diff --git a/Book4_Ch08_Python_Codes/Bk4_Ch8_01.py b/Book4_Ch08_Python_Codes/Bk4_Ch8_01.py
new file mode 100644
index 0000000..be711ae
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+++ b/Book4_Ch08_Python_Codes/Bk4_Ch8_01.py
@@ -0,0 +1,73 @@
+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch8_01.py
+
+import matplotlib.pyplot as plt 
+import numpy as np
+
+def plot_shape(X,copy = False):
+    if copy:
+        fill_color = np.array([255,236,255])/255
+        edge_color = np.array([255,0,0])/255
+    else:
+        fill_color = np.array([219,238,243])/255
+        edge_color = np.array([0,153,255])/255
+    
+    plt.fill(X[:,0], X[:,1],
+             color = fill_color,
+             edgecolor = edge_color)
+    
+    plt.plot(X[:,0], X[:,1],marker = 'x',
+             markeredgecolor = edge_color*0.5,
+             linestyle = 'None') 
+
+X = np.array([[1,1],
+              [0,-1],
+              [-1,-1],
+              [-1,1]])
+
+# visualizations
+
+fig, ax = plt.subplots()
+
+plot_shape(X)      # plot original
+
+# translation
+t1 = np.array([3,2]);
+Z = X + t1
+plot_shape(Z,True) # plot copy
+
+t2 = np.array([-3,-2]);
+Z = X + t2
+plot_shape(Z,True) # plot copy
+
+t3 = np.array([-2,3]);
+Z = X + t3
+plot_shape(Z,True) # plot copy
+
+t4 = np.array([3,-3]);
+Z = X + t4
+plot_shape(Z,True) # plot copy
+
+# Decorations
+ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
+plt.axis('equal')
+plt.axis('square')
+plt.axhline(y=0, color='k', linewidth = 0.25)
+plt.axvline(x=0, color='k', linewidth = 0.25)
+plt.xticks(np.arange(-5, 6))
+plt.yticks(np.arange(-5, 6))
+ax.set_xlim(-5,5)
+ax.set_ylim(-5,5)
+ax.spines['top'].set_visible(False)
+ax.spines['right'].set_visible(False)
+ax.spines['bottom'].set_visible(False)
+ax.spines['left'].set_visible(False)
+plt.xlabel('$x_1$')
+plt.ylabel('$x_2$')
diff --git a/Book4_Ch08_Python_Codes/Bk4_Ch8_02.py b/Book4_Ch08_Python_Codes/Bk4_Ch8_02.py
new file mode 100644
index 0000000..1a83b33
--- /dev/null
+++ b/Book4_Ch08_Python_Codes/Bk4_Ch8_02.py
@@ -0,0 +1,68 @@
+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch8_02.py
+
+import matplotlib.pyplot as plt 
+import numpy as np
+
+def plot_shape(X,copy = False):
+    if copy:
+        fill_color = np.array([255,236,255])/255
+        edge_color = np.array([255,0,0])/255
+    else:
+        fill_color = np.array([219,238,243])/255
+        edge_color = np.array([0,153,255])/255
+    
+    plt.fill(X[:,0], X[:,1],
+             color = fill_color,
+             edgecolor = edge_color)
+    
+    plt.plot(X[:,0], X[:,1],marker = 'x',
+             markeredgecolor = edge_color*0.5,
+             linestyle = 'None') 
+
+X = np.array([[1,1],
+              [0,-1],
+              [-1,-1],
+              [-1,1]]) + np.array([3,3])
+
+# visualizations
+
+thetas = np.linspace(30, 330, num=11)
+
+for theta in thetas:
+    
+    fig, ax = plt.subplots()
+    
+    theta = theta/180*np.pi;
+    # rotation
+    R = np.array([[np.cos(theta),  np.sin(theta)],
+                  [-np.sin(theta), np.cos(theta)]])
+    
+    Z = X@R;
+    plot_shape(Z,True) # plot copy
+    
+    plot_shape(X)      # plot original
+    
+    # Decorations
+    ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
+    plt.axis('equal')
+    plt.axis('square')
+    plt.axhline(y=0, color='k', linewidth = 0.25)
+    plt.axvline(x=0, color='k', linewidth = 0.25)
+    plt.xticks(np.arange(-5, 6))
+    plt.yticks(np.arange(-5, 6))
+    ax.set_xlim(-5,5)
+    ax.set_ylim(-5,5)
+    ax.spines['top'].set_visible(False)
+    ax.spines['right'].set_visible(False)
+    ax.spines['bottom'].set_visible(False)
+    ax.spines['left'].set_visible(False)
+    plt.xlabel('$x_1$')
+    plt.ylabel('$x_2$')
diff --git a/Book4_Ch08_几何变换__数学要素__从加减乘除到机器学习.pdf b/Book4_Ch08_几何变换__数学要素__从加减乘除到机器学习.pdf
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index 0000000..87b6ef2
Binary files /dev/null and b/Book4_Ch08_几何变换__数学要素__从加减乘除到机器学习.pdf differ