import tkinter as tk from tkinter import ttk, scrolledtext, messagebox import math class MathFormulaApp: def __init__(self, root): self.root = root self.root.title("数学公式查询工具") self.root.geometry("800x600") self.root.resizable(True, True) # 设置样式 style = ttk.Style() style.configure("TFrame", background="#f0f0f0") style.configure("TLabel", background="#f0f0f0", font=("Arial", 10)) style.configure("TButton", font=("Arial", 10)) # 创建主框架 self.create_widgets() self.load_formulas() def create_widgets(self): # 主框架 main_frame = ttk.Frame(self.root, padding="10") main_frame.grid(row=0, column=0, sticky=(tk.W, tk.E, tk.N, tk.S)) # 配置网格权重 self.root.columnconfigure(0, weight=1) self.root.rowconfigure(0, weight=1) main_frame.columnconfigure(1, weight=1) main_frame.rowconfigure(1, weight=1) # 标题 title_label = ttk.Label(main_frame, text="数学公式查询工具", font=("Arial", 16, "bold")) title_label.grid(row=0, column=0, columnspan=2, pady=(0, 10)) # 左侧分类树 tree_frame = ttk.LabelFrame(main_frame, text="公式分类", padding="5") tree_frame.grid(row=1, column=0, sticky=( tk.W, tk.E, tk.N, tk.S), padx=(0, 10)) tree_frame.rowconfigure(0, weight=1) tree_frame.columnconfigure(0, weight=1) # 创建树形视图 self.tree = ttk.Treeview(tree_frame, show="tree") self.tree.grid(row=0, column=0, sticky=(tk.W, tk.E, tk.N, tk.S)) # 滚动条 tree_scroll = ttk.Scrollbar( tree_frame, orient="vertical", command=self.tree.yview) tree_scroll.grid(row=0, column=1, sticky=(tk.N, tk.S)) self.tree.configure(yscrollcommand=tree_scroll.set) # 右侧公式显示区域 formula_frame = ttk.LabelFrame(main_frame, text="公式详情", padding="5") formula_frame.grid(row=1, column=1, sticky=(tk.W, tk.E, tk.N, tk.S)) formula_frame.rowconfigure(0, weight=1) formula_frame.columnconfigure(0, weight=1) # 公式显示文本框 self.formula_text = scrolledtext.ScrolledText( formula_frame, wrap=tk.WORD, font=("Consolas", 11), bg="white", fg="black" ) self.formula_text.grid( row=0, column=0, sticky=(tk.W, tk.E, tk.N, tk.S)) self.formula_text.config(state=tk.DISABLED) # 底部按钮 button_frame = ttk.Frame(main_frame) button_frame.grid(row=2, column=0, columnspan=2, pady=(10, 0), sticky=(tk.W, tk.E)) clear_btn = ttk.Button(button_frame, text="清空", command=self.clear_formula) clear_btn.pack(side=tk.RIGHT, padx=5) copy_btn = ttk.Button(button_frame, text="复制公式", command=self.copy_formula) copy_btn.pack(side=tk.RIGHT, padx=5) # 绑定树形视图选择事件 self.tree.bind("<>", self.on_formula_select) def load_formulas(self): """加载所有数学公式""" # 清空现有项目 for item in self.tree.get_children(): self.tree.delete(item) # 数学公式数据库 self.formulas_db = { # 代数 "代数": { "二次方程求根公式": { "formula": "x = (-b ± √(b² - 4ac)) / (2a)", "description": "用于求解 ax² + bx + c = 0 的根", "example": "例如：x² + 5x + 6 = 0\na=1, b=5, c=6\nx = (-5 ± √(25-24))/2 = (-5±1)/2\n所以 x₁ = -2, x₂ = -3" }, "平方差公式": { "formula": "a² - b² = (a + b)(a - b)", "description": "两个数的平方差等于它们的和与差的乘积", "example": "16 - 9 = 4² - 3² = (4+3)(4-3) = 7×1 = 7" }, "完全平方公式": { "formula": "(a ± b)² = a² ± 2ab + b²", "description": "二项式的完全平方展开", "example": "(x + 3)² = x² + 6x + 9" }, "立方和/差公式": { "formula": "a³ ± b³ = (a ± b)(a² ∓ ab + b²)", "description": "立方和与立方差的因式分解", "example": "8 + 27 = 2³ + 3³ = (2+3)(4-6+9) = 5×7 = 35" } }, # 几何 "几何": { "勾股定理": { "formula": "a² + b² = c²", "description": "直角三角形中，两直角边的平方和等于斜边的平方", "example": "直角边为3和4，斜边c = √(9+16) = √25 = 5" }, "圆的面积": { "formula": "S = πr²", "description": "圆的面积等于π乘以半径的平方", "example": "半径r=3，面积S = π×9 ≈ 28.27" }, "圆的周长": { "formula": "C = 2πr = πd", "description": "圆的周长等于2π乘以半径，或π乘以直径", "example": "半径r=5，周长C = 2π×5 = 10π ≈ 31.42" }, "三角形面积": { "formula": "S = (1/2)bh", "description": "三角形面积等于底乘高除以2", "example": "底b=6，高h=4，面积S = (1/2)×6×4 = 12" }, "梯形面积": { "formula": "S = (a + b)h/2", "description": "梯形面积等于上底加下底的和乘高除以2", "example": "上底a=3，下底b=7，高h=4，面积S = (3+7)×4/2 = 20" } }, # 三角函数 "三角函数": { "基本关系": { "formula": "sin²θ + cos²θ = 1", "description": "正弦和余弦的基本恒等式", "example": "如果 sinθ = 0.6，则 cosθ = √(1-0.36) = √0.64 = 0.8" }, "和角公式": { "formula": "sin(α±β) = sinαcosβ ± cosαsinβ\n" "cos(α±β) = cosαcosβ ∓ sinαsinβ", "description": "三角函数的和角与差角公式", "example": "sin(45°+30°) = sin45°cos30° + cos45°sin30°\n= (√2/2)(√3/2) + (√2/2)(1/2) = √2(√3+1)/4" }, "倍角公式": { "formula": "sin2θ = 2sinθcosθ\n" "cos2θ = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ", "description": "三角函数的二倍角公式", "example": "如果 sinθ = 0.5，则 sin2θ = 2×0.5×√(1-0.25) = √0.75 ≈ 0.866" } }, # 微积分 "微积分": { "导数基本公式": { "formula": "(xⁿ)' = nxⁿ⁻¹\n" "(eˣ)' = eˣ\n" "(ln x)' = 1/x\n" "(sin x)' = cos x\n" "(cos x)' = -sin x", "description": "常见函数的导数公式", "example": "(x³)' = 3x²\n(e²ˣ)' = 2e²ˣ (使用链式法则)" }, "积分基本公式": { "formula": "∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n≠-1)\n" "∫eˣ dx = eˣ + C\n" "∫1/x dx = ln|x| + C\n" "∫sin x dx = -cos x + C\n" "∫cos x dx = sin x + C", "description": "常见函数的不定积分公式", "example": "∫x² dx = x³/3 + C\n∫2x dx = x² + C" }, "牛顿-莱布尼茨公式": { "formula": "∫ₐᵇ f(x)dx = F(b) - F(a)", "description": "定积分的基本定理，其中F是f的原函数", "example": "∫₀¹ x² dx = [x³/3]₀¹ = 1/3 - 0 = 1/3" } }, # 概率统计 "概率统计": { "期望值": { "formula": "E(X) = Σxᵢpᵢ (离散)\n" "E(X) = ∫xf(x)dx (连续)", "description": "随机变量的期望值（均值）", "example": "掷骰子的期望值 E(X) = (1+2+3+4+5+6)/6 = 3.5" }, "方差": { "formula": "Var(X) = E[(X-E(X))²] = E(X²) - [E(X)]²", "description": "随机变量的方差，衡量数据的离散程度", "example": "掷骰子的方差 Var(X) = E(X²) - [E(X)]² = 91/6 - (3.5)² ≈ 2.92" }, "正态分布": { "formula": "f(x) = (1/σ√(2π))e^(-(x-μ)²/(2σ²))", "description": "正态分布的概率密度函数，μ为均值，σ为标准差", "example": "标准正态分布：μ=0, σ=1，f(x) = (1/√(2π))e^(-x²/2)" } } } # 将公式添加到树形视图 for category, formulas in self.formulas_db.items(): category_id = self.tree.insert( "", "end", text=category, open=False) for formula_name in formulas.keys(): self.tree.insert(category_id, "end", text=formula_name) def on_formula_select(self, event): """当选择公式时显示详细信息""" selection = self.tree.selection() if not selection: return item = selection[0] item_text = self.tree.item(item, "text") # 检查是否是叶子节点（具体公式） if self.tree.parent(item): # 有父节点，说明是公式 parent_id = self.tree.parent(item) parent_text = self.tree.item(parent_id, "text") if parent_text in self.formulas_db and item_text in self.formulas_db[parent_text]: formula_info = self.formulas_db[parent_text][item_text] self.display_formula(formula_info, item_text) def display_formula(self, formula_info, title): """显示公式详细信息""" self.formula_text.config(state=tk.NORMAL) self.formula_text.delete(1.0, tk.END) # 格式化显示 content = f"【{title}】\n\n" content += f"公式：\n{formula_info['formula']}\n\n" content += f"说明：\n{formula_info['description']}\n\n" content += f"示例：\n{formula_info['example']}" self.formula_text.insert(tk.END, content) self.formula_text.config(state=tk.DISABLED) def clear_formula(self): """清空公式显示区域""" self.formula_text.config(state=tk.NORMAL) self.formula_text.delete(1.0, tk.END) self.formula_text.config(state=tk.DISABLED) # 清除树形视图的选择 self.tree.selection_remove(self.tree.selection()) def copy_formula(self): """复制当前显示的公式到剪贴板""" try: content = self.formula_text.get(1.0, tk.END).strip() if content: self.root.clipboard_clear() self.root.clipboard_append(content) messagebox.showinfo("复制成功", "公式已复制到剪贴板！") else: messagebox.showwarning("警告", "没有可复制的内容") except Exception as e: messagebox.showerror("错误", f"复制失败：{str(e)}") def main(): root = tk.Tk() app = MathFormulaApp(root) root.mainloop() if __name__ == "__main__": main()