Bài 16 Đường Trung Bình Của Tam Giác —

เส้นกลางของสามเหลี่ยม

เส้นกลาง Midsegment Midline สามเหลี่ยม จุดกึ่งกลาง Midpoint ขนาน ครึ่งหนึ่ง Coordinate Geometry Python คำนวณ

เนื้อหาเกี่ยวข้อง — อ่านต่อ: ชมรมนกลงทุน — คู่มือฉบับสมบูรณ์ 2026

ทฤษฎี	สูตร	ตัวอย่าง
Midpoint	((x1+x2)/2, (y1+y2)/2)	M(2,3) N(6,7) → (4,5)
Distance	√((x2-x1)²+(y2-y1)²)	A(0,0) B(3,4) → 5
Midsegment	= ½ × ด้านที่สาม	ด้าน=10 → เส้นกลาง=5
Area	½\|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)\|	พื้นที่สามเหลี่ยม
Centroid	((x1+x2+x3)/3, (y1+y2+y3)/3)	จุดศูนย์ถ่วง

Visualization

# visualization.py — Triangle Visualization

# import matplotlib.pyplot as plt

# import numpy as np

#

# def plot_triangle(A, B, C):

#     fig, ax = plt.subplots(1, 1, figsize=(8, 6))

#

#     # Draw triangle

#     triangle = plt.Polygon([A, B, C], fill=False, edgecolor='blue', linewidth=2)

#     ax.add_patch(triangle)

#

#     # Draw midsegments

#     M_AB = ((A[0]+B[0])/2, (A[1]+B[1])/2)

#     M_BC = ((B[0]+C[0])/2, (B[1]+C[1])/2)

#     M_AC = ((A[0]+C[0])/2, (A[1]+C[1])/2)

#

#     for p1, p2 in [(M_AB, M_BC), (M_BC, M_AC), (M_AB, M_AC)]:

#         ax.plot([p1[0], p2[0]], [p1[1], p2[1]], 'r--', linewidth=1.5)

#

#     # Label vertices

#     for point, label in [(A, 'A'), (B, 'B'), (C, 'C')]:

#         ax.annotate(label, point, fontsize=14, ha='center', va='bottom')

#

#     # Label midpoints

#     for point, label in [(M_AB, 'M_AB'), (M_BC, 'M_BC'), (M_AC, 'M_AC')]:

#         ax.plot(*point, 'ro', markersize=6)

#         ax.annotate(label, point, fontsize=10, color='red')

#

#     ax.set_aspect('equal')

#     ax.grid(True, alpha=0.3)

#     ax.set_title('Triangle with Midsegments')

#     plt.savefig('triangle_midsegments.png', dpi=150)

#     plt.show()

#

# plot_triangle((0, 0), (8, 0), (4, 6))



# Distance Formulas for IT

formulas = {

    "Euclidean": {

        "formula": "√(Σ(xi-yi)²)",

        "use": "Straight-line distance, Default metric",

        "python": "np.linalg.norm(a - b)",

    },

    "Manhattan": {

        "formula": "Σ|xi-yi|",

        "use": "Grid-based distance, City blocks",

        "python": "np.sum(np.abs(a - b))",

    },

    "Cosine": {

        "formula": "1 - (a·b)/(|a||b|)",

        "use": "Text similarity, Embeddings",

        "python": "1 - np.dot(a, b)/(np.linalg.norm(a)*np.linalg.norm(b))",

    },

    "Haversine": {

        "formula": "2r·arcsin(√(sin²(Δφ/2)+cos(φ1)cos(φ2)sin²(Δλ/2)))",

        "use": "GPS distance on Earth surface",

        "python": "haversine(lat1, lon1, lat2, lon2)",

    },

}



print("Distance Formulas:")

for name, info in formulas.items():

    print(f"\n  [{name}]")

    for k, v in info.items():

        print(f"    {k}: {v}")