, | |
| "source": [ | |
| "from matplotlib.font_manager import FontProperties\n", | |
| "\n", | |
| "font_path = '/usr/share/fonts/truetype/NotoSansCJKsc-Medium.otf'\n", | |
| "ChineseFont = FontProperties(fname=font_path)\n", | |
| "\n", | |
| "plt.figure(figsize=(10,3))\n", | |
| "a = [1,2,5,6,9,11,15,17,18]\n", | |
| "\n", | |
| "# plt.hlines(1,1,21) # Draw a horizontal line\n", | |
| "plt.arrow(0,1,20,0, fc='k', ec='k', length_includes_head=True, head_length=0.5, head_width=0.1)\n", | |
| "\n", | |
| "plt.eventplot(a, orientation='horizontal', colors='black', linelength=0)\n", | |
| "plt.scatter(10, 1, s=30, color='black', marker=2)\n", | |
| "for i in range(-9,10):\n", | |
| " xi = i+10\n", | |
| " plt.scatter(xi, 1, s=30, color='black', marker=2)\n", | |
| " plt.annotate(str(i), (xi-0.15,0.85))\n", | |
| "\n", | |
| "plt.scatter(10,1,s=80,color='red')\n", | |
| "plt.arrow(10,1,3,0, fc='b', ec='b', length_includes_head=True, head_width=0.1)\n", | |
| "plt.annotate('向右移动3个单位，\\n 到达3。', (10,0.5), fontproperties=ChineseFont)\n", | |
| "\n", | |
| "plt.scatter(13,1,s=80,color='red')\n", | |
| "plt.arrow(13,1.2,-5,0, fc='orange', ec='orange', length_includes_head=True, head_width=0.1)\n", | |
| "plt.annotate('再向左移动5个单位，\\n 到达-2。', (9,1.3), fontproperties=ChineseFont)\n", | |
| "\n", | |
| "plt.scatter(8,1,s=80,color='red')\n", | |
| "\n", | |
| "plt.axis('off')\n", | |
| "plt.show()" | |
| ], | |
| "execution_count": 146, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "image/png": 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3XO9I4KR6f0XgUWBcl9r6buDnLddYltL1+Zr69UpdaNd2wIVd/rkZDfwcuAjYo+Va45l/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\neAAAAABJRU5ErkJggg==\n", | |
| "text/plain": [ | |
| "<Figure size 720x216 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "NyqHZQ8c_HQ_", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "接下来，请你来设计一条路径，在我们的数轴范围内，让小圆点从原点出发， **经过 3 天的旅程到达位置 -3**，下面给出了一个范例：" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "OrmxSwkYCe6q", | |
| "colab_type": "code", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 276 | |
| }, | |
| "outputId": "cdab126f-1645-47bc-8927-defcdfe0c46a" | |
| }, | |
| "source": [ | |
| "\n", | |
| "def dot_travel(steps):\n", | |
| " x = 0\n", | |
| " formula = list()\n", | |
| " font_path = '/usr/share/fonts/truetype/NotoSansCJKsc-Medium.otf'\n", | |
| " ChineseFont = FontProperties(fname=font_path)\n", | |
| "\n", | |
| " plt.figure(figsize=(10,3))\n", | |
| " a = [1,2,5,6,9,11,15,17,18]\n", | |
| "\n", | |
| " # Draw axis\n", | |
| " plt.arrow(0,1,20,0, fc='k', ec='k', length_includes_head=True, head_length=0.5, head_width=0.1)\n", | |
| " plt.eventplot(a, orientation='horizontal', colors='black', linelength=0)\n", | |
| " plt.scatter(10, 1, s=30, color='black', marker=2)\n", | |
| " for i in range(-9,10):\n", | |
| " xi = i+10\n", | |
| " plt.scatter(xi, 1, s=30, color='black', marker=2)\n", | |
| " plt.annotate(str(i), (xi-0.15,0.85))\n", | |
| "\n", | |
| "\n", | |
| " plt.scatter(10,1,s=80,color='red')\n", | |
| " offset = 1.\n", | |
| " for direction, unit in steps:\n", | |
| " vector = unit\n", | |
| " dir_label = '右'\n", | |
| " if direction == 'L':\n", | |
| " vector *= -1\n", | |
| " dir_label = '左'\n", | |
| " formula.append(\"({})\".format(vector))\n", | |
| " else:\n", | |
| " formula.append(str(vector))\n", | |
| "\n", | |
| " \n", | |
| " plt.arrow(10+x,offset,vector,0, fc='b', ec='b', length_includes_head=True, head_width=0.1)\n", | |
| " \n", | |
| " offset += 0.2\n", | |
| " x += vector\n", | |
| "\n", | |
| " t = x + 5.5\n", | |
| " if direction == 'L':\n", | |
| " t = x + 10\n", | |
| " plt.annotate('向{}移动{}个单位，\\n 到达{}。'.format(dir_label, unit, x), (t,offset), fontproperties=ChineseFont)\n", | |
| " \n", | |
| " plt.scatter(10+x,1,s=80,color='red')\n", | |
| " offset += 0.1\n", | |
| "\n", | |
| " plt.axis('off')\n", | |
| " plt.show()\n", | |
| " formula = \" + \".join(formula)\n", | |
| " return \"{} = {}\".format(formula, x)\n", | |
| "\n", | |
| "\n", | |
| "### 范例\n", | |
| "steps = [\n", | |
| " (\"R\", 5), # 第一天，先向右（R）移动 5 个单位\n", | |
| " (\"L\", 6), # 第二天，再向左（L）移动 6 个单位\n", | |
| " (\"L\", 2), # 第三天，再向左（L）移动 1 个单位\n", | |
| "]\n", | |
| "\n", | |
| "print(dot_travel(steps))" | |
| ], | |
| "execution_count": 192, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "/usr/local/lib/python3.6/dist-packages/matplotlib/figure.py:2369: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n", | |
| " warnings.warn(\"This figure includes Axes that are not compatible \"\n" | |
| ], | |
| "name": "stderr" | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
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20tBQ41gdWD0zp0Sp0f4jsGenr0mdqWtYZj4dEYMoNY6HZebvOhlHI54jgK2B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\nyJIkSVLD/wOFVv4qi2x8EQAAAABJRU5ErkJggg==\n", | |
| "text/plain": [ | |
| "<Figure size 720x216 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| } | |
| }, | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "5 + (-6) + (-2) = -3\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "pgBGAWzrKCKX", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "在上面的代码中，我们首先写了一个 **列表**，并给它起名叫做 “`steps`”。Python 中可以通过一对中括号来制造一个列表，在列表中我们可以**按顺序地放置任何我们想放的东西**，例如在这个列表中，我们就放置了这三点的旅程计划。\n", | |
| "\n", | |
| "在 `steps` 里，我们又生成了三个小列表，每个小列表中又先放置了小圆点的移动方向（向左为 \"L\" （英文 Left），向右为 \"R\" （英文为 Right）），再放置移动的长度。这样，一个完整的旅行计划就写好啦！\n", | |
| "\n", | |
| "最后，我们把 `steps`放到 `dot_travel` 这个函数（在数学和编程中，函数的概念都非常重要，有关“数学的函数”以及“编程的函数”会在八年级的课程中学习到）里，就可以看到地图啦！\n", | |
| "\n", | |
| "现在该你了！请再设计一条路径，能够让小圆点从原点出发， 经过 3 天的旅程到达位置 -3。" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "7-SOKKF3MmDm", | |
| "colab_type": "code", | |
| "colab": {} | |
| }, | |
| "source": [ | |
| "### 在这里补充 steps 的内容\n", | |
| "### 使得小圆点可以通过三天的时间从原点到达 -3 点\n", | |
| "\n", | |
| "### 补充时请注意观察范例代码中列表的格式细节哟\n", | |
| "steps = \n", | |
| "\n", | |
| "print(dot_travel(steps))" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "v0nptLOtBWUQ", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "### 旅行的意义" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "V9xcG9qUBox1", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "这样看来，两个数的 “和”就可以看作是这个小红点经过多日的旅行后，最终到达的位置。\n", | |
| "\n", | |
| "把加法理解成旅行有什么好处？旅行的意义是什么呢？我们通过一道题目来感受一番。\n", | |
| "\n", | |
| "（未完待续）" | |
| ] | |
| } | |
| ] | |
| } |
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