美国数学建模竞赛翻译名词英汉表

Aabsolute value 绝对值accept 接受acceptable region 接受域additivity 可加性adjusted 调整的alternative hypothesis 对立假设analysis 分析analysis of covariance 协方差分析analysis of variance 方差分析arithmetic mean 算术平均值association 相关性assumption 假设assumption checking 假设检验availability 有效度average 均值Bbalanced 平衡的band 带宽bar chart 条形图beta-distribution 贝塔分布between groups 组间的bias 偏倚binomial distribution 二项分布binomial test 二项检验Ccalculate 计算case 个案category 类别center of gravity 重心central tendency 中心趋势chi-square distribution 卡方分布chi-square test 卡方检验classify 分类cluster analysis 聚类分析coefficient 系数coefficient of correlation 相关系数collinearity 共线性column 列compare 比较comparison 对照components 构成，分量compound 复合的confidence interval 置信区间consistency 一致性constant 常数continuous variable 连续变量control charts 控制图correlation 相关covariance 协方差covariance matrix 协方差矩阵critical point 临界点critical value 临界值crosstab 列联表cubic 三次的，立方的cubic term 三次项cumulative distributionfunction 累加分布函数curve estimation 曲线估计Ddata 数据default 默认的definition 定义deleted residual 剔除残差density function 密度函数dependent variable 因变量description 描述design of experiment 试验设计deviations 差异df.(degree of freedom) 自由度diagnostic 诊断dimension 维discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析distance 距离distribution 分布D-optimal design D-优化设计Eeaqual 相等effects of interaction 交互效应efficiency 有效性eigenvalue 特征值equal size 等含量equation 方程error 误差estimate 估计estimation of parameters参数估计estimations 估计量evaluate 衡量exact value 精确值expectation 期望expected value 期望值exponential 指数的exponential distributon 指数分布extreme value 极值Ffactor 因素，因子factor analysis 因子分析factor score 因子得分factorial designs 析因设计factorial experiment 析因试验fit 拟合fitted line 拟合线fitted value 拟合值fixed model 固定模型fixed variable 固定变量fractional factorial design部分析因设计frequency 频数F-test F检验full factorial design 完全析因设计function 函数Ggamma distribution 伽玛分布geometric mean 几何均值group 组Hharmomic mean 调和均值heterogeneity 不齐性histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性hypothesis 假设hypothesis test 假设检验Iindependence 独立independent variable 自变量independent-samples 独立样本index 指数index of correlation 相关指数interaction 交互作用interclass correlation 组内相关interval estimate 区间估计intraclass correlation 组间相关inverse 倒数的iterate 迭代Kkernal 核Kolmogorov-Smirnov test 柯尔莫哥洛夫-斯米诺夫检验kurtosis 峰度Llarge sample problem 大样本问题layer 层least-significant difference 最小显著差数least-square estimation 最小二乘估计least-square method 最小二乘法level 水平level of significance 显著性水平leverage value 中心化杠杆值life 寿命life test 寿命试验likelihood function 似然函数likelihood ratio test 似然比检验linear 线性的linear estimator 线性估计linear model 线性模型linear regression 线性回归linear relation 线性关系linear term 线性项logarithmic 对数的logarithms 对数logistic 逻辑的lost function 损失函数Mmain effect 主效应matrix 矩阵maximum 最大值maximum likelihoodestimation 极大似然估计mean squareddeviation(MSD) 均方差mean sum of square 均方和measure 衡量media 中位数M-estimator M估计minimum 最小值missing values 缺失值mixed model 混合模型mode 众数model 模型Monte Carle method 蒙特卡罗法moving average 移动平均值multicollinearity 多元共线性multiple comparison 多重比较multiple correlation 多重相关multiple correlationcoefficient 复相关系数multiple correlationcoefficient 多元相关系数multiple regression analysis多元回归分析multiple regressionequation 多元回归方程multiple response 多响应multivariate analysis 多元分析Nnegative relationship 负相关nonadditively 不可加性nonlinear 非线性nonlinear regression 非线性回归noparametric tests 非参数检验normal distribution 正态分布null hypothesis 零假设number of cases 个案数Oone-sample 单样本one-tailed test 单侧检验one-way ANOVA 单向方差分析one-way classification 单向分类optimal 优化的optimum allocation 最优配制order 排序order statistics 次序统计量origin 原点orthogonal 正交的outliers 异常值Ppaired observations 成对观测数据paired-sample 成对样本parameter 参数parameter estimation 参数估计partial correlation 偏相关partial correlation coefficient 偏相关系数partial regression coefficient 偏回归系数percent 百分数percentiles 百分位数pie chart 饼图point estimate 点估计poisson distribution 泊松分布polynomial curve 多项式曲线polynomial regression 多项式回归polynomials 多项式positive relationship 正相关power 幂P-P plot P-P概率图predict 预测predicted value 预测值prediction intervals 预测区间principal component analysis 主成分分析proability 概率probability density function 概率密度函数probit analysis 概率分析proportion 比例Qqadratic 二次的Q-Q plot Q-Q概率图quadratic term 二次项quality control 质量控制quantitative 数量的，度量的quartiles 四分位数Rrandom 随机的random number 随机数random number 随机数random sampling 随机取样random seed 随机数种子random variable 随机变量randomization 随机化range 极差rank 秩rank correlation 秩相关rank statistic 秩统计量regression analysis 回归分析regression coefficient 回归系数regression line 回归线reject 拒绝rejection region 拒绝域relationship 关系reliability 可靠性repeated 重复的report 报告，报表residual 残差residual sum of squares 剩余平方和response 响应risk function 风险函数robustness 稳健性root mean square 标准差row 行run 游程run test 游程检验Ssample 样本sample size 样本容量sample space 样本空间sampling 取样sampling inspection 抽样检验scatter chart 散点图S-curve S形曲线separately 单独地sets 集合sign test 符号检验significance 显著性significance level 显著性水平significance testing 显著性检验significant 显著的，有效的significant digits 有效数字skewed distribution 偏态分布skewness 偏度small sample problem 小样本问题smooth 平滑sort 排序soruces of variation 方差来源space 空间spread 扩展square 平方standard deviation 标准离差standard error of mean 均值的标准误差standardization 标准化standardize 标准化statistic 统计量statistical quality control 统计质量控制std. residual 标准残差stepwise regressionanalysis 逐步回归stimulus 刺激strong assumption 强假设stud. deleted residual 学生化剔除残差stud. residual 学生化残差subsamples 次级样本sufficient statistic 充分统计量sum 和sum of squares 平方和summary 概括，综述Ttable 表t-distribution t分布test 检验test criterion 检验判据test for linearity 线性检验test of goodness of fit 拟合优度检验test of homogeneity 齐性检验test of independence 独立性检验test rules 检验法则test statistics 检验统计量testing function 检验函数time series 时间序列tolerance limits 容许限total 总共，和transformation 转换treatment 处理trimmed mean 截尾均值true value 真值t-test t检验two-tailed test 双侧检验Uunbalanced 不平衡的unbiased estimation 无偏估计unbiasedness 无偏性uniform distribution 均匀分布Vvalue of estimator 估计值variable 变量variance 方差variance components 方差分量variance ratio 方差比various 不同的vector 向量Wweight 加权，权重weighted average 加权平均值within groups 组内的ZZ score Z分数Ⅱ.2 最优化方法词汇英汉对照表Aactive constraint 活动约束active set method 活动集法analytic gradient 解析梯度approximate 近似arbitrary 强制性的argument 变量attainment factor 达到因子Bbandwidth 带宽be equivalent to 等价于best-fit 最佳拟合bound 边界Ccoefficient 系数complex-value 复数值component 分量constant 常数constrained 有约束的constraint 约束constraint function 约束函数continuous 连续的converge 收敛cubic polynomialinterpolation method三次多项式插值法curve-fitting 曲线拟合Ddata-fitting 数据拟合default 默认的，默认的define 定义diagonal 对角的direct search method 直接搜索法direction of search 搜索方向discontinuous 不连续Eeigenvalue 特征值empty matrix 空矩阵equality 等式exceeded 溢出的Ffeasible 可行的feasible solution 可行解finite-difference 有限差分first-order 一阶GGauss-Newton method 高斯-牛顿法goal attainment problem 目标达到问题gradient 梯度gradient method 梯度法Hhandle 句柄Hessian matrix 海色矩阵Iindependent variables 独立变量inequality 不等式infeasibility 不可行性infeasible 不可行的initial feasible solution 初始可行解initialize 初始化inverse 逆invoke 激活iteration 迭代iteration 迭代JJacobian 雅可比矩阵LLagrange multiplier 拉格朗日乘子large-scale 大型的least square 最小二乘least squares sense 最小二乘意义上的Levenberg-Marquardtmethod列文伯格-马夸尔特法line search 一维搜索linear 线性的linear equality constraints线性等式约束linear programmingproblem 线性规划问题local solution 局部解Mmedium-scale 中型的minimize 最小化mixed quadratic and cubic polynomial interpolation and extrapolation method 混合二次、三次多项式内插、外插法multiobjective 多目标的Nnonlinear 非线性的norm 范数Oobjective function 目标函数observed data 测量数据optimization routine 优化过程optimize 优化optimizer 求解器over-determined system 超定系统Pparameter 参数partial derivatives 偏导数polynomial interpolation method多项式插值法Qquadratic 二次的quadratic interpolation method 二次内插法quadratic programming 二次规划Rreal-value 实数值residuals 残差robust 稳健的robustness 稳健性，鲁棒性Sscalar 标量semi-infinitely problem 半无限问题Sequential Quadratic Programming method序列二次规划法simplex search method 单纯形法solution 解sparse matrix 稀疏矩阵sparsity pattern 稀疏模式sparsity structure 稀疏结构starting point 初始点step length 步长subspace trust regionmethod 子空间置信域法sum-of-squares 平方和symmetric matrix 对称矩阵Ttermination message 终止信息termination tolerance 终止容限the exit condition 退出条件the method of steepestdescent 最速下降法transpose 转置Uunconstrained 无约束的under-determined system负定系统Vvariable 变量vector 矢量Wweighting matrix 加权矩阵Ⅱ.3 样条词汇英汉对照表Aapproximation 逼近array 数组a spline in b-form/b-splineb样条a spline of polynomial piece/ppform spline分段多项式样条Bbivariate spline function 二元样条函数break/breaks 断点Ccoefficient/coefficients 系数cubic interpolation 三次插值/三次内插cubic polynomial 三次多项式cubic smoothing spline 三次平滑样条cubic spline 三次样条cubic spline interpolation三次样条插值/三次样条内插curve 曲线Ddegree of freedom 自由度dimension 维数Eend conditions 约束条件Iinput argument 输入参数interpolation 插值/内插interval 取值区间Kknot/knots 节点Lleast-squaresapproximation 最小二乘拟合Mmultiplicity 重次multivariate function 多元函数Ooptional argument 可选参数order 阶次output argument 输出参数Ppoint/points 数据点Rrational spline 有理样条rounding error 舍入误差（相对误差）Sscalar 标量sequence 数列（数组）spline 样条spline approximation 样条逼近/样条拟合spline function 样条函数spline curve 样条曲线spline interpolation 样条插值/样条内插spline surface 样条曲面smoothing spline 平滑样条Ttolerance 允许精度Uunivariate function 一元函数Vvector 向量Wweight/weights 权重Ⅱ.4 偏微分方程数值解词汇英汉对照表Aabsolute error 绝对误差absolute tolerance 绝对容限adaptive mesh 适应性网格Bboundary condition 边界条件Ccontour plot 等值线图converge 收敛coordinate 坐标系Ddecomposed 分解的decomposed geometry matrix 分解几何矩阵diagonal matrix 对角矩阵Dirichlet boundary conditionsDirichlet边界条件Eeigenvalue 特征值elliptic 椭圆形的error estimate 误差估计exact solution 精确解Ggeneralized Neumann boundary condition推广的Neumann边界条件geometry 几何形状geometry descriptionmatrix 几何描述矩阵geometry matrix 几何矩阵graphical user interface（GUI）图形用户界面Hhyperbolic 双曲线的Iinitial mesh 初始网格Jjiggle 微调LLagrange multipliers 拉格朗日乘子Laplace equation 拉普拉斯方程linear interpolation 线性插值loop 循环Mmachine precision 机器精度mixed boundary condition混合边界条件NNeuman boundarycondition Neuman边界条件node point 节点nonlinear solver 非线性求解器normal vector 法向量PParabolic 抛物线型的partial differential equation偏微分方程plane strain 平面应变plane stress 平面应力Poisson's equation 泊松方程polygon 多边形positive definite 正定Qquality 质量Rrefined triangular mesh 加密的三角形网格relative tolerance 相对容限relative tolerance 相对容限residual 残差residual norm 残差范数Ssingular 奇异的sparce matrix 稀疏矩阵stiffness matrix 刚度矩阵subregion 子域Ttriangular mesh 三角形网格Uundetermined 未定的uniform refinement 均匀加密uniform triangle net 均匀三角形网络Wwave equation 波动方程Algebraic Equation代数方程Elementary Operations-Addition基础混算-加法ElementaryOperations-Subtaction基础混算-减法ElementaryOperations-Multiplication基础混算-乘法Elementary Operations-Division基础混算-除法Elementary Operation基础四则混算Decimal Operations 小数混算Fractional Operations分数混算Convert fractional no. intodecimal no.分数转小数Convert fractional no. intopercentage.分数转百分数Convert decimal no. intopercentage.小数转百分数Convert percentage into decimal no.百分数转小数Percentage百分数Numerals数字符号Common factors and multiples公因子及公倍数Sorting数字排序Area图形面积Perimeter图形周界Change Units : Time单位转换-时间Change Units : Weight 单位转换-重量Change Units :Length单位转换-长度Directed Numbers 有向数Fractional Operations 分数混算Decimal Operations 小数混算Convert fractional no. into decimal no.分数转小数Convert fractional no. into percentage.分数转百分数Convert decimal no. into percentage.小数转百分数Convert percentage into decimal no.百分数转小数Percentage百分数Indices指数Algebraic Substitution 代数代入Polynomials多项式Co-Geometry坐标几何学Solving Linear Equation解一元线性方程Solving Simultaneous Equation解联立方程Slope直线斜率Equation of Straight Line直线方程x-intercept ( Equation of St. Line )直线x轴截距y-intercept ( Equation of St. Line )直线y轴截距Factorization因式分解Quadratic Equation 二次方程x-intercept ( Quadratic Equation )二次曲线x轴截距Geometry几何学Inequalities不等式Rate and Ratio比和比例Bearing方位角Trigonometry三角学Probability概率Statistics-Graph统计学-统计图表Statistics-Measure of centraltendency统计学-量度集中趋势Salary Tax薪俸税Bridging Game汉英对对碰Indices指数Function函数Rate and Ratio比和比例Trigonometry三角学Inequalities不等式Linear Programming线性规划Co-Geometry坐标几何学Slope直线斜率Equation of Straight Line直线方程x-intercept ( Equation of St. Line )直线x轴截距y-intercept ( Equation of St. Line )直线y轴截距Factorization因式分解Quadratic Equation二次方程x-intercept ( Quadratic Equation )二次曲线x轴截距Method of Bisection分半方法Polynomials多项式Probability概率Statistics-Graph统计学-统计图表Statistics-Measure of centraltendency统计学-量度集中趋势Statistics-Measure of dispersion统计学-量度分布Statistics-Normal Distribution统计学-正态分布Surds根式Probability概率Statistics-Measure of dispersion统计学-量度离差Statistics-Normal Distribution统计学-正态分布Statistics-Binomial Distribution统计学Statistics-Poisson Distribution统计学Statistics-Geometric Distribution统计学Co-Geometry坐标几何学Sequence序列十万Hundred thousand三位数3-digit number千Thousand千万Ten million小数Decimal分子Numerator分母Denominator分数Fraction五位数5-digit number公因子Common factor公倍数Common multiple中国数字Chinese numeral平方Square平方根Square root古代计时工具Ancient timingdevice古代记时工具Ancienttime-recording device古代记数方法Ancient countingmethod古代数字Ancient numeral包含Grouping四位数4-digit number四则计算Mixed operations (Thefour operations)加Plus加法Addition加法交换性质Commutativeproperty of addition未知数Unknown百分数Percentage百万Million合成数Composite number多位数Large number因子Factor折扣Discount近似值Approximation阿拉伯数字Hindu-Arabic numeral定价Marked price括号Bracket计算器Calculator差Difference真分数Proper fraction退位Decomposition除Divide除法Division除数Divisor乘Multiply乘法Multiplication乘法交换性质Commutative property of multiplication乘法表Multiplication table乘法结合性质Associative property of multiplication被除数Dividend珠算Computation using Chinese abacus倍数Multiple假分数Improper fraction带分数mixed number现代计算工具Modern calculating devices售价Selling price万Ten thousand最大公因子Highest Common Factor (H.C.F.)最小公倍数Lowest Common Multiple (L.C.M.)减Minus / Subtract减少Decrease减法Subtraction等分Sharing 等于Equal进位Carrying短除法Short division单数Odd number循环小数Recurring decimal零Zero算盘Chinese abacus亿Hundred million增加Increase质数Prime number积Product整除性Divisibility双数Even number罗马数字Roman numeral数学mathematics, maths(BrE),math(AmE)公理axiom定理theorem计算calculation运算operation证明prove假设hypothesis, hypotheses(pl.)命题proposition算术arithmetic加plus(prep.), add(v.),addition(n.)被加数augend, summand加数addend和sum减minus(prep.), subtract(v.),subtraction(n.)被减数minuend减数subtrahend差remainder乘times(prep.), multiply(v.),multiplication(n.)被乘数multiplicand, faciend乘数multiplicator积product除divided by(prep.), divide(v.),division(n.)被除数dividend除数divisor商quotient等于equals, is equal to, isequivalent to大于is greater than小于is lesser than大于等于is equal or greater than小于等于is equal or lesser than运算符operator平均数mean算术平均数arithmatic mean几何平均数geometric mean n个数之积的n次方根倒数（reciprocal）x的倒数为1/x有理数rational number无理数irrational number实数real number虚数imaginary number数字digit数number自然数natural number整数integer小数decimal小数点decimal point分数fraction分子numerator分母denominator比ratio正positive负negative零null, zero, nought, nil十进制decimal system二进制binary system十六进制hexadecimal system权weight, significance进位carry截尾truncation四舍五入round下舍入round down上舍入round up有效数字significant digit无效数字insignificant digit代数algebra公式formula, formulae(pl.)单项式monomial多项式polynomial, multinomial 系数coefficient未知数unknown, x-factor, y-factor, z-factor等式，方程式equation一次方程simple equation二次方程quadratic equation三次方程cubic equation四次方程quartic equation不等式inequation阶乘factorial对数logarithm指数，幂exponent乘方power二次方，平方square三次方，立方cube四次方the power of four, the fourth powern次方the power of n, the nth power开方evolution, extraction二次方根，平方根square root 三次方根，立方根cube root四次方根the root of four, the fourth rootn次方根the root of n, the nth rootsqrt(2)=1.414sqrt(3)=1.732sqrt(5)=2.236常量constant变量variable坐标系coordinates坐标轴x-axis, y-axis, z-axis横坐标x-coordinate纵坐标y-coordinate原点origin象限quadrant截距(有正负之分)intercede（方程的）解solution几何geometry点point线line面plane 体solid线段segment射线radial平行parallel相交intersect角angle角度degree弧度radian锐角acute angle直角right angle钝角obtuse angle平角straight angle周角perigon底base边side高height三角形triangle锐角三角形acute triangle直角三角形right triangle直角边leg斜边hypotenuse勾股定理Pythagorean theorem钝角三角形obtuse triangle不等边三角形scalene triangle等腰三角形isosceles triangle等边三角形equilateral triangle四边形quadrilateral平行四边形parallelogram矩形rectangle长length宽width周长perimeter面积area相似similar全等congruent三角trigonometry正弦sine余弦cosine正切tangent余切cotangent正割secant余割cosecant反正弦arc sine反余弦arc cosine反正切arc tangent反余切arc cotangent反正割arc secant反余割arc cosecant补充：集合aggregate元素element空集void子集subset交集intersection并集union补集complement映射mapping函数function定义域domain, field ofdefinition值域range单调性monotonicity奇偶性parity周期性periodicity图象image数列，级数series微积分calculus微分differential导数derivative极限limit无穷大infinite(a.) infinity(n.)无穷小infinitesimal积分integral定积分definite integral不定积分indefinite integral复数complex number矩阵matrix行列式determinant圆circle圆心centre(BrE), center(AmE)半径radius直径diameter圆周率pi弧arc半圆semicircle扇形sector环ring椭圆ellipse圆周circumference轨迹locus, loca(pl.)平行六面体parallelepiped立方体cube七面体heptahedron八面体octahedron九面体enneahedron十面体decahedron十一面体hendecahedron十二面体dodecahedron二十面体icosahedron多面体polyhedron旋转rotation轴axis球sphere半球hemisphere底面undersurface表面积surface area体积volume空间space双曲线hyperbola抛物线parabola四面体tetrahedron五面体pentahedron六面体hexahedron菱形rhomb, rhombus, rhombi(pl.), diamond正方形square梯形trapezoid直角梯形right trapezoid等腰梯形isosceles trapezoid五边形pentagon六边形hexagon七边形heptagon八边形octagon九边形enneagon十边形decagon十一边形hendecagon十二边形dodecagon多边形polygon正多边形equilateral polygon相位phase周期period振幅amplitude内心incentre(BrE), incenter(AmE)外心excentre(BrE),excenter(AmE)旁心escentre(BrE),escenter(AmE)垂心orthocentre(BrE),orthocenter(AmE)重心barycentre(BrE),barycenter(AmE)内切圆inscribed circle外切圆circumcircle统计statistics平均数average加权平均数weighted average方差variance标准差root-mean-squaredeviation, standard deviation比例propotion百分比percent百分点percentage百分位数percentile排列permutation组合combination概率，或然率probability分布distribution正态分布normal distribution非正态分布abnormaldistribution图表graph条形统计图bar graph柱形统计图histogram折线统计图broken line graph曲线统计图curve diagram扇形统计图pie diagramEnglish Chineseabbreviation 简写符号；简写abscissa 横坐标absolute complement 绝对补集absolute error 绝对误差absolute inequality 绝不等式absolute maximum 绝对极大值absolute minimum 绝对极小值absolute monotonic 绝对单调absolute value 绝对值accelerate 加速acceleration 加速度acceleration due to gravity 重力加速度; 地心加速度accumulation 累积accumulative 累积的accuracy 准确度act on 施于action 作用; 作用力acute angle 锐角acute-angled triangle 锐角三角形add 加addition 加法addition formula 加法公式addition law 加法定律addition law(of probability) （概率）加法定律additive inverse 加法逆元; 加法反元additive property 可加性adjacent angle 邻角adjacent side 邻边adjoint matrix 伴随矩阵algebra 代数algebraic 代数的algebraic equation 代数方程algebraic expression 代数式algebraic fraction 代数分式；代数分数式algebraic inequality 代数不等式algebraic number 代数数algebraic operation 代数运算algebraically closed 代数封闭algorithm 算法系统; 规则系统alternate angle （交）错角alternate segment 内错弓形alternating series 交错级数alternative hypothesis 择一假设;备择假设; 另一假设altitude 高；高度；顶垂线；高线ambiguous case 两义情况；二义情况amount 本利和；总数analysis 分析；解析analytic geometry 解析几何angle 角angle at the centre 圆心角angle at the circumference 圆周角angle between a line and a plane 直 与平面的交角angle between two planes 两平面的交角angle bisection 角平分angle bisector 角平分线 ；分角线angle in the alternate segment 交错弓形的圆周角angle in the same segment 同弓形内的圆周角angle of depression 俯角angle of elevation 仰角angle of friction 静摩擦角; 极限角angle of greatest slope 最大斜率的角angle of inclination 倾斜角angle of intersection 相交角；交角angle of projection 投射角angle of rotation 旋转角angle of the sector 扇形角angle sum of a triangle 三角形内角和angles at a point 同顶角angular displacement 角移位angular momentum 角动量angular motion 角运动angular velocity 角速度annum(X% per annum) 年（年利率X%）anti-clockwise direction 逆时针方向；返时针方向anti-clockwise moment 逆时针力矩anti-derivative 反导数; 反微商anti-logarithm 逆对数；反对数anti-symmetric 反对称apex 顶点approach 接近；趋近approximate value 近似值approximation 近似；略计；逼近Arabic system 阿刺伯数字系统arbitrary 任意arbitrary constant 任意常数arc 弧arc length 弧长arc-cosine function 反余弦函数arc-sin function 反正弦函数arc-tangent function 反正切函数area 面积Argand diagram 阿根图, 阿氏图argument (1)论证; (2)辐角argument of a complex number 复数的辐角argument of a function 函数的自变量arithmetic 算术arithmetic mean 算术平均；等差中顶；算术中顶arithmetic progression 算术级数；等差级数arithmetic sequence 等差序列arithmetic series 等差级数arm 边array 数组; 数组arrow 前号ascending order 递升序ascending powers of X X 的升幂assertion 断语; 断定associative law 结合律assumed mean 假定平均数assumption 假定；假设asymmetrical 非对称asymptote 渐近asymptotic error constant 渐近误差常数at rest 静止augmented matrix 增广矩阵auxiliary angle 辅助角auxiliary circle 辅助圆auxiliary equation 辅助方程average 平均；平均数；平均值average speed 平均速率axiom 公理axiom of existence 存在公理axiom of extension 延伸公理axiom of inclusion 包含公理axiom of pairing 配对公理axiom of power 幂集公理axiom of specification 分类公理axiomatic theory of probability 概率公理论axis 轴axis of parabola 拋物线的轴axis of revolution 旋转轴axis of rotation 旋转轴axis of symmetry 对称轴back substitution 回代bar chart 棒形图；条线图；条形图；线条图base （1）底；（2）基；基数base angle 底角base area 底面base line 底线base number 底数；基数base of logarithm 对数的底basis 基Bayes' theorem 贝叶斯定理bearing 方位（角）；角方向（角）bell-shaped curve 钟形图belong to 属于Bernoulli distribution 伯努利分布Bernoulli trials 伯努利试验bias 偏差；偏倚biconditional 双修件式; 双修件句bijection 对射; 双射; 单满射bijective function 对射函数; 只射函数billion 十亿bimodal distribution 双峰分布binary number 二进数binary operation 二元运算binary scale 二进法binary system 二进制binomial 二项式binomial distribution 二项分布binomial expression 二项式binomial series 二项级数binomial theorem 二项式定理bisect 平分；等分bisection method 分半法；分半方法bisector 等分线 ；平分线Boolean algebra 布尔代数boundary condition 边界条件boundary line 界（线）；边界bounded 有界的bounded above 有上界的；上有界的bounded below 有下界的；下有界的bounded function 有界函数bounded sequence 有界序列brace 大括号bracket 括号breadth 阔度broken line graph 折线图calculation 计算calculator 计算器；计算器calculus (1) 微积分学; (2) 演算cancel 消法；相消canellation law 消去律canonical 典型; 标准capacity 容量cardioid 心脏Cartesian coordinates 笛卡儿坐标Cartesian equation 笛卡儿方程Cartesian plane 笛卡儿平面Cartesian product 笛卡儿积category 类型；范畴catenary 悬链Cauchy sequence 柯西序列Cauchy's principal value 柯西主值Cauchy-Schwarz inequality 柯西- 许瓦尔兹不等式central limit theorem 中心极限定理central line 中线central tendency 集中趋centre 中心；心centre of a circle 圆心centre of gravity 重心centre of mass 质量中心centrifugal force 离心力centripedal acceleration 向心加速度centripedal force force 向心力centroid 形心；距心certain event 必然事件chain rule 链式法则chance 机会change of axes 坐标轴的变换change of base 基的变换change of coordinates 坐标轴的变换change of subject 主项变换change of variable 换元；变量的换characteristic equation 特征(征)方程characteristic function 特征(征)函数characteristic of logarithm 对数的首数; 对数的定位部characteristic root 特征(征)根chart 图；图表check digit 检验数位checking 验算chord 弦chord of contact 切点弦circle 圆circular 圆形；圆的circular function 圆函数；三角函数circular measure 弧度法circular motion 圆周运动circular permutation 环形排列;圆形排列; 循环排列circumcentre 外心；外接圆心circumcircle 外接圆circumference 圆周circumradius 外接圆半径circumscribed circle 外接圆cissoid 蔓叶class 区；组；类class boundary 组界class interval 组区间；组距class limit 组限；区限class mark 组中点；区中点classical theory of probability 古典概率论classification 分类clnometer 测斜仪clockwise direction 顺时针方向clockwise moment 顺时针力矩closed convex region 闭凸区域closed interval 闭区间coaxial 共轴coaxial circles 共轴圆coaxial system 共轴系coded data 编码数据coding method 编码法co-domain 上域coefficient 系数coefficient of friction 摩擦系数coefficient of restitution 碰撞系数; 恢复系数coefficient of variation 变差系数cofactor 余因子; 余因式cofactor matrix 列矩阵coincide 迭合；重合collection of terms 并项collinear 共线collinear planes 共线面collision 碰撞column (1)列；纵行；(2) 柱column matrix 列矩阵column vector 列向量combination 组合common chord 公弦common denominator 同分母；公分母common difference 公差。

1999 MCM A: Deep ImpactFor some time, the National Aeronautics and Space Administration (NASA) has been considering the consequences of a large asteroid impact on the earth. As part of this effort, your team has been asked to consider the effects of such an impact were the asteroid to land in Antarctica. There are concerns that an impact there could have considerably different consequences than one striking elsewhere on the planet.You are to assume that an asteroid is on the order of 1000 m in diameter, and that it strikes the Antarctic continent directly at the South Pole.Your team has been asked to provide an assessment of the impact of such an asteroid. In particular, NASA would like an estimate of the amount and location of likely human casualties from this impact, an estimate of the damage done to the food production regions in the oceans of the southern hemisphere, and an estimate of possible coastal flooding caused by large-scale melting of the Antarctic polar ice sheet.NASA（航空航天管理局）常常考虑这样一个问题：一颗较大的小行星与地球的碰撞将会产生怎样的后果。

美国数学建模题目2017至2017翻译篇一：2017年建模美赛C题带翻译Problem C: “Cooperate and navigate”Traffic capacity is limited in many regions of the United States due to the number of lanes of roads.For example, in the Greater Seattle area drivers experience long delays during peak traffic hoursbecause the volume of traffic exceeds the designed capacity of the road networks. This is particularlypronounced on Interstates 5, 90, and 405, as well as State Route 520, the roads of particular interestfor this problem.Self-driving, cooperating cars have been proposed as a solution to increase capacity of highwayswithout increasing number of lanes or roads. The behavior of these cars interacting with the existingtraffic flow and each other is not well understood at this point.The Governor of the state of Washington has asked for analysis of the effects of allowing self-driving,cooperating cars on the roads listed above in Thurston, Pierce, King, and Snohomish counties. (Seethe provided map and Excel spreadsheet).In particular, how do the effects change as thepercentage of self-driving cars increases from 10% to 50% to 90%? Do equilibria exist? Is there atipping point where performance changes markedly? Under what conditions, if any, should lanes bededicated to these cars? Does your analysis of your model suggest any other policy changes?Your answer should include a model of the effects on traffic flow of the number of lanes, peak and/oraverage traffic volume, and percentage of vehicles using self-driving, cooperating systems. Yourmodel should address cooperation between self-driving cars as well as the interaction between self-driving and non-self-driving vehicles. Your model should then be applied to the data for the roads ofinterest, provided in the attached Excel spreadsheet.Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to theGovernor’s office, and your solution (not to exceed 20 pages) for a maximum of 23 pages. Note: Theappendix and references do not count toward the 23 page limit. Some useful background information:On average, 8% of the daily traffic volume occurs during peak travel hours. ? The nominal speed limit for all these roads is 60 miles per hour.? Mileposts are numbered from south to north, and west to east.? Lane widths are the standard 12 feet.? Highway 90 is classified as a state route until it intersects Interstate 5.? In case of any conflict between the data provided in this problem and any other source, use thedata provided in this problem.Definitions:milepost: A marker on the road that measures distance in miles from either the start of the route or astate boundary.average daily traffic: The average number of cars per day driving on the road.interstate: A limited access highway, part of a national system.state route: A state highway that may or may not be limited access.route ID: The number of the highway.increasing direction: Northbound for N-S roads, Eastbound for E-W roads.decreasing direction: Southbound for N-S roads, Westbound for E-W roads.问题C：“合作和导航”由于道路的数量，美国许多地区的交通容量有限。

2013 MCM ProblemsPROBLEM A: The Ultimate Brownie PanWhen baking in a rectangular（矩形的）pan heat is concentrated（集中）in the 4 corners and the product gets overcooked（焙烧过度）at the corners (and to a lesser extent(较小程度上) at the edges). In a round（圆）pan the heat is distributed evenly（均匀的）over the entire outer edge and the product is not overcooked at the edges. However, since most ovens（烤箱）are rectangular in shape using round pans is not efficient（高效）with respect to（关于）using the space in an oven. Develop a model to show the distribution（分布规律）of heat across the outer edge of a pan for pans of different shapes - rectangular to circular（圆形）and other shapes in between.Assume1. A width to length ratio（···比）of W/L for the oven which is rectangular in shape.2. Each pan must have an area of A.3. Initially two racks in the oven, evenly spaced（均匀分布）.Develop a model that can be used to select the best type of pan (shape) under the following conditions（条件）:1. Maximize number of pans（平底锅）that can fit in the oven (N)2. Maximize even distribution （均匀分布）of heat (H) for the pan3. Optimize（最优化）a combination of （···的综合）conditions (1) and (2) where weights p and (1- p) are assigned to（被分配···）illustrate（阐明）how the results vary with different values of W/L and p.In addition to your MCM formatted solution, prepare a one to two page advertising sheet for the new Brownie Gourmet Magazine highlighting（使··突显出来）your design and results.在矩形烤盘烘焙的时候，热量会被集中到4个角，食物会被烘焙过度（热量较小程度上在边缘）。

Problem c:背景：社会正致力于运用和开发模型来预测地球的生物和环境情况。

很多科学研究总结了逐渐增长的地球环境和生物系统压力，但很少有人用全球范围的模型来检测这些观点。

联合国发表的千年生态系统评估综合报告发现：近三分之二的地球生命支持生态系统——包括净水，洁净的空气，稳定的气候——正在因非可持续性使用而逐渐衰减。

其中大部分破坏归咎于人类行为。

暴增的对于食物，淡水，燃料，木材的需求导致了剧烈的环境变化；从森林砍伐到空气，土壤和水污染。

尽管已存在大量关于局部习惯和地区因素的研究，目前的模型还不能告知决定人他们的局部策略是如何影响整个地球的健康的。

许多模型忽略了复杂的全球因素，这些模型无法判断重大政策的长期影响。

尽管科学家们意识到巨大环境和生物系统中存在的复杂关系和交叉作用，当前的模型通常忽略这些管理或限定了系统间的影响。

系统的复杂性体现在多元交互（多个元素的相关性），反馈，突发行为，即将发生的状态变化或触发点。

最近的自然杂志中一篇由22位国际知名科学家撰写的题为“迫近地球生物圈的状态变化”的文章讨论了许多有关科学模型对于预测行星健康系统潜在状态变化的重要性与必需性。

文章提供了两种具体定性的模型，并寻求更好的预测模型：1）通过在全球模型中加入相关系统的复杂性（包括局部情况对全球系统的影响，反之亦然）来优化生物状态预测。

2）辨别不同因素在产生非健康全球状态变化中的作用并展示如何运用有效的生态系统管理来预防或限制这些即将发生的状态变化。

研究最终归结于问题：我们是否能利用全球健康的局部或地区性组成部分预测潜在状态变化来帮助决策者制定基于对全球健康状况潜在影响的，有效的策略。

尽管有越来越多的警示信号出现，没人知道地球是否确实在接近全球性的转折点（极端状态），这种极端的状态是否是不可避免的。

自然杂志等研究指出了地球生态系统中的一些重要工作元素。

（例如：局部因素，全球变化，多维元素与关系，变化的时间与空间范围）。

2013年美国大学生数学建模竞赛（MCMICM）参赛规则中英文对照2 ICM:The InterdisciplinaryContest in ModelingICM：交叉学科建模竞赛ContestRules, Registration and Instructions比赛规则，报名注册和指导(All rules and instructions apply to both ICM and MCM contests, except where otherwisenoted.)（所有MCM的说明和规则除特别说明以外都适用于ICM）To participate in a contest, each team must be sponsored by a faculty advisor fromits institution.参加MCM的每个队伍需有一名在职的高校老师负责指导。

TeamAdvisors: Please read these instructions carefully. It isyour responsibility to make sure that teams are correctly registered and thatall of the following steps required for participation in the contest arecompleted:Pleaseprint a copy of these contest instructions for reference before, during, andafter the contest. Click here for the printer friendly version.指导老师：请认真阅读这些说明事项，确保完成了所有相关的项。

每位指导教师的责任包括确保每个参赛队正确注册并正确完成参加MCM/ICM所要求的相关步骤。

AMC数学单词表分类（汉英）几何geometry点point线line面plane体solid线段segment射线radial平行parallel相交intersect角angle角度degree弧度radian锐角acute angle直角right angle钝角obtuse angle平角straight angle周角paragon底base边side高height线段line segment长length平行线parallel lines正三角形regular triangle等腰三角形isosceles triangle平行四边形parallelogram n.梯形trapezia n.菱形rhombus正方体，立方体，立方cube n.长方体cuboid adj.圆柱column n.圆锥cone尺寸measure n.，v.半圆semicircle半径radius n. (radii pl.)直径diameter n.表面积surface area多边形polygon凸多边形convex polygon正多边形regular polygon直角right-angle直角三角形right-triangle锐角acute-angle空间space四面体tetrahedron五面体pentahedron六面体hexahedron平行六面体parallelepiped立方体cube七面体heptahedron八面体octahedron九面体enneahedron十面体decahedron十一面体hendecahedron十二面体dodecahedron二十面体icosahedron多面体polyhedron棱锥pyramid棱柱prism棱台frustum of a prism旋转rotation轴axis圆锥cone圆柱cylinder圆台frustum of a cone球sphere半球hemisphere底面undersurface表面积surface area体积volume圆circle圆心centre（BrE），center（AmE）半径radius直径diameter圆周率pi弧arc半圆semicircle扇形sector环ring椭圆ellipse圆周circumference周长perimeter面积area轨迹locus，loci（pl.）相似similar全等congruent三角trigonometry正弦sine余弦cosine正切tangent余切cotangent正割secant余割cosecant反正弦arcsine反余弦arccosine反正切arctangent反余切arccotangent反正割arcsecant反余割arccosecant相位phase周期period振幅amplitude内心incentre（BrE）外心excentre（BrE）旁心escentre（BrE）垂心orthocentre（BrE）重心barycentre（BrE）内切圆inscribedcircle外切圆circumcircle三角形triangle锐角三角形acute triangle直角三角形right triangle直角边leg斜边hypotenuse勾股定理Pythagorean theorem钝角三角形obtuse triangle不等边三角形scalene triangle 等腰三角形isosceles triangle 等边三角形equilateral triangle 四边形quadrilateral平行四边形parallelogram矩形rectangle长length宽width菱形rhomb，rhombus，rhombi（pl.），diamond 正方形square梯形trapezoid直角梯形right trapezoid等腰梯形isosceles trapezoid正多边形equilateral polygon代数 algebra整数integer，whole number小数decimal小数点decimal point分数fraction分子numerator分母denominator比ratio正positive负negative零null，zero，nil十进制decimal system二进制binary system十六进制hexadecimal system权weight，significance进位carry截尾truncation四舍五入round下舍入round down上舍入roundup有效数字significant digit无效数字insignificant digit公式formula，formulae（pl.）单项式monomial多项式polynomial，multinomial系数coefficient数学mathematics，maths（BrE），math（AmE）等于equals，is equal to大于is greater than小于is lesser than大于等于is equal or greater than小于等于is equal or lesser than运算符operator数字digit数number自然数natural number公理axiom定理theorem计算calculation运算operation证明prove假设hypothesis，hypotheses（pl.）命题proposition算术arithmetic加plus（prep.），add（v.），addition（n.）被加数augend，summand加数addend和sum减minus（prep.），subtract（v.），subtraction（n.）被减数minuend减数subtrahend余数remainder乘times（prep.），multiply（v.），multiplication（n.）被乘数multiplicand乘法multiplication积product除divided by（prep.），divide（v.），division（n.）质数prime number合数composite number正数positive number平均数mean奇数odd adj.偶数even n.偶数even integer, even number值value最小值minimum最大的，最大值maximum n.最小的，最小值minimum n.最小可能值least possible value约数，除数divisor n.最小公倍数least common multiple正整数positive integer真分数proper fraction普通分数vulgar fraction分母denominator最小公分母least common denominator分子numerator带分数mixed number余数remainder简分数simple(common)fraction 循环小数 circulating decimal 纯小数decimal faction混合小数mixed decimal百分比percentage四分之一quarter大于more than小于less than不大于not more than数字，阿拉伯数字digit n.个位数字unit’s digit十位数字tens digit个位units十位tens十分位tenths和，总数sum n.减，负，负数minus(take away) 乘数multiple差difference相等，等于equal被整除，红利dividend平均数average n.乘方power商quotient方程equation n.满足satisfy v.增加increase n.减少reduce v.坐标系coordinates坐标轴x-axis，y-axis，z-axis 横坐标x-coordinate纵坐标y-coordinate原点origin双曲线hyperbola抛物线parabola集合set元素element空集void子集subset交集intersection并集union补集complement映射mapping函数function定义域domain，field of definition值域range常量constant变量variable单调性monotonicity奇偶性parity周期性periodicity图象image数列，级数series微积分calculus微分differential导数derivative极限limit无穷大infinite（a.）infinity（n.）无穷小infinitesimal积分integral定积分definite integral不定积分indefinite integral有理数rational number无理数irrational number实数real number虚数imaginary number复数complex number矩阵matrix行列式determinant未知数unknown，x-factor，y-factor，z-factor 等式，方程式equation一次方程simple equation二次方程quadratic equation三次方程cubic equation四次方程quartic equation不等式inequation阶乘factorial对数logarithm指数，幂exponent乘方power二次方，平方square三次方，立方cuben次方the power of n，the nth power开方evolution，extraction二次方根，平方根square root三次方根，立方根cube rootn次方根the root of n，the nth root统计statistics平均数average加权平均数weighted average方差variance标准差root-mean-square deviation，standard deviation 比例proportion百分比percent百分点percentage百分位数percentile排列permutation组合combination概率probability分布distribution正态分布normal distribution非正态分布abnormal distribution图表graph条形统计图bar graph柱形统计图histogram折线统计图broken line graph曲线统计图curve diagram扇形统计图pie diagramAMC数学单词表分类（英汉）1常见单词side 边长perimeter n. 周长circumference 周长，圆周width宽area n.面积volume体积arithmetic progression(sequence)等差数列altitude高bisect平分divisor因子factor因子common factor公因子common multiple公倍数common divisor公因数common fraction普通分数complex fraction繁分数consecutive number连续整数consecutive even integer连续偶数consecutive odd integer连续奇数direct proportion正比inverse proportion反比distinct不同的factorial阶乘inverse倒数reciprocal倒数progression数列the extremes of a proportion比例外项the means of a proportion比例内medmedian中位数，中值mode众数，一组数据中出现最多的数arranged安排的add，plus加subtract减difference差multiply, times乘product积divide除divisible可被整除的divided evenly被整除dividend被除数divisor因子，除数quotient商remainder余数factorial阶乘power乘方radical sign, root sign根号round to四舍五入to the nearest四舍五入2.有关集合union并集proper subset真子集solution set解集3.有关代数式、方程和不等式algebraic term代数项like terms, similar terms同类项numerical coefficient数字系数literal coefficient字母系数inequality不等式triangle inequality三角不等式range值域original equation原方程equivalent equation同解方程等价方程linear equation线性方程(e.g.2x +6=22)4.有关分数和小数proper fraction真分数improper fraction假分数mixed number带分数vulgar fraction，common fraction普通分数 simple fraction简分数complex fraction繁分数numerator分子denominator分母(least)common denominator(最小)公分母quarter四分之一decimal fraction纯小数infinite decimal无穷小数recurring decimal循环小数tenths unit十分位5.基本数学概念arithmetic mean算术平均值weighted average加权平均值geometric mean几何平均数exponent指数，幂base乘幂的底数,底边cube立方数，立方体square root平方根cube root立方根common logarithm常用对数digit数字constant常数variable变量inverse function反函数complementary function余函数linear一次的，线性的factorization因式分解absolute value绝对值round off四舍五入6.有关数论natural number自然数positive number正数negative number负数odd integer, odd number奇数even integer, even number偶数integer, whole number整数positive whole number正整数negative whole number负整数consecutive number连续整数real number实数rational number有理数irrational(number)无理数inverse倒数composite number合数e.g.4,6,8,9,10,12,14,15…… prime number质数e.g.2,3,5,7,11,13,15……reciprocal倒数common divisor公约数multiple倍数(least)common multiple(最小)公倍数(prime)factor(质)因子common factor公因子ordinary scale, decimal scale十进制nonnegative非负的tens十位units个位mode众数median中数common ratio公比7.数列arithmetic progression(sequence)等差数列 geometric progression(sequence)等比数列8.其它approximate近似(anti)clockwise(逆)顺时针方向cardinal基数ordinal序数direct proportion正比distinct不同的estimation估计，近似parentheses括号proportion比例permutation排列combination组合table表格trigonometric function三角函数unit单位,位几何部分1.所有的角alternate angle内错角corresponding angle同位角vertical angle对顶角central angle圆心角interior angle内角exterior angle外角supplementary angles补角complementary angle余角adjacent angle邻角acute angle锐角obtuse angle钝角right angle直角round angle周角straight angle平角included angle夹角2.所有的三角形equilateral triangle等边三角形scalene triangle不等边三角形isosceles triangle等腰三角形right triangle直角三角形oblique斜三角形inscribed triangle内接三角形3.有关平面图形，除三角形外semicircle半圆concentric circles同心圆quadrilateral四边形pentagon五边形hexagon六边形heptagon七边形octagon八边形nonagon九边形decagon十边形polygon多边形parallelogram平行四边形equilateral等边形plane平面square正方形，平方rectangle长方形regular polygon正多边形rhombus菱形trapezoid梯形4.其它平面图形arc弧line, straight line直线line segment线段parallel lines平行线segment of a circle弧形5.有关立体图形cube立方体，立方数rectangular solid长方体regular solid/regular polyhedron正多面体 circular cylinder圆柱体cone圆锥sphere球体solid立体的6.有关图形上的附属物altitude高depth深度side边长circumference, perimeter周长radian弧度surface area表面积volume体积arm直角三角形的股cross section横截面center of a circle圆心chord弦radius半径angle bisector角平分线diagonal对角线diameter直径edge棱/边face of a solid立体的面hypotenuse斜边included side夹边leg三角形的直角边median of a triangle三角形的中线base底边，底数(e.g.2的5次方，2就是底数) opposite直角三角形中的对边midpoint中点endpoint端点vertex(复数形式vertices)顶点tangent切线的transversal截线intercept截距7.有关坐标coordinate system坐标系rectangular coordinate直角坐标系origin原点abscissa横坐标ordinate纵坐标number line数轴quadrant象限slope斜率complex plane复平面8.其它plane geometry平面几何trigonometry三角学bisect平分circumscribe外切inscribe内切intersect相交perpendicular垂直Pythagorean theorem勾股定理congruent全等的multilateral多边的单位类cent美分penny 1美分硬币nickel5美分硬币dime一角硬币dozen打(12个)score廿(20个)Centigrade摄氏Fahrenheit华氏quart夸脱gallon加仑(1gallon=4quart)yard码meter米micron微米inch英寸foot英尺minute分(角度的度量单位，60分=1度) square measure平方单位制cubic meter立方米pint品脱(干量或液量的单位。

美国数学竞赛（AMC）常用单词abnormal distribution 非正态分布acute angle 锐角acute triangle 锐角三角形addend 加数aggregate 集合algebra 代数amplitude 振幅angle 角arc 弧arc cosecant 反余割arc cosine 反余弦arc cotangent 反余切arc secant 反正割arc sine 反正弦arc tangent 反正切area 面积arithmetic 算术augend，summand 被加数average 平均数axiom 公理axis 轴bar graph 条形统计图barycentre（BrE），barycenter（AmE）重心base 底binary system 二进制broken line graph 折线统计图calculation 计算calculus 微积分carry 进位centre（BrE），center（AmE）圆心circle 圆circumcircle 外切圆circumference 圆周coefficient 系数combination 组合complement 补集complex number 复数cone 圆锥congruent 全等constant 常量coordinates 坐标系cosecant 余割cosine 余弦cotangent 余切cube 三次方，立方cube 立方体cube root 三次方根，立方根cubic equation 三次方程curve diagram 曲线统计图cylinder 圆柱decagon 十边形decahedron 十面体decimal 小数decimal point 小数点decimal system 十进制definite integral 定积分degree 角度denominator 分母derivative 导数determinant 行列式diameter 直径differential 微分digit 数字distribution 分布divided by（prep.），divide（v.），division（n.）除dividend 被除数divisor 除数dodecagon 十二边形dodecahedron 十二面体domain，field of definition 定义域element 元素ellipse 椭圆enneagon 九边形enneahedron 九面体equals，is equal to，is equivalent to 等于equation 等式，方程式equilateral polygon 正多边形equilateral triangle 等边三角形escentre（BrE），escenter（AmE）旁心evolution，extraction 开方excentre（BrE），excenter（AmE）外心exponent 指数，幂factorial 阶乘formula，formulae（pl.）公式fraction 分数frustum of a cone 圆台frustum of a prism 棱台function 函数geometry 几何graph 图表height 高hemisphere 半球hendecagon 十一边形hendecahedron 十一面体heptagon 七边形heptahedron 七面体hexadecimal system 十六进制hexagon 六边形hexahedron 六面体histogram 柱形统计图hyperbola 双曲线hypotenuse 斜边hypothesis，hypotheses（pl.）假设icosahedron 二十面体image 图象imaginary number 虚数incentre（BrE），incenter（AmE）内心indefinite integral 不定积分inequation 不等式infinite（a.）infinity（n.）无穷大infinitesimal 无穷小inscribed circle 内切圆insignificant digit 无效数字integer 整数integral 积分intersect 相交intersection 交集irrational number 无理数is equal or greater than 大于等于is equal or lesser than 小于等于is greater than 大于is lesser than 小于isosceles trapezoid 等腰梯形isosceles triangle 等腰三角形leg 直角边length 长limit 极限line 线locus，loca（pl.）轨迹logarithm 对数mapping 映射mathematics，maths（BrE），math（AmE）数学matrix 矩阵minuend 被减数minus（prep.），subtract（v.），subtraction（n.）减monomial 单项式monotonicity 单调性multiplicand，faciend 被乘数multiplicator 乘数natural number 自然数negative 负normal distribution 正态分布null，zero，nought，nil 零number 数numerator 分子obtuse angle 钝角obtuse triangle 钝角三角形octagon 八边形octahedron 八面体operation 运算operator 运算符origin 原点orthocentre（BrE），orthocenter（AmE）垂心parabola 抛物线parallel 平行parallelepiped 平行六面体parallelogram 平行四边形parity 奇偶性pentagon 五边形pentahedron 五面体percent 百分比percentage 百分点percentile 百分位数perigon 周角perimeter 周长period 周期periodicity 周期性permutation 排列phase 相位pi 圆周率pie diagram 扇形统计图plane 面plus（prep.），add（v.），addition（n.）加point 点polygon 多边形polyhedron 多面体polynomial，multinomial 多项式positive 正power 乘方prism 棱柱probability 概率，或然率product 积proposition 命题propotion 比例prove 证明pyramid 棱锥Pythagorean theorem 勾股定理quadratic equation 二次方程quadrilateral 四边形quartic equation 四次方程quotient 商radial 射线radian 弧度radius 半径range 值域ratio 比rational number 有理数real number 实数rectangle 矩形remainder 差rhomb，rhombus，rhombi（pl.），diamond 菱形right angle 直角right trapezoid 直角梯形right triangle 直角三角形ring 环root-mean-square deviation，standard deviation 标准差rotation 旋转round 四舍五入round down 下舍入round up 上舍入scalene triangle 不等边三角形secant 正割sector 扇形segment 线段semicircle 半圆series 数列，级数side 边significant digit 有效数字similar 相似simple equation 一次方程sine 正弦solid 体space 空间sphere 球square 二次方，平方square 正方形square root 二次方根，平方根statistics 统计straight angle 平角subset 子集subtrahend 减数sum 和surface area 表面积tangent 正切tetrahedron 四面体the power of four，the fourth power 四次方the power of n，the nth power n次方the root of four，the fourth root 四次方根the root of n，the nth root n次方根theorem 定理times（prep.），multiply（v.），multiplication（n.）乘trapezoid 梯形triangle 三角形trigonometry 三角truncation 截尾undersurface 底面union 并集unknown，x-factor，y-factor，z-factor 未知数variable 变量variance 方差void 空集volume 体积weight，significance 权weighted average 加权平均数width 宽x-axis，y-axis，z-axis 坐标轴x-coordinate 横坐标y-coordinate 纵坐标。

B＄美元符号m Adegree measure of A A 的角度Aabove 前述；上文；在…上方accept 接受；接收acceptable 可接受的accurate 精确的act 表演；幕；3-act play: 三幕剧(三幕剧就是把整个剧本切分成三个板块) acute angle 锐角add 计算...总和；加；做加法addition 加；加法additional 附加的；额外的address 地址adjacent angle 邻角adjacent 邻近的adult 成年人after all 毕竟；终究；最后alien 外星人all together 总共almond 杏仁alone 独自；孤独；单独；只有alphabet 字母表altitude (尤指海拔)高度A.M.上午amount 数量angle 角annual 一年一次的；每年的apart 分开；相距appear 出现appearance 外观appetizer (餐前的)开胃品apple 苹果applicant 申请人application 申请approach 接近；靠近April四月arc 弧；弓形area 范围；区域；面积arithmetic 算术；算法arithmetic sequence 等差数列armful 一抱之量；满怀arrange 安排；排列；整理；布置arrangement 安排；布置；排列assign 指定；指派assume 假定at least 至少at most 至多；最多athlete 运动员attend 加入August 八月average 平均；平均数；平均的backpack 双肩包；书包bag 包bagel 百吉圈(硬面包) bake 烹饪baker 面包师balance 平衡banana 香蕉base 底baseball 棒球basket 篮子basketball 篮球bat 球棒；球拍；蝙蝠beach 海滩beam 光线beaver 河狸；海狸；水獭bee 蜜蜂bend 把…弄弯(或折起) between 位于...之间bill 帐单；钞票billion 十亿；十亿的bisector 二等分线；平分线blacksmith 铁匠blindfold 眼睛被蒙住的blond 白肤金发碧眼的both 两个bowl 碗breakfast 早餐bridge 桥broken 坏的；出了毛病的bronze 铜牌bullseye 靶心bush 灌木；灌木丛business 商业；生意；业务buy (bought bought) 买Ccake 糕饼；饼cat 猫category 种类；类别calculate 计算calculation 计算calendar 日历campsite 野营地；度假营地capacity 容量carrot 胡萝卜carton 硬纸盒castle 城堡cent 美分center 中心；中央的centimeter 厘米chance 机会change变化；零钱chapter章节chef 厨师cherry 樱桃chess 棋chest 胸部；箱子chocolate 巧克力choir 合唱团；合奏；合唱队choose (chose, chosen) 选择chord 弦circle 圆周；圆circular 圆形的circumference 圆周circus 马戏团clap 鼓掌clock 钟；表cloud 云cm centimeter 的缩写厘米2coconut 椰子coefficient 系数coin 硬币collect 收集column 列combination 组合common 共通的；公约的；共同的competition 竞赛complementary angle either oftwo angles whose sum is 90°；余角complex number 复数composite 合数concert音乐会conduct 实施；执行congruent 全等的consecutive 连续的consist 构成；包含constant 常数；不变的construct 建造construction 施工contribute 贡献cookie饼干coordinate 坐标coordinate axes 坐标轴corner 角cost 花费count 数；计算；计数；计算couple 夫妻cousin 堂[表]兄弟；堂[表]姐妹cover 盖；覆盖crack: 裂缝crate 箱子create 创建；创造；造成；创作cross 交叉；穿越；越过cube 立方体；立方cubic立方体的；立方的customer 顾客；客户cycle 循环；周期；自行车；骑自行车cylindrical 圆柱的certain 确定chain 链条；链子cm 平方厘米coastal 沿海的；靠近海岸的consumption 消费；消耗量Dcontain 包含；含有dance 跳舞darken 变黑dart飞镖December 十二月decimal 十进制的；小数的；小数define 定义degree 度数degree-measure (角的)角度denominator 分母dessert 甜点determine 确定diagonal 对角线的；对角线diagram 图表diameter 直径diamond 菱形dice 骰子die 死亡difference 差额；差异different 不同的digit 数字；阿拉伯数字digit sum In mathematics, the digit sum of a given integer is the sum of all its digits (e.g. the digitsum of 84001 is calculated as8+4+0+0+1 = 13).dime (美元)十美分dimension 尺寸dine就餐；聚餐dinner晚餐display 展览distance 距离distinct 不同的distribute 分发；分配divide 除；划分；分开；等分divisible 可除尽的division 除法divisor 除数；约数divorce 离婚dodecahedron 十二面体dollar (符号为＄)美元double 两倍；使加倍dough (用于制面包和糕点的)生面团download 下载dozen 12 个drain 排空；流出draw (drew, drawn) 绘制；绘图；画画dress 衣服drum 鼓；打鼓Eeach 每；每个earn 获得；挣钱；赚的eastbound 向东的；往东的eat (ate; eaten) 吃egg 鸡蛋eight 八；第八eighteen 十八的；十八个的empty 空的energy 能量entire 全部entree 主菜；正菜equal 相等的；等于equation 方程式；等式equilateral 等边的；等边形equivalent 相等的；相当的；相等erase 抹去；清除；消除escape 逃脱；逃逸estate财产estimate 估计evaluate 估计；求...的值even 偶数的；偶数；持平evenly 均匀的ex-husband 前夫ex-wife 前妻exactly 确切地；准确地；精确地example 例子；例题execute 处决exhaust 耗尽；用完expand, expansion 展开expensive 贵的；昂贵的express 表达；表示expression 表达式；符号；算式exterior 外部的external 外部的；外面的Fface 表面；脸factor 因子；因数fair coin 公平硬币fall apart 崩溃；损坏family 家；家庭fan 风扇；扇子；狂热爱好者；粉丝farm 农场fat 脂肪fate 命运favorite 中意的；喜欢的February 二月female 女的；雌性的fence 篱笆；栅栏few少field 场地fifteen 十五fifth 第五的figure 图形file 文件fill 填充；装满；充满find 找；找到fine 美好的；精致的；罚款finger 手指fire 火；发射first 首先；第一；第一的five 五；五个flavor 味道；香料；口味flip 翻转；空翻；轻抛flour 面粉fly (flew, flown) 飞following 如下；下述food 食物foot 足；英尺(复数: feet)(1 foot = 30.48 cm)fork 叉子forklift 铲车form 形成formula 公式fortune 大笔的钱；巨款four 四；四个fraction 分数free 自由的；免费的French 法语freshman 一年级学生Friday 星期五fruit 水果function 函数Ggang 帮派；黑帮；团伙garage 车库gene 基因geometric sequence 等比数列geometrical 几何学的；几何的giant 巨大的gifted 有才华的gold 金牌grade 年级；成绩graph 图表greatest 最大的greatest common divisor(greatest common factor) 最大公约数；最大公因子gumball 口香糖Hhalf 一半；一半的hand 手hate 讨厌；憎恨heads 头；硬币的正面hectare公顷(等于1 万平方米) height高度；海拔heir 继承人hexadecimal system 16 进制hexagon 六角形；六边形hexahedron 六面体high 高highlighte r 荧光笔；亮光色hill 山hire 雇佣hold 抓；握；拿；支撑hole 洞honest dice 均匀的骰子horizonta l 水平的hostess 女主人hour 小时how 多少；多么hundred 百；百个hundreds digit 百位hyperbola 双曲线hypotenuse 直角三角形之斜边Iice cream 冰激凌icosahedron 二十面体identical 相同的imaginary 想象中的；幻想的；虚构的；虚数immediate 立即impossible 不可能的improper fraction 分子比分母大的分数in a row 连续in turn one after the other income 收入increase 增加；增长；增多independent 独立的indistinguishable if two things are indistinguishable, you cannot see any difference between them. inequality 不等式infinite 无限的；无数的initial 最初的；开始的inner 内部的inscribe 使内切insist 坚持instrument 仪器；工具；乐器integer 整数integral 整数的；整体的interior 内部的intersect相交；交叉intersection 交集；交叉点interval 间隔；区间；时间间隔interview 面试inverse 倒数isosceles 等腰三角形item 项目；一件物品或商品JJane 女孩的名字January 一月jar缸；坛子jelly bean 果冻豆；软糖豆job 工作John 男孩的名字July 七月June 六月juxtapose 把…并列Kkilometer 千米；公里km kilometer 的缩写千米knife 刀Lland 土地landscape 景色；做园林美化lap 一圈large 大last 持续；持久；延续；最后lay (laid laid) 下蛋；产卵；放置leap year 闰年least 最小的least common multiple 最小公倍数least possible value 最小可能值leave 留下left 剩余的leg 直角三角形的直角边；等腰三角形的腰；In an isosceles trianglethat has exactly two equal sides, theequal sides are called legs and thethird side is called the base.length 长度less 少的；较少；减去；扣除；较小的；较次的letter 字母lift 举起；使升起；提起；抬起likely 可能的；预料的；有希望的；似乎合适的line segment 线段line 直线link 链接；纽带list 表；名单liter 公升(1 liter = 1000 cubiccentimeters)long 长的lose 丢失；输掉；失败loss 亏损；损失lovely 可爱的Mm meter 的缩写米m2平方米male 男的；雄性的map 地图；图marathon 马拉松March 三月mark 记号；符号；标记marry 结婚mass 质量；大量mathematics 数学maximum 最大量；最大极限的May 五月meal 一顿饭mean 平均的；平均数measure 测量medal 奖章；勋章median For a sample of n elements arranged in ascendingorder, the median is the 1/2(n+1)thelement if n is odd, and the mean ofthe 1/2nth and (1/2n + 1)th elementif n is even.menu 菜单meter 米；公尺middle 中间midnight 凌晨midpoint 中点；正中央mile 英里millimeter 毫米million 百万；百万个min minute 的缩写；分钟miner 旷工；采矿者minimum最小的；最低的mint 薄荷；薄荷糖；铸币厂；大量的钱minus 减去minute 分钟miserable 痛苦的；非常难受的；可怜的mixed number 带分数Monday 星期一monomial 单项式motorist 汽车司机；开车的人multiple 倍数multiplicative 乘法的multiply 乘Nnatural number 自然数negative 负数；负的near 近的necessary 必需的；必要的net loss 净亏损net profit 净利润next 下一个的；紧接着的；接下来的nickel (美元)五美分nine 九；九个ninety 九十non-deterministic 不能确定的November 十一月number 数；数量；号；数字numerato r 分子numerical 数字的；用数表示的Oobject 物体obtuse angle 钝角octagon 八边形；八角形October 十月odd 奇数的off 关；关闭offer 提供offspring 后代；子女on 开；打开；上面on sale 减价；打折once 一次one 一；一个ones digit 个位oneself 自己；自身operation 运算opponent 对手opposite 反面；对立面；绝对值相等、正负相反的数orange 橘子order次序；顺序ordered 有序的ore 矿；矿石origin 原点original 原来的；起初的；最早的outcome 结果over 结束；超过overlap 重叠overtake (overtook；overtaken) 超过owe 欠own 拥有Ppace 步伐；节奏；步速paint 画画painting 画pair 对；一对；一双pal 朋友parabola 抛物线parallel 平行的parallelogram 平行四边形parity In mathematics, parity is theproperty of an integer's inclusion in oneof two categories: even or odd. 奇偶性park 公园participate 参加partition 划分；分割；隔墙；部分peanut 花生penny 一美分pentagon 五角形；五边形per 每一percent 百分比；百分数percentage 百分比；百分数；百分率perfect cube 完全立方perfect square 完全平方数；完全平方perfect score 满分perform 表演performance 表现；表演perimete r 周长；周界perpendicular 垂直的；正交的personal 个人的phrase 短语；词组pick 挑选；选择pie 饼pig 猪piece 快；条；段pile 一堆；一叠；桩pirate 海盗place 地方；位置；放置planet 星球play 玩；戏剧；演奏；比赛plug 封堵；堵塞；塞子plum 李子；梅子plus 加上P.M. 下午point 点；分数pole 棍子polygon 多边形；多角形polyhedron (plural polyhedral)多面体polynomial 多项式；Inmathematics, a polynomial is anexpression consisting of variablesand coefficients, that involves onlythe operations of addition,subtraction, multiplication, andnon-negative integer exponents ofvariables. An example of apolynomial of a single variable, x,is x2- 4x + 7. An example in threevariables is x3 + 2xyz2- yz + 1.pool 游泳池population 人口portion 部分positive 正的possess 拥有；控制；具有(特质)possible 可能的pot 罐；壶；锅pound 磅(重量单位= 0.45 千克)power 幂preceding 在先的；前面的；先前的previous 上一个；前一个price 价格prime质数print 打印；印刷printer 打印机；印刷机prism 棱柱probability 概率product 乘积profit 利润；收益；利益；赢利project 工程；方案；项目proportion 比例prototype 原型pump 泵；抽水机；打气筒pyramid 角锥；棱锥Qquadrilateral 四边形quarter 四分之一；二十五美分quotient 商Rrace 赛跑；竞争；竞赛racehorse 赛马radius (复数radii) 半径rain 雨；下雨raise 增长；涨工资；抚养random 随机的range the difference between thelargest and smallest values in a dataset. 区间；范围；值域；rate 速率、速度ratio 比；比率rational number 有理数real 真实的；实数real number 实数realize 实现；认识到；意识到receive 收到；接收；接受reciprocal 倒数；倒数的rectangle 长方形；矩形rectangular 矩形的；成直角的rectangular solid 长方体redistribute 重新分配reduction 减少reflection 反射；反思；倒影region 区域regular 等边的release 释放；发布；发行；排放remain 留下；剩下；停留remainder 余数remove 去除；去掉；移开repetition 重复represent 表示；代表require 需要respectively 分别地；各自地rest 其余的restaurant 餐馆；餐厅rhombus 菱形；斜方形reverse 相反的；反面的；颠倒；反转ride 骑；乘坐；骑马；搭乘rider 骑手right 右边；正确的right angle 直角right triangle 直角三角形rock 石头root 根rotation 旋转；轮转；循环round 四舍五入；圆的；回合；一轮row 行runner 跑步者Ssalad 沙拉sales 销售satisfy 满足Saturday 星期六save 储存；保存；拯救savings 存款scale 比例；天平scalene 不等边三角形scoop 勺；铲子；一勺(的量)score 得分sec s econd 的缩写；秒second 秒；第二sector 扇形segment 段selection 选择sell(sold, sold) 卖semi 半sentence 句子；判决separately 分别地September 九月sequence 数列；序列series 连续；系列；级数serve 服务；提供set 集合seven 七；七个seventh 第七shaded 阴影；阴影的shake (shook shaken) 摇动；抖动shape 外形share 份额；分担；分摊shelf 架子；书架；货架short 短的shout 喊；喊叫sibling 兄；弟；姐；妹side 边side-length 边长sign 符号silver 银牌similar 相似simplify 简化simultaneous 同时的sing (sang sung) 唱歌situation 情况six 六；六个size 大小；尺寸skill 技能skip 略过；跳过slope 斜率small 小sneaker运动鞋solid 立体solution 解答；解决solve 解决song 歌曲；歌soup 汤Spanish 西班牙的；西班牙spare 饶恕sphere 球；球体；范围split 分裂；分离；划分spoon 勺子；调羹spot 地点square root 平方根square 正方形；平方stack 堆栈；(使)放成整齐的一叠stamp 邮票standard 标准的star 星start 开始steady 平稳的stick 棍子stool 凳子straight 直的strawberry 草莓strength 力量student 学生subtract 减去；减subtraction 减少sugar 糖suit 西装；西服sum 总和Sunday 星期天suppose 假设surface 表面surface area 表面积surround 包围survival 生存；存活symmetric 对称性的Ttake turns 轮流tails 尾巴；硬币的反面take off 起飞talent show 才艺表演tally 计分；计算tangent 相切；切线tariff 关税task 任务teacher 老师ten 十；十个tens digit 十位tenth 第十；十分之一term 项territory 领地than 与...相比较third 第三；三分之一thirty 三十thousand 一千；一千个thousands digit 千位three 三Thursday 星期四tie 平局tile 地砖；瓦片time 时间；次；度；回；倍toss 扔；投；抛total 总共tournament 比赛tower 塔toy 玩具train 训练；培训transaction 交易trapezoid 梯形travel 旅游tree 树triangle 三角形triple 三倍数；成为三倍trisection 三分；三等分trot 小跑；快步跑tub 桶Tuesday 星期二tunnel 隧道turn around 掉头twelve 十二twenty 二十；二十个twice 两倍的twins 双胞胎two 二；两个Uunequal 不相等的；不同的uniformly 一律地；一致地；均匀地unique 唯一的；独一无二的；不同的unit 单元；单位units digit 个位unshaded 无遮蔽的；未遮住的utopia 乌托邦Vvalue 值；价值vanilla 有香子兰香味的；香草味的；普通的；寻常的variable 变数；变量的vertex (复数：vertices)顶点vertical 垂直的volume 体积Wwand 魔杖watch手表wave 挥动；波浪wealth 财富wealthy 富有的；富裕的Wednesday 星期三weigh 称；称重；量体重weight 重量；重物；砝码weld 焊接；熔接westbound 向西的；往西的whole number Whole Numbersare simply the numbers 0, 1, 2, 3, 4,5, ... (and so on)width 宽度will 遗嘱wine 葡萄酒write (wrote; written) 写Yyard 码(1 yard = 91.44 cm; 1yard = 3 feet)yearly 一年一次的；每年的Zzero 零点；零。

PROBLEM B: Camping along the Big Long River问题B：沿着大长河露营Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. 游客到大长河（225英里）可以享受风景和令人兴奋的白色水急流。

The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires河是徒步旅行者无法进入的，所以唯一享受它的方法是采取河之旅，需要几天的露营several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225河旅行都开始在第一次启动和退出河在最后退出，225英里下游。

miles downstream. Passengers take either oar- powered rubber rafts, which travel on average 4乘客乘橡皮艇桨驱动平均每小时4英里，或摩托艇，平均每小时8英里的速度行驶。

mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of旅程从开始到完成6到18个晚上，camping on the river, start to finish.. The government agency responsible for managing this river负责管理这条河的政府机关想要，以最少的接触与其他群体在河的小船，享受荒野之旅。