import tkinter as tk from tkinter import ttk, messagebox, scrolledtext import json from PIL import Image, ImageTk import math class MathFormulaApp: """数学公式查询系统 - 图形界面版""" def __init__(self, root): self.root = root self.root.title("数学公式查询系统 v2.0") self.root.geometry("1000x700") self.root.configure(bg='#f0f0f0') # 设置样式 self.setup_styles() # 公式数据库 self.formulas = self.init_formulas() # 创建界面 self.create_widgets() # 绑定事件 self.setup_bindings() def setup_styles(self): """设置界面样式""" self.colors = { 'bg': '#f5f5f5', 'header': '#2c3e50', 'button': '#3498db', 'button_hover': '#2980b9', 'formula_bg': '#ffffff', 'highlight': '#e8f4f8' } # 配置ttk样式 style = ttk.Style() style.theme_use('clam') style.configure('TButton', padding=6, font=('微软雅黑', 10)) style.configure('TLabel', background=self.colors['bg'], font=('微软雅黑', 10)) style.configure('Header.TLabel', font=('微软雅黑', 16, 'bold'), foreground='white') style.configure('Formula.TLabel', font=('Consolas', 12), background=self.colors['formula_bg']) def init_formulas(self): """初始化公式数据库""" return { # 代数公式 "quadratic": { "name": "一元二次方程求根公式", "category": "代数", "formula": "x = [-b ± √(b² - 4ac)] / (2a)", "latex": "x = \\frac{-b \\pm \\sqrt{b^2-4ac}}{2a}", "description": "求解 ax² + bx + c = 0 的根", "variables": {"a": "二次项系数", "b": "一次项系数", "c": "常数项"}, "example": "解方程 2x² + 5x - 3 = 0，a=2, b=5, c=-3" }, "difference_squares": { "name": "平方差公式", "category": "代数", "formula": "a² - b² = (a + b)(a - b)", "latex": "a^2 - b^2 = (a+b)(a-b)", "description": "两个数的平方差等于它们的和乘以差" }, "perfect_square": { "name": "完全平方公式", "category": "代数", "formula": "(a ± b)² = a² ± 2ab + b²", "latex": "(a \\pm b)^2 = a^2 \\pm 2ab + b^2", "description": "两数和（差）的平方" }, # 几何公式 "circle_area": { "name": "圆的面积", "category": "几何", "formula": "S = πr²", "latex": "S = \\pi r^2", "description": "圆的面积计算公式", "variables": {"S": "面积", "r": "半径", "π": "圆周率 ≈ 3.14159"} }, "circle_perimeter": { "name": "圆的周长", "category": "几何", "formula": "C = 2πr", "latex": "C = 2\\pi r", "description": "圆的周长计算公式" }, "triangle_area": { "name": "三角形面积", "category": "几何", "formula": "S = (1/2) × 底 × 高", "latex": "S = \\frac{1}{2} \\times \\text{底} \\times \\text{高}", "description": "三角形面积公式" }, "rectangle_area": { "name": "矩形面积", "category": "几何", "formula": "S = 长 × 宽", "latex": "S = l \\times w", "description": "矩形面积公式" }, "pythagorean": { "name": "勾股定理", "category": "几何", "formula": "a² + b² = c²", "latex": "a^2 + b^2 = c^2", "description": "直角三角形中，两直角边的平方和等于斜边的平方" }, # 三角学公式 "sine": { "name": "正弦函数", "category": "三角学", "formula": "sin(θ) = 对边 / 斜边", "latex": "\\sin\\theta = \\frac{\\text{对边}}{\\text{斜边}}", "description": "直角三角形中角θ的正弦值" }, "cosine": { "name": "余弦函数", "category": "三角学", "formula": "cos(θ) = 邻边 / 斜边", "latex": "\\cos\\theta = \\frac{\\text{邻边}}{\\text{斜边}}", "description": "直角三角形中角θ的余弦值" }, "tangent": { "name": "正切函数", "category": "三角学", "formula": "tan(θ) = 对边 / 邻边 = sinθ / cosθ", "latex": "\\tan\\theta = \\frac{\\sin\\theta}{\\cos\\theta}", "description": "直角三角形中角θ的正切值" }, "sin2θ": { "name": "正弦二倍角公式", "category": "三角学", "formula": "sin(2θ) = 2sinθ·cosθ", "latex": "\\sin(2\\theta) = 2\\sin\\theta\\cos\\theta", "description": "正弦二倍角公式" }, # 微积分公式 "derivative_power": { "name": "幂函数求导", "category": "微积分", "formula": "d/dx (xⁿ) = n·xⁿ⁻¹", "latex": "\\frac{d}{dx}x^n = nx^{n-1}", "description": "幂函数的导数" }, "integral_power": { "name": "幂函数积分", "category": "微积分", "formula": "∫ xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ -1)", "latex": "\\int x^n dx = \\frac{x^{n+1}}{n+1} + C", "description": "幂函数的不定积分" } } def create_widgets(self): """创建界面组件""" # 顶部标题栏 header_frame = tk.Frame(self.root, bg=self.colors['header'], height=80) header_frame.pack(fill=tk.X) header_frame.pack_propagate(False) title_label = tk.Label(header_frame, text="📐 数学公式查询系统", font=('微软雅黑', 20, 'bold'), fg='white', bg=self.colors['header']) title_label.pack(pady=20) # 主内容区域 main_paned = ttk.PanedWindow(self.root, orient=tk.HORIZONTAL) main_paned.pack(fill=tk.BOTH, expand=True, padx=10, pady=10) # 左侧：搜索和列表区域 left_frame = tk.Frame(main_paned, bg=self.colors['bg']) main_paned.add(left_frame, weight=1) # 搜索框 search_frame = tk.LabelFrame(left_frame, text="🔍 搜索公式", font=('微软雅黑', 11, 'bold'), bg=self.colors['bg']) search_frame.pack(fill=tk.X, padx=5, pady=5) self.search_var = tk.StringVar() self.search_var.trace('w', self.on_search) search_entry = tk.Entry(search_frame, textvariable=self.search_var, font=('微软雅黑', 11), width=30) search_entry.pack(side=tk.LEFT, padx=5, pady=5, fill=tk.X, expand=True) search_btn = tk.Button(search_frame, text="搜索", command=self.search_formulas, bg=self.colors['button'], fg='white', font=('微软雅黑', 10), cursor='hand2') search_btn.pack(side=tk.RIGHT, padx=5, pady=5) # 分类浏览 category_frame = tk.LabelFrame(left_frame, text="📂 分类浏览", font=('微软雅黑', 11, 'bold'), bg=self.colors['bg']) category_frame.pack(fill=tk.X, padx=5, pady=5) categories = ["全部"] + sorted(list(set(f['category'] for f in self.formulas.values()))) self.category_var = tk.StringVar(value="全部") category_combo = ttk.Combobox(category_frame, textvariable=self.category_var, values=categories, state='readonly', width=25) category_combo.pack(padx=5, pady=5, fill=tk.X) category_combo.bind('<>', self.on_category_change) # 公式列表 list_frame = tk.LabelFrame(left_frame, text="📋 公式列表", font=('微软雅黑', 11, 'bold'), bg=self.colors['bg']) list_frame.pack(fill=tk.BOTH, expand=True, padx=5, pady=5) # 创建带滚动条的列表框 list_container = tk.Frame(list_frame) list_container.pack(fill=tk.BOTH, expand=True, padx=5, pady=5) scrollbar = tk.Scrollbar(list_container) scrollbar.pack(side=tk.RIGHT, fill=tk.Y) self.formula_listbox = tk.Listbox(list_container, yscrollcommand=scrollbar.set, font=('微软雅黑', 10), selectmode=tk.SINGLE, height=15) self.formula_listbox.pack(side=tk.LEFT, fill=tk.BOTH, expand=True) scrollbar.config(command=self.formula_listbox.yview) self.formula_listbox.bind('<>', self.on_formula_select) # 右侧：详细信息区域 right_frame = tk.Frame(main_paned, bg=self.colors['bg']) main_paned.add(right_frame, weight=2) # 公式详情 detail_frame = tk.LabelFrame(right_frame, text="📖 公式详情", font=('微软雅黑', 11, 'bold'), bg=self.colors['bg']) detail_frame.pack(fill=tk.BOTH, expand=True, padx=5, pady=5) # 公式显示区域 self.formula_display = tk.Text(detail_frame, height=8, wrap=tk.WORD, font=('Consolas', 14), bg='white') self.formula_display.pack(fill=tk.X, padx=10, pady=10) # 描述区域 desc_frame = tk.LabelFrame(detail_frame, text="💡 说明", font=('微软雅黑', 10, 'bold'), bg=self.colors['bg']) desc_frame.pack(fill=tk.BOTH, expand=True, padx=10, pady=5) self.desc_text = scrolledtext.ScrolledText(desc_frame, height=6, wrap=tk.WORD, font=('微软雅黑', 10), bg='white') self.desc_text.pack(fill=tk.BOTH, expand=True, padx=5, pady=5) # 变量说明 var_frame = tk.LabelFrame(detail_frame, text="📊 变量说明", font=('微软雅黑', 10, 'bold'), bg=self.colors['bg']) var_frame.pack(fill=tk.BOTH, expand=True, padx=10, pady=5) self.var_text = scrolledtext.ScrolledText(var_frame, height=4, wrap=tk.WORD, font=('微软雅黑', 10), bg='white') self.var_text.pack(fill=tk.BOTH, expand=True, padx=5, pady=5) # 计算器区域 calc_frame = tk.LabelFrame(right_frame, text="🧮 公式计算器", font=('微软雅黑', 11, 'bold'), bg=self.colors['bg']) calc_frame.pack(fill=tk.X, padx=5, pady=5) self.calc_container = tk.Frame(calc_frame, bg=self.colors['bg']) self.calc_container.pack(fill=tk.X, padx=10, pady=10) self.calc_label = tk.Label(self.calc_container, text="选择公式后可使用计算器", font=('微软雅黑', 10), bg=self.colors['bg']) self.calc_label.pack() # 状态栏 status_frame = tk.Frame(self.root, bg=self.colors['header'], height=30) status_frame.pack(fill=tk.X, side=tk.BOTTOM) status_frame.pack_propagate(False) self.status_label = tk.Label(status_frame, text="就绪", font=('微软雅黑', 9), fg='white', bg=self.colors['header']) self.status_label.pack(side=tk.LEFT, padx=10, pady=5) # 初始化公式列表 self.update_formula_list() def setup_bindings(self): """设置事件绑定""" # 回车键搜索 self.root.bind('', lambda e: self.search_formulas()) def update_formula_list(self, formulas=None): """更新公式列表""" self.formula_listbox.delete(0, tk.END) if formulas is None: formulas = self.formulas for key, formula in formulas.items(): display_text = f"{formula['name']} [{formula['category']}]" self.formula_listbox.insert(tk.END, display_text) # 存储公式key作为列表项的数据 self.formula_listbox.itemconfig(tk.END, {'fg': '#333333'}) # 保存公式key的映射 self.formula_keys = list(formulas.keys()) if self.formula_listbox.size() > 0: self.formula_listbox.selection_set(0) self.on_formula_select() def search_formulas(self): """搜索公式""" keyword = self.search_var.get().strip() if not keyword: self.update_formula_list() return results = {} for key, formula in self.formulas.items(): if (keyword.lower() in formula['name'].lower() or keyword.lower() in formula['description'].lower()): results[key] = formula if results: self.update_formula_list(results) self.status_label.config(text=f"找到 {len(results)} 个相关公式") else: messagebox.showinfo("提示", "未找到相关公式") self.update_formula_list() def on_search(self, *args): """实时搜索""" self.search_formulas() def on_category_change(self, event): """分类改变事件""" category = self.category_var.get() if category == "全部": self.update_formula_list() else: results = {} for key, formula in self.formulas.items(): if formula['category'] == category: results[key] = formula self.update_formula_list(results) def on_formula_select(self, event=None): """公式选择事件""" selection = self.formula_listbox.curselection() if not selection: return index = selection[0] if index >= len(self.formula_keys): return formula_key = self.formula_keys[index] formula = self.formulas[formula_key] # 更新显示 self.formula_display.delete(1.0, tk.END) self.formula_display.insert(1.0, formula['formula']) self.formula_display.config(font=('Consolas', 14, 'bold'), fg='#2c3e50') self.desc_text.delete(1.0, tk.END) self.desc_text.insert(1.0, formula['description']) self.var_text.delete(1.0, tk.END) if 'variables' in formula: for var, desc in formula['variables'].items(): self.var_text.insert(tk.END, f"• {var}: {desc}\n") else: self.var_text.insert(tk.END, "无变量说明") # 更新计算器界面 self.update_calculator(formula_key) self.status_label.config(text=f"当前公式：{formula['name']}") def update_calculator(self, formula_key): """根据选择的公式更新计算器界面""" # 清除原有组件 for widget in self.calc_container.winfo_children(): widget.destroy() if formula_key == "quadratic": self.create_quadratic_calculator() elif formula_key == "circle_area" or formula_key == "circle_perimeter": self.create_circle_calculator() elif formula_key == "rectangle_area": self.create_rectangle_calculator() elif formula_key == "triangle_area": self.create_triangle_calculator() elif formula_key == "pythagorean": self.create_pythagorean_calculator() else: label = tk.Label(self.calc_container, text="该公式暂无计算器功能", font=('微软雅黑', 10), bg=self.colors['bg']) label.pack() def create_quadratic_calculator(self): """创建二次方程计算器""" tk.Label(self.calc_container, text="解一元二次方程 ax² + bx + c = 0", font=('微软雅黑', 10, 'bold'), bg=self.colors['bg']).pack() input_frame = tk.Frame(self.calc_container, bg=self.colors['bg']) input_frame.pack(pady=5) tk.Label(input_frame, text="a =", bg=self.colors['bg']).pack(side=tk.LEFT, padx=5) self.a_entry = tk.Entry(input_frame, width=8) self.a_entry.pack(side=tk.LEFT, padx=5) tk.Label(input_frame, text="b =", bg=self.colors['bg']).pack(side=tk.LEFT, padx=5) self.b_entry = tk.Entry(input_frame, width=8) self.b_entry.pack(side=tk.LEFT, padx=5) tk.Label(input_frame, text="c =", bg=self.colors['bg']).pack(side=tk.LEFT, padx=5) self.c_entry = tk.Entry(input_frame, width=8) self.c_entry.pack(side=tk.LEFT, padx=5) calc_btn = tk.Button(self.calc_container, text="计算", command=self.calc_quadratic, bg=self.colors['button'], fg='white', cursor='hand2') calc_btn.pack(pady=5) self.quadratic_result = tk.Label(self.calc_container, text="", font=('微软雅黑', 10), bg=self.colors['bg'], fg='green') self.quadratic_result.pack() def create_circle_calculator(self): """创建圆计算器""" tk.Label(self.calc_container, text="计算圆的面积和周长", font=('微软雅黑', 10, 'bold'), bg=self.colors['bg']).pack() input_frame = tk.Frame(self.calc_container, bg=self.colors['bg']) input_frame.pack(pady=5) tk.Label(input_frame, text="半径 r =", bg=self.colors['bg']).pack(side=tk.LEFT, padx=5) self.radius_entry = tk.Entry(input_frame, width=10) self.radius_entry.pack(side=tk.LEFT, padx=5) calc_btn = tk.Button(self.calc_container, text="计算", command=self.calc_circle, bg=self.colors['button'], fg='white', cursor='hand2') calc_btn.pack(pady=5) self.circle_result = tk.Label(self.calc_container, text="", font=('微软雅黑', 10), bg=self.colors['bg'], fg='green') self.circle_result.pack() def create_rectangle_calculator(self): """创建矩形计算器""" tk.Label(self.calc_container, text="计算矩形面积", font=('微软雅黑', 10, 'bold'), bg=self.colors['bg']).pack() input_frame = tk.Frame(self.calc_container, bg=self.colors['bg']) input_frame.pack(pady=5) tk.Label(input_frame, text="长度 =", bg=self.colors['bg']).pack(side=tk.LEFT, padx=5) self.length_entry = tk.Entry(input_frame, width=10) self.length_entry.pack(side=tk.LEFT, padx=5) tk.Label(input_frame, text="宽度 =", bg=self.colors['bg']).pack(side=tk.LEFT, padx=5) self.width_entry = tk.Entry(input_frame, width=10) self.width_entry.pack(side=tk.LEFT, padx=5) calc_btn = tk.Button(self.calc_container, text="计算", command=self.calc_rectangle, bg=self.colors['button'], fg='white', cursor='hand2') calc_btn.pack(pady=5) self.rect_result = tk.Label(self.calc_container, text="", font=('微软雅黑', 10), bg=self.colors['bg'], fg='green') self.rect_result.pack() def create_triangle_calculator(self): """创建三角形计算器""" tk.Label(self.calc_container, text="计算三角形面积", font=('微软雅黑', 10, 'bold'), bg=self.colors['bg']).pack() input_frame = tk.Frame(self.calc_container, bg=self.colors['bg']) input_frame.pack(pady=5) tk.Label(input_frame, text="底边长 =", bg=self.colors['bg']).pack(side=tk.LEFT, padx=5) self.base_entry = tk.Entry(input_frame, width=10) self.base_entry.pack(side=tk.LEFT, padx=5) tk.Label(input_frame, text="高 =", bg=self.colors['bg']).pack(side=tk.LEFT, padx=5) self.height_entry = tk.Entry(input_frame, width=10) self.height_entry.pack(side=tk.LEFT, padx=5) calc_btn = tk.Button(self.calc_container, text="计算", command=self.calc_triangle, bg=self.colors['button'], fg='white', cursor='hand2') calc_btn.pack(pady=5) self.triangle_result = tk.Label(self.calc_container, text="", font=('微软雅黑', 10), bg=self.colors['bg'], fg='green') self.triangle_result.pack() def create_pythagorean_calculator(self): """创建勾股定理计算器""" tk.Label(self.calc_container, text="计算直角三角形斜边长度", font=('微软雅黑', 10, 'bold'), bg=self.colors['bg']).pack() input_frame = tk.Frame(self.calc_container, bg=self.colors['bg']) input_frame.pack(pady=5) tk.Label(input_frame, text="直角边 a =", bg=self.colors['bg']).pack(side=tk.LEFT, padx=5) self.side_a_entry = tk.Entry(input_frame, width=10) self.side_a_entry.pack(side=tk.LEFT, padx=5) tk.Label(input_frame, text="直角边 b =", bg=self.colors['bg']).pack(side=tk.LEFT, padx=5) self.side_b_entry = tk.Entry(input_frame, width=10) self.side_b_entry.pack(side=tk.LEFT, padx=5) calc_btn = tk.Button(self.calc_container, text="计算", command=self.calc_pythagorean, bg=self.colors['button'], fg='white', cursor='hand2') calc_btn.pack(pady=5) self.pyth_result = tk.Label(self.calc_container, text="", font=('微软雅黑', 10), bg=self.colors['bg'], fg='green') self.pyth_result.pack() def calc_quadratic(self): """计算二次方程""" try: a = float(self.a_entry.get()) b = float(self.b_entry.get()) c = float(self.c_entry.get()) discriminant = b**2 - 4*a*c if discriminant < 0: self.quadratic_result.config(text="方程无实数根", fg='red') elif discriminant == 0: x = -b / (2*a) self.quadratic_result.config(text=f"方程有重根：x = {x:.4f}", fg='green') else: x1 = (-b + discriminant**0.5) / (2*a) x2 = (-b - discriminant**0.5) / (2*a) self.quadratic_result.config(text=f"x₁ = {x1:.4f}, x₂ = {x2:.4f}", fg='green') except ValueError: messagebox.showerror("错误", "请输入有效的数字！") def calc_circle(self): """计算圆""" try: r = float(self.radius_entry.get()) area = math.pi * r**2 perimeter = 2 * math.pi * r self.circle_result.config(text=f"面积 = {area:.4f}\n周长 = {perimeter:.4f}", fg='green') except ValueError: messagebox.showerror("错误", "请输入有效的半径！") def calc_rectangle(self): """计算矩形""" try: length = float(self.length_entry.get()) width = float(self.width_entry.get()) area = length * width self.rect_result.config(text=f"面积 = {area:.4f}", fg='green') except ValueError: messagebox.showerror("错误", "请输入有效的长度和宽度！") def calc_triangle(self): """计算三角形""" try: base = float(self.base_entry.get()) height = float(self.height_entry.get()) area = 0.5 * base * height self.triangle_result.config(text=f"面积 = {area:.4f}", fg='green') except ValueError: messagebox.showerror("错误", "请输入有效的底边长和高！") def calc_pythagorean(self): """计算勾股定理""" try: a = float(self.side_a_entry.get()) b = float(self.side_b_entry.get()) c = math.sqrt(a**2 + b**2) self.pyth_result.config(text=f"斜边长度 = {c:.4f}", fg='green') except ValueError: messagebox.showerror("错误", "请输入有效的边长！") def main(): """主函数""" root = tk.Tk() app = MathFormulaApp(root) root.mainloop() if __name__ == "__main__": main()