Create app.py

app.py

@@ -0,0 +1,269 @@
+import streamlit as st
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.patches import Polygon, Circle
+
+# Function to calculate the distance between two points
+def calculate_distance(x1, y1, x2, y2):
+    return np.sqrt((x2 - x1) * 2 + (y2 - y1) * 2)
+
+# Function to calculate angles using the Law of Cosines
+def calculate_angle(a, b, c):
+    try:
+        angle = np.degrees(np.acos((b * 2 + c * 2 - a ** 2) / (2 * b * c)))
+    except ValueError:
+        angle = 0  # Handle possible domain error in acos
+    return angle
+
+# Function to calculate area using Heron's formula
+def calculate_area(a, b, c):
+    s = (a + b + c) / 2
+    area = np.sqrt(s * (s - a) * (s - b) * (s - c))
+    return area
+
+# Function to calculate the perimeter
+def calculate_perimeter(a, b, c):
+    return a + b + c
+
+# Function to calculate the radius of the inscribed circle
+def calculate_radius_inscribed_circle(a, b, c):
+    try:
+        s = (a + b + c) / 2
+        area = calculate_area(a, b, c)
+        radius = area / s
+    except ZeroDivisionError:
+        radius = 0  # Handle case where area or perimeter is zero
+    return radius
+
+# Function to calculate the radius of the circumscribed circle
+def calculate_radius_circumscribed_circle(a, b, c):
+    try:
+        area = calculate_area(a, b, c)
+        radius = (a * b * c) / (4 * area)
+    except ZeroDivisionError:
+        radius = 0  # Handle case where area is zero
+    return radius
+
+# Function to calculate the centroid coordinates
+def calculate_centroid(x1, y1, x2, y2, x3, y3):
+    G_x = (x1 + x2 + x3) / 3
+    G_y = (y1 + y2 + y3) / 3
+    return G_x, G_y
+
+# Function to calculate the incenter coordinates
+def calculate_incenter(x1, y1, x2, y2, x3, y3, a, b, c):
+    try:
+        I_x = (a * x1 + b * x2 + c * x3) / (a + b + c)
+        I_y = (a * y1 + b * y2 + c * y3) / (a + b + c)
+    except ZeroDivisionError:
+        I_x, I_y = 0, 0  # Handle division by zero if sides sum to zero
+    return I_x, I_y
+
+# Function to calculate the circumcenter coordinates
+def calculate_circumcenter(x1, y1, x2, y2, x3, y3, a, b, c):
+    try:
+        D = 2 * (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))
+        U_x = ((x1*2 + y12) * (y2 - y3) + (x22 + y22) * (y3 - y1) + (x32 + y3*2) * (y1 - y2)) / D
+        U_y = ((x1*2 + y12) * (x3 - x2) + (x22 + y22) * (x1 - x3) + (x32 + y3*2) * (x2 - x1)) / D
+    except ZeroDivisionError:
+        U_x, U_y = 0, 0  # Handle division by zero in circumcenter calculation
+    return U_x, U_y
+
+# Function to calculate midpoints of sides
+def calculate_midpoints(x1, y1, x2, y2, x3, y3):
+    # Midpoint of AB
+    M1_x = (x1 + x2) / 2
+    M1_y = (y1 + y2) / 2
+    # Midpoint of BC
+    M2_x = (x2 + x3) / 2
+    M2_y = (y2 + y3) / 2
+    # Midpoint of CA
+    M3_x = (x3 + x1) / 2
+    M3_y = (y3 + y1) / 2
+    return (M1_x, M1_y), (M2_x, M2_y), (M3_x, M3_y)
+
+# Function to format values close to zero as 0
+def format_zero(val):
+    if abs(val) < 1e-6:
+        return 0.0
+    return val
+
+# Function to plot the triangle with all points in different colors and a legend
+def plot_triangle(x1, y1, x2, y2, x3, y3, I_x, I_y, U_x, U_y, G_x, G_y, midpoints, a, b, c):
+    fig, ax = plt.subplots(figsize=(8, 6))
+    triangle = Polygon([(x1, y1), (x2, y2), (x3, y3)], closed=True, edgecolor='b', facecolor='lightblue')
+    ax.add_patch(triangle)
+    
+    # Define colors for different points
+    vertex_color = 'blue'
+    midpoint_color = 'green'
+    centroid_color = 'orange'
+    incenter_color = 'red'
+    circumcenter_color = 'purple'
+    
+    # Plot the triangle vertices
+    vertices = [(x1, y1), (x2, y2), (x3, y3)]
+    vertex_labels = [f"Vertex A ({x1:.3f}, {y1:.3f})", f"Vertex B ({x2:.3f}, {y2:.3f})", f"Vertex C ({x3:.3f}, {y3:.3f})"]
+    for i, (vx, vy) in enumerate(vertices):
+        ax.scatter(vx, vy, color=vertex_color, zorder=3)
+        
+    # Plot key points with their corresponding colors
+    key_points = [
+        (I_x, I_y, incenter_color),
+        (U_x, U_y, circumcenter_color),
+        (G_x, G_y, centroid_color)
+    ]
+    key_points_labels = [f"Incenter ({I_x:.3f}, {I_y:.3f})", f"Circumcenter ({U_x:.3f}, {U_y:.3f})", f"Centroid ({G_x:.3f}, {G_y:.3f})"]
+    
+    for x, y, color in key_points:
+        ax.scatter(x, y, color=color, zorder=4)
+
+    # Plot midpoints of sides
+    for i, (mx, my) in enumerate(midpoints):
+        ax.scatter(mx, my, color=midpoint_color, zorder=5)
+
+    # Draw the inscribed circle (incircle)
+    radius_in = calculate_radius_inscribed_circle(a, b, c)
+    incircle = Circle((I_x, I_y), radius_in, color=incenter_color, fill=False, linestyle='--', linewidth=2, label="Inscribed Circle")
+    ax.add_patch(incircle)
+    
+    # Draw the circumscribed circle (circumcircle)
+    radius_circum = calculate_radius_circumscribed_circle(a, b, c)
+    circumcircle = Circle((U_x, U_y), radius_circum, color=circumcenter_color, fill=False, linestyle='--', linewidth=2, label="Circumscribed Circle")
+    ax.add_patch(circumcircle)
+    
+    # Add legend
+    handles = [
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=8, label=vertex_labels[0]),
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=8, label=vertex_labels[1]),
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=8, label=vertex_labels[2]),
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=8, label=midpoints[0]),
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=8, label=midpoints[1]),
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=8, label=midpoints[2]),
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=incenter_color, markersize=8, label=key_points_labels[0]),
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=circumcenter_color, markersize=8, label=key_points_labels[1]),
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=centroid_color, markersize=8, label=key_points_labels[2])
+    ]
+    ax.legend(handles=handles, loc='upper left', fontsize=12)
+    
+    # Adjust the plot limits and aspect ratio
+    padding = 3
+    ax.set_xlim([min(x1, x2, x3) - padding, max(x1, x2, x3) + padding])
+    ax.set_ylim([min(y1, y2, y3) - padding, max(y1, y2, y3) + padding])
+    ax.set_aspect('equal', adjustable='datalim')
+    
+    ax.set_title('Solved Triangle', fontsize=18)
+    ax.set_xlabel('X-axis', fontsize=12)
+    ax.set_ylabel('Y-axis', fontsize=12)
+    
+    plt.grid(True)
+    st.pyplot(fig)
+
+# Function to check if the sides form a valid triangle
+def is_valid_triangle(a, b, c):
+    # Check if the sum of two sides is greater than the third side (Triangle Inequality Theorem)
+    return a + b > c and b + c > a and c + a > b
+
+# Main function to interact with the user
+def main():
+    st.title("Advanced Triangle Solver")
+
+    st.sidebar.header("Enter the coordinates of the three points:")
+
+    # Coordinates input (X1, Y1), (X2, Y2), (X3, Y3)
+    x1 = st.sidebar.number_input("X1", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
+    y1 = st.sidebar.number_input("Y1", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
+    x2 = st.sidebar.number_input("X2", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
+    y2 = st.sidebar.number_input("Y2", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
+    x3 = st.sidebar.number_input("X3", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
+    y3 = st.sidebar.number_input("Y3", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
+
+    if st.sidebar.button("Calculate"):
+        # Calculate the lengths of the sides of the triangle using Euclidean distance
+        a = calculate_distance(x2, y2, x3, y3)
+        b = calculate_distance(x1, y1, x3, y3)
+        c = calculate_distance(x1, y1, x2, y2)
+
+        # Validate if it's a valid triangle
+        if not is_valid_triangle(a, b, c):
+            st.error("The entered points do not form a valid triangle.")
+            return
+        
+        # Calculate angles using the Law of Cosines
+        A = calculate_angle(a, b, c)
+        B = calculate_angle(b, a, c)
+        C = calculate_angle(c, a, b)
+
+        # Check if angles sum up to 180 degrees
+        if abs(A + B + C - 180) > 1e-2:
+            st.error("The sum of the angles is not 180 degrees.")
+            return
+
+        # Calculate area, perimeter, and radius of inscribed and circumscribed circles
+        area = calculate_area(a, b, c)
+        perimeter = calculate_perimeter(a, b, c)
+        radius_in = calculate_radius_inscribed_circle(a, b, c)
+        radius_circum = calculate_radius_circumscribed_circle(a, b, c)
+
+        # Calculate centroid, incenter, and circumcenter coordinates
+        G_x, G_y = calculate_centroid(x1, y1, x2, y2, x3, y3)
+        I_x, I_y = calculate_incenter(x1, y1, x2, y2, x3, y3, a, b, c)
+        U_x, U_y = calculate_circumcenter(x1, y1, x2, y2, x3, y3, a, b, c)
+
+        # Calculate midpoints of the sides
+        midpoints = calculate_midpoints(x1, y1, x2, y2, x3, y3)
+
+        # Display results in columns
+        col1, col2 = st.columns(2)
+        
+        with col1:
+            st.subheader("Coordinates of Triangle:")
+            st.markdown(f"Vertex A: *({x1:.3f}, {y1:.3f})*")
+            st.markdown(f"Vertex B: *({x2:.3f}, {y2:.3f})*")
+            st.markdown(f"Vertex C: *({x3:.3f}, {y3:.3f})*")
+        
+        with col2:
+            st.subheader("Mid-Points of Triangle:")
+            st.markdown(f"Midpoint of AB: ({midpoints[0][0]:.3f}, {midpoints[0][1]:.3f})")
+            st.markdown(f"Midpoint of BC: ({midpoints[1][0]:.3f}, {midpoints[1][1]:.3f})")
+            st.markdown(f"Midpoint of CA: ({midpoints[2][0]:.3f}, {midpoints[2][1]:.3f})")
+
+        
+        col1, col2 = st.columns(2)
+           
+        with col1:
+            st.subheader("Angles of Triangle:")
+            st.markdown(f"Angle A: *{format_zero(A):.3f}°*")
+            st.markdown(f"Angle B: *{format_zero(B):.3f}°*")
+            st.markdown(f"Angle C: *{format_zero(C):.3f}°*")
+
+        with col2:
+            st.subheader("Sides of Triangle:")
+            st.markdown(f"Side a: *{format_zero(a):.3f}* units")
+            st.markdown(f"Side b: *{format_zero(b):.3f}* units")
+            st.markdown(f"Side c: *{format_zero(c):.3f}* units")
+
+        
+        col1, col2, col3 = st.columns(3)
+
+        with col1:
+            st.subheader("Incenter of Triangle:")
+            st.markdown(f"Coordinates: *({format_zero(I_x):.3f}, {format_zero(I_y):.3f})*")
+            st.markdown(f"Radius: *{radius_in:.3f}* units")
+        
+        with col2:
+            st.subheader("Circumcenter of Triangle:")
+            st.markdown(f"Coordinates: *({format_zero(U_x):.3f}, {format_zero(U_y):.3f})*")
+            st.markdown(f"Radius: *{radius_circum:.3f}* units")
+        
+        with col3:
+            st.subheader("Other Properties:")
+            st.markdown(f"Area: *{format_zero(area):.3f}* square units")
+            st.markdown(f"Perimeter: *{format_zero(perimeter):.3f}* units")
+            st.markdown(f"Centroid: *({format_zero(G_x):.3f}, {format_zero(G_y):.3f})*")
+
+        # Display triangle graph with midpoints and colored points
+        plot_triangle(x1, y1, x2, y2, x3, y3, I_x, I_y, U_x, U_y, G_x, G_y, midpoints, a, b, c)
+
+if _name_ == "_main_":
+    main()