diff --git a/Bridge resistance measurement.py b/Bridge resistance measurement.py index 823e100..ad6aec5 100644 --- a/Bridge resistance measurement.py +++ b/Bridge resistance measurement.py @@ -1,5 +1,5 @@ import math -from decimal import Decimal, ROUND_HALF_EVEN +from decimal import Decimal from utils import ( scientific_round, calculate_stats, diff --git a/Excel/导热比热系数.xlsx b/Excel/导热比热系数.xlsx new file mode 100644 index 0000000..3317e9a --- /dev/null +++ b/Excel/导热比热系数.xlsx @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ca2a2c9c2061258f4e8d8e5adcc505cf1d9a87e1daedc5a416ce87fad687a3f7 +size 19961 diff --git a/Hall effect.py b/Hall effect.py index 91675b2..f902a9c 100644 --- a/Hall effect.py +++ b/Hall effect.py @@ -1,5 +1,4 @@ import math -from decimal import Decimal, ROUND_HALF_EVEN """ Hall Effect Experiment Data Processor diff --git a/Newton's rings.py b/Newton's rings.py index 6a2bd6b..5e93950 100644 --- a/Newton's rings.py +++ b/Newton's rings.py @@ -1,5 +1,5 @@ import math -from decimal import Decimal, ROUND_HALF_EVEN +from decimal import Decimal """ Newton's Rings Curvature Radius Calculator (Successive Difference Method) diff --git a/Speed of sound.py b/Speed of sound.py index e76ad35..45e9c96 100644 --- a/Speed of sound.py +++ b/Speed of sound.py @@ -1,5 +1,5 @@ import math -from decimal import Decimal, ROUND_HALF_EVEN +from decimal import Decimal """ Speed of Sound Calculator (Successive Difference Method) diff --git a/Surface tension coefficient.py b/Surface tension coefficient.py index 71a3502..b8529a7 100644 --- a/Surface tension coefficient.py +++ b/Surface tension coefficient.py @@ -1,5 +1,5 @@ import math -from decimal import Decimal, ROUND_HALF_EVEN +from decimal import Decimal """ Surface Tension Coefficient Calculator (Pull-off Method) diff --git a/Thermal conductivity.py b/Thermal conductivity.py new file mode 100644 index 0000000..344fc57 --- /dev/null +++ b/Thermal conductivity.py @@ -0,0 +1,471 @@ +import math +from decimal import Decimal + +""" +Thermal Conductivity & Specific Heat Calculator (Steady-State Plate Method) +导热系数与比热容计算器 (稳态平板法 — 一维无限大平板) + +实验原理: + 利用稳态平板法测量不良导体的导热系数。 + 当加热板和样品达到热平衡（稳态）时，通过样品的热流密度 q_c 等于 + 样品两面温差 ΔT 除以厚度 R 再乘以导热系数 λ。 + 断电后由冷却曲线斜率计算样品比热容 c。 + +核心公式: + 1. 热流密度: + q_c = V² / (2 · F · r) + 其中 V = 加热电压, F = 有效加热面积, r = 加热电阻 + + 2. 导热系数: + λ = q_c · R / (2 · ΔT) + 其中 R = 样品厚度, ΔT = 加热面温度 - 中心面温度 + + 3. 温度转换 (热电偶): + ΔT = ΔU / S + 其中 S = 热电偶灵敏度系数 (mV/K), ΔU = U_加热面 - U_中心面 + + 4. 比热容 (冷却法): + c = q_c · F / (m · |κ|) + 其中 m = 样品质量, κ = dT/dτ|_冷却 为冷却曲线在稳态温度处的斜率 + + 5. 不确定度传递 — 导热系数 λ = V²·R / (4·F·r·ΔT): + u_r(λ) = √[ (2·u_V/V)² + (u_R/R)² + (u_F/F)² + (u_r/r)² + (u_ΔT/ΔT)² ] + u(ΔU) 取稳态区间多点的 A 类 + 仪器 B 类合成; u_r(ΔT) ≈ u(ΔU)/|ΔU| + + 6. 不确定度传递 — 比热容 c = V² / (2·r·m·|κ|): + u_r(c) = √[ (2·u_V/V)² + (u_r/r)² + (u_m/m)² + (u_κ/|κ|)² ] + u_κ 由冷却曲线线性拟合的斜率标准差给出 +""" + +from utils import ( + scientific_round, + calculate_stats, + input_data_group, + linear_regression +) + + +# ────────────────────────────────────────────── +# 数据输入辅助函数 +# ────────────────────────────────────────────── + +def input_voltage_series(name, n_points=18): + """输入 1~n_points 分钟的电压数据 (单位: uV)""" + print(f"\n请输入 {name} 的 {n_points} 个电压值 (uV), 可用空格/逗号分隔一次输入:") + + data = [] + while len(data) < n_points: + remaining = n_points - len(data) + try: + raw = input(f" [{len(data)+1}~{len(data)+remaining}] > ").strip() + if not raw: + continue + tokens = raw.replace(',', ' ').split() + for tok in tokens: + data.append(Decimal(tok)) + if len(data) >= n_points: + break + except Exception: + print(" 输入无效，请重新输入。") + + return data + + +# ────────────────────────────────────────────── +# 稳态判断 +# ────────────────────────────────────────────── + +def find_steady_state(voltages, window=3, threshold=Decimal("0.5")): + """ + 判断电压序列何时达到稳态。 + 使用滑动窗口：当连续 window 个读数的极差 < threshold (uV) 时认为稳态。 + 返回稳态起始索引（从 0 开始），若未达到稳态则返回最后 window 个的起始。 + """ + for i in range(len(voltages) - window + 1): + w = voltages[i:i + window] + if max(w) - min(w) < threshold: + return i + return len(voltages) - window + + +# ────────────────────────────────────────────── +# 核心计算函数 +# ────────────────────────────────────────────── + +def compute_thermal_conductivity( + center_uV, # 中心面电压序列 (uV) + heating_uV, # 加热面电压序列 (uV) + V_heat, # 加热电压 (V) + F, # 有效加热面积 (m²) + r, # 加热电阻 (Ω) + R_thickness, # 样品厚度 (m) + S_sensitivity, # 热电偶灵敏度 (mV/K) + material_name="" # 材料名称 + ): + """计算单一材料的导热系数，并保留稳态 ΔU 列表供不确定度分析使用""" + + n = len(center_uV) + time_min = list(range(1, n + 1)) # 1 ~ n 分钟 + + # --- 1. 转换为温度差 ΔT(t) --- + delta_uV = [heating_uV[i] - center_uV[i] for i in range(n)] + delta_T = [dv / S_sensitivity for dv in delta_uV] + + # --- 2. 判断稳态 --- + ss_idx_center = find_steady_state(center_uV) + ss_idx_heating = find_steady_state(heating_uV) + ss_idx = max(ss_idx_center, ss_idx_heating) + + # 稳态区间 ΔU 列表（A 类不确定度来源） + steady_delta_uV = delta_uV[ss_idx:] + delta_T_steady = sum(steady_delta_uV) / Decimal(len(steady_delta_uV)) / S_sensitivity + + center_steady_avg = sum(center_uV[ss_idx:]) / Decimal(len(center_uV[ss_idx:])) + heating_steady_avg = sum(heating_uV[ss_idx:]) / Decimal(len(heating_uV[ss_idx:])) + + # --- 3. 热流密度 q_c --- + q_c = V_heat ** 2 / (Decimal("2") * F * r) + + # --- 4. 导热系数 λ --- + lam = q_c * R_thickness / (Decimal("2") * delta_T_steady) + + # --- 5. 加热趋近速率 dT/dτ (用于验证是否达到稳态) --- + if n >= 3: + last_n = min(5, n) + x_fit = [Decimal(str(t * 60)) for t in time_min[-last_n:]] # 秒 + y_fit = [center_uV[i] / S_sensitivity for i in range(-last_n, 0)] # K (相对) + dT_dtau, _, _, _ = linear_regression(x_fit, y_fit) # K/s + else: + dT_dtau = Decimal("0") + + return { + "material": material_name, + "q_c": q_c, + "delta_T_steady": delta_T_steady, + "lambda": lam, + "ss_start_min": ss_idx + 1, + "center_steady_uV": center_steady_avg, + "heating_steady_uV": heating_steady_avg, + "dT_dtau": dT_dtau, + "time_min": time_min, + "center_uV": center_uV, + "heating_uV": heating_uV, + "delta_uV": delta_uV, + "delta_T": delta_T, + "steady_delta_uV": steady_delta_uV, # 稳态区间 ΔU 列表，供不确定度分析使用 + } + + +def compute_specific_heat(cooling_uV, S_sensitivity, q_c, F, m_sample): + """ + 由冷却曲线计算比热容 c。 + + cooling_uV : 断电后中心面电压序列 (uV), 每隔 60 s 一个点 + S_sensitivity: 热电偶灵敏度 (mV/K) + q_c : 热流密度 (W/m²) + F : 有效加热面积 (m²) + m_sample : 样品质量 (kg) + + 返回: (c, dT_dtau_cool, u_dTdtau) + c — 比热容 J/(kg·K) + dT_dtau_cool — 冷却速率绝对值 |κ| (K/s) + u_dTdtau — |κ| 的不确定度 (K/s), 由线性拟合给出 + """ + n = len(cooling_uV) + x_cool = [Decimal(str(i * 60)) for i in range(n)] # 秒 + y_cool = [uv / S_sensitivity for uv in cooling_uV] # 相对温度 (K) + + k, _, _, u_k = linear_regression(x_cool, y_cool) + dT_dtau_cool = abs(k) # 冷却时斜率为负，取绝对值 + u_dTdtau = abs(u_k) + + c = (q_c * F / (m_sample * dT_dtau_cool)) if dT_dtau_cool != 0 else Decimal("0") + return c, dT_dtau_cool, u_dTdtau + + +def compute_uncertainties( + result, # dict from compute_thermal_conductivity + dT_dtau_cool, # 冷却速率 |κ| (K/s, Decimal, 已取绝对值) + u_dTdtau, # |κ| 的不确定度 (K/s) + m_sample, # 样品质量 (kg) + delta_m, # 质量仪器误差 (kg) + V_heat, delta_V, # 加热电压及仪器误差 (V) + F, delta_F, # 面积及仪器误差 (m²) + r, delta_r, # 电阻及仪器误差 (Ω) + R_thickness, delta_R, # 厚度及仪器误差 (m) + delta_uV_inst, # 电压表仪器误差 (uV) + S_sensitivity, # 热电偶灵敏度 (mV/K, 预留接口，暂不计入不确定度) + ): + """ + 计算导热系数 λ 和比热容 c 的合成不确定度。 + + λ = V²·R / (4·F·r·ΔT) + u_r(λ) = √[ (2·u_V/V)² + (u_R/R)² + (u_F/F)² + (u_r/r)² + (u_ΔT/ΔT)² ] + u(ΔU): 稳态区间多点的 A 类 + 仪器 B 类合成; u_r(ΔT) ≈ u(ΔU)/|ΔU_mean| + + c = V² / (2·r·m·|κ|) + u_r(c) = √[ (2·u_V/V)² + (u_r/r)² + (u_m/m)² + (u_κ/|κ|)² ] + u_κ 来自冷却曲线线性拟合 + """ + sqrt3 = Decimal(str(math.sqrt(3))) + lam = result["lambda"] + q_c = result["q_c"] + + # --- u(ΔU): A 类 + B 类 --- + steady_delta_uV = result["steady_delta_uV"] + delta_U_mean, u_delta_U, u_a_dU, u_b_dU, _ = calculate_stats( + steady_delta_uV, delta_uV_inst + ) + # u_r(ΔT) ≈ u(ΔU) / |ΔU_mean|，忽略 S 的不确定度 + ur_deltaT = (u_delta_U / abs(delta_U_mean)) if delta_U_mean != 0 else Decimal("0") + + # --- 单次测量的 B 类相对不确定度 --- + ur_V = (delta_V / sqrt3) / V_heat + ur_F = (delta_F / sqrt3) / F + ur_r = (delta_r / sqrt3) / r + ur_R = (delta_R / sqrt3) / R_thickness + ur_m = (delta_m / sqrt3) / m_sample + + # --- u_r(λ) --- + ur_lam_sq = (Decimal("2") * ur_V)**2 + ur_R**2 + ur_F**2 + ur_r**2 + ur_deltaT**2 + ur_lam = Decimal(str(math.sqrt(float(ur_lam_sq)))) + u_lam = lam * ur_lam + + # --- u_r(c) --- + ur_cool = (u_dTdtau / dT_dtau_cool) if dT_dtau_cool != 0 else Decimal("0") + ur_c_sq = (Decimal("2") * ur_V)**2 + ur_r**2 + ur_m**2 + ur_cool**2 + ur_c = Decimal(str(math.sqrt(float(ur_c_sq)))) + + c_val = (q_c * F / (m_sample * dT_dtau_cool)) if dT_dtau_cool != 0 else Decimal("0") + u_c = c_val * ur_c + + return { + "u_lam": u_lam, + "ur_lam": ur_lam, + "u_c": u_c, + "ur_c": ur_c, + "delta_U_mean": delta_U_mean, + "u_delta_U": u_delta_U, + "u_a_dU": u_a_dU, + "u_b_dU": u_b_dU, + "ur_deltaT": ur_deltaT, + "ur_V": ur_V, + "ur_F": ur_F, + "ur_r": ur_r, + "ur_R": ur_R, + "ur_m": ur_m, + "ur_cool": ur_cool, + } + + +# ────────────────────────────────────────────── +# 输出函数 +# ────────────────────────────────────────────── + +def print_data_table(result, S): + """打印加热阶段数据表格""" + n = len(result["time_min"]) + print(f"\n{'时间(min)':>10} {'中心面(uV)':>12} {'加热面(uV)':>12} {'ΔU(uV)':>10} {'ΔT(K)':>10}") + print("-" * 60) + for i in range(n): + t = result["time_min"][i] + uc = result["center_uV"][i] + uh = result["heating_uV"][i] + du = result["delta_uV"][i] + dt = result["delta_T"][i] + marker = " ← 稳态起始" if t == result["ss_start_min"] else "" + print(f"{t:>10} {uc:>12} {uh:>12} {du:>10} {float(dt):>10.2f}{marker}") + + +def print_full_result(result, c_val, dT_dtau_cool, u_result): + """打印含不确定度的完整计算结果""" + lam = result["lambda"] + lam_final, u_lam_final = scientific_round(lam, u_result["u_lam"]) + c_final, u_c_final = scientific_round(c_val, u_result["u_c"]) + + W = 58 + print(f"\n{'='*W}") + print(f" {result['material']} — 计算结果") + print(f"{'='*W}") + print(f" 稳态起始时间 = 第 {result['ss_start_min']} 分钟") + print(f" 稳态温差 ΔT = {float(result['delta_T_steady']):.4f} K") + print(f" 加热趋近速率 dT/dτ = {float(result['dT_dtau']):.6f} K/s") + print(f" 冷却速率 |κ| = |dT/dτ| = {float(dT_dtau_cool):.6f} K/s") + print(f" 热流密度 q_c = {float(result['q_c']):.4f} W/m²") + print(f"-" * W) + print(f" 稳态 ΔU (均值) = {float(u_result['delta_U_mean']):.3f} uV") + print(f" u_A(ΔU) = {float(u_result['u_a_dU']):.4f} uV") + print(f" u_B(ΔU) = {float(u_result['u_b_dU']):.4f} uV") + print(f" u(ΔU) = {float(u_result['u_delta_U']):.4f} uV") + print(f"-" * W) + print(f" 不确定度贡献 (相对):") + print(f" u_r(V) = {float(u_result['ur_V'])*100:6.3f}% (λ & c 共用)") + print(f" u_r(F) = {float(u_result['ur_F'])*100:6.3f}% (λ)") + print(f" u_r(r) = {float(u_result['ur_r'])*100:6.3f}% (λ & c 共用)") + print(f" u_r(R) = {float(u_result['ur_R'])*100:6.3f}% (λ)") + print(f" u_r(ΔT) = {float(u_result['ur_deltaT'])*100:6.3f}% (λ)") + print(f" u_r(m) = {float(u_result['ur_m'])*100:6.3f}% (c)") + print(f" u_r(κ) = {float(u_result['ur_cool'])*100:6.3f}% (c)") + print(f"-" * W) + print(f" u_r(λ) = {float(u_result['ur_lam'])*100:.2f}% → u(λ) = {float(u_result['u_lam']):.6f} W/(m·K)") + print(f" u_r(c) = {float(u_result['ur_c'])*100:.2f}% → u(c) = {float(u_result['u_c']):.2f} J/(kg·K)") + print(f"{'='*W}") + print(f" ★ 导热系数 λ = ({lam_final} ± {u_lam_final}) W/(m·K)") + print(f" ★ 比热容 c = ({c_final} ± {u_c_final}) J/(kg·K)") + print(f"{'='*W}") + + +# ────────────────────────────────────────────── +# 主程序 +# ────────────────────────────────────────────── + +def main(): + # --- 1. 实验参数设置 --- + W = 58 + print("=" * W) + print(" 导热系数 & 比热容计算 (稳态平板法 — 一维无限大平板)") + print("=" * W) + + # 默认实验参数 + V_HEAT_DEFAULT = "18.00" # 加热电压 (V) + F_DEFAULT = "0.006885" # 有效加热面积 = 0.85 × 0.09 × 0.09 (m²) + R_RESISTANCE_DEFAULT = "110" # 加热电阻 (Ω) + R_THICKNESS_DEFAULT = "0.01" # 样品厚度 (m) + S_SENSITIVITY_DEFAULT = "0.04" # 热电偶灵敏度 (mV/K) + N_POINTS_DEFAULT = 18 # 加热段数据点数 + N_COOL_DEFAULT = 5 # 冷却段数据点数 + + print(f"\n--- 实验参数 (按 Enter 使用默认值) ---") + + V_heat = Decimal(input(f"加热电压 V (V, 默认 {V_HEAT_DEFAULT}): ").strip() or V_HEAT_DEFAULT) + + F_input = input(f"有效加热面积 F (m², 默认 {F_DEFAULT} = 0.85×0.09×0.09): ").strip() + F = Decimal(F_input) if F_input else Decimal(F_DEFAULT) + + r_input = input(f"加热电阻 r (Ω, 默认 {R_RESISTANCE_DEFAULT}): ").strip() + r = Decimal(r_input) if r_input else Decimal(R_RESISTANCE_DEFAULT) + + R_input = input(f"样品厚度 R (m, 默认 {R_THICKNESS_DEFAULT}): ").strip() + R_thickness = Decimal(R_input) if R_input else Decimal(R_THICKNESS_DEFAULT) + + S_input = input(f"热电偶灵敏度 S (mV/K, 默认 {S_SENSITIVITY_DEFAULT}): ").strip() + S = Decimal(S_input) if S_input else Decimal(S_SENSITIVITY_DEFAULT) + + n_input = input(f"加热段数据点数 (默认 {N_POINTS_DEFAULT}): ").strip() + n_points = int(n_input) if n_input else N_POINTS_DEFAULT + + n_cool_input = input(f"冷却段数据点数 (默认 {N_COOL_DEFAULT}): ").strip() + n_cool = int(n_cool_input) if n_cool_input else N_COOL_DEFAULT + + # --- 2. 仪器误差输入 --- + print(f"\n--- 仪器误差 (按 Enter 使用默认值) ---") + delta_V = Decimal(input(" 加热电压仪器误差 δV (V, 默认 0.01): ").strip() or "0.01") + delta_F = Decimal(input(" 面积仪器误差 δF (m², 默认 0.00001): ").strip() or "0.00001") + delta_r = Decimal(input(" 电阻仪器误差 δr (Ω, 默认 0.1): ").strip() or "0.1") + delta_R = Decimal(input(" 厚度仪器误差 δR (m, 默认 0.0001): ").strip() or "0.0001") + delta_uV = Decimal(input(" 电压表仪器误差 δU (uV, 默认 2.0): ").strip() or "2.0") + + # --- 3. 逐材料数据输入 --- + # 默认密度 (kg/m³); 样品为两块相同材料叠放 + materials = [ + ("橡胶 (Rubber)", Decimal("1374")), + ("有机玻璃 (PMMA)", Decimal("1196")), + ] + results = [] + extra_data = [] + + for mat_name, rho_default in materials: + print(f"\n{'#'*W}") + print(f" 材料: {mat_name}") + print(f"{'#'*W}") + + # 加热阶段电压 + center_uV = input_voltage_series(f"{mat_name} — 中心面电压 (加热阶段)", n_points) + heating_uV = input_voltage_series(f"{mat_name} — 加热面电压 (加热阶段)", n_points) + + result = compute_thermal_conductivity( + center_uV=center_uV, + heating_uV=heating_uV, + V_heat=V_heat, + F=F, + r=r, + R_thickness=R_thickness, + S_sensitivity=S, + material_name=mat_name + ) + + print_data_table(result, S) + + # 比热容测量 (冷却法) — 质量由密度与几何尺寸推算 + print(f"\n--- {mat_name} — 比热容测量 (冷却法) ---") + rho_str = input(f" 材料密度 ρ (kg/m³, 默认 {rho_default}): ").strip() + rho = Decimal(rho_str) if rho_str else rho_default + # 两块样品叠放: m = 2 × ρ × F × R + m_sample = Decimal("2") * rho * F * R_thickness + print(f" → 样品质量 m = 2 × {rho} × {F} × {R_thickness} = {float(m_sample):.6f} kg") + # δm 由 δF、δR 传递: u_r(m) = √[(u_F/F)² + (u_R/R)²], delta_m_eff = m·√[(δF/F)²+(δR/R)²] + delta_m = m_sample * Decimal(str(math.sqrt( + float((delta_F / F)**2 + (delta_R / R_thickness)**2) + ))) + + # 冷却段中心面电压采用加热段中心面电压的最后几项反向填充（即从稳态开始降温） + cooling_uV = list(reversed(center_uV[-n_cool:])) + print(f" → 冷却阶段中心面电压 (反向填充自加热段): {[float(x) for x in cooling_uV]} uV") + + results.append(result) + extra_data.append({"m_sample": m_sample, "delta_m": delta_m, "cooling_uV": cooling_uV}) + + # --- 4. 汇总计算与输出 --- + print("\n" + "=" * W) + print(" 汇 总 结 果") + print("=" * W) + + q_c = results[0]["q_c"] + print(f"\n 加热电压 V = {V_heat} V") + print(f" 有效面积 F = {F} m²") + print(f" 加热电阻 r = {r} Ω") + print(f" 样品厚度 R = {R_thickness} m") + print(f" 热电偶灵敏度 S = {S} mV/K") + print(f" 热流密度 q_c = V²/(2·F·r) = {float(q_c):.4f} W/m²") + + for res, extra in zip(results, extra_data): + m_sample = extra["m_sample"] + delta_m = extra["delta_m"] + cooling_uV = extra["cooling_uV"] + + c_val, dT_dtau_cool, u_dTdtau = compute_specific_heat( + cooling_uV=cooling_uV, + S_sensitivity=S, + q_c=res["q_c"], + F=F, + m_sample=m_sample, + ) + + u_result = compute_uncertainties( + result=res, + dT_dtau_cool=dT_dtau_cool, + u_dTdtau=u_dTdtau, + m_sample=m_sample, + delta_m=delta_m, + V_heat=V_heat, delta_V=delta_V, + F=F, delta_F=delta_F, + r=r, delta_r=delta_r, + R_thickness=R_thickness, delta_R=delta_R, + delta_uV_inst=delta_uV, + S_sensitivity=S, + ) + + print_full_result(res, c_val, dT_dtau_cool, u_result) + + # --- 5. 参考值对比 --- + print("\n" + "-" * W) + print(" 参考值 (室温):") + print(f" 橡胶: λ ≈ 0.13–0.16 W/(m·K), c ≈ 1000–2000 J/(kg·K)") + print(f" PMMA: λ ≈ 0.17–0.25 W/(m·K), c ≈ 1400–1500 J/(kg·K)") + print("-" * W) + + input("\n按 Enter 退出...") + + +if __name__ == "__main__": + main() diff --git a/Viscosity coefficient.py b/Viscosity coefficient.py index 5b36fd1..5686b8d 100644 --- a/Viscosity coefficient.py +++ b/Viscosity coefficient.py @@ -1,5 +1,5 @@ import math -from decimal import Decimal, ROUND_HALF_EVEN +from decimal import Decimal """ Viscosity Coefficient Calculator (Stokes' Law) diff --git a/Young's modulus.py b/Young's modulus.py index 22945c5..1ba01c6 100644 --- a/Young's modulus.py +++ b/Young's modulus.py @@ -1,5 +1,5 @@ import math -from decimal import Decimal, ROUND_HALF_EVEN +from decimal import Decimal """ Young's Modulus Calculator (Optical Lever & Successive Difference Method) diff --git a/degree.py b/degree.py index 7add66f..30268b7 100644 --- a/degree.py +++ b/degree.py @@ -1,5 +1,5 @@ import math -from decimal import Decimal, ROUND_HALF_EVEN +from decimal import Decimal from utils import ( parse_angle_to_minutes,