mathematics
Mathematics数学-附答案（1）
Mathematics数学-附答案（1）MathematicsAnswer all questions1.Given that 2x+y= 16 and In (2x–y) = ? In 5, find the value of x and of y, leaving youranswers in surd form. [8]X=(4+√5)/3 Y=(8-√5)/32.Given that A = {x:-5 < 2x-3 ≤ 15}, B = {x: -4 ≤ x + 1 < 7} andA UB = {x: a ≤ x -1≤ b}, find the value of a and of b. [5]a=-6 b=83.Functions f, g and h are defined byf:x→ 2 + xg:x→ -|x-1|h:x→ -x2 + 2(a)Find the values of gh(-2) and f-1gh(-2).-3and-1 [4](b)Find in similar form, gf, fg and gh. gf=-|x+1| fg=2-|x-1| gh=-|-x2+1|[3](c)Find the values of x such that fg(x) = -1 x=4 or x=-2[3](d)Show that hg(x) = 1 + 2x- x2. ∵hg(x)=h(-|x-1|)=-(-|x-1|)2+2=-(x-1)2+2=-x2+2x+1 [4]4.Three points have coordinates A(5, -3), B(-2,1) and C(a , 5).(a)Find, in terms of a, the coordinates of M, which is the midpoint of BC. [4]The midpoint of BC is ((a-2)/2,3)(b)Find the value of a for which AM is perpendicular to ABa=132/7. [6]5.Find the fifth and sixth terms of binomial expansion of ( 2- ? x2)9. Hence find thecoefficient of x10 in ( 2- ? x2 )9 (3x2+5 ) . 5th:(-19/3)9 6th:( -10) 9[8]6.Find the coordinates of the points of intersection of the line x + y = 3 and the curvex2– 2x +2y2= 3. [6] x=3, y=0 or x=3/5,y=12/57.Find the range of values of k for which the equation x2– 6x + k2– 7 = 0 has real roots. 36-4×1×（k2-7）≥0 the result is -4≤k≤4 [6] 8.Find all the angles between 0° and 360° inclusive which satisfysinxsec2x– 2tan x = 0 x=60°[6] 9. A body moves in a straight line so that its displacement, S m, from a point O at time tsec, is given by S = 5 + 15t2– 5t3.Find(a)The time when the body is instantaneously at rest, [4](b)The acceleration when t = 4, Answer:75[3](c)The total distance moved by the body in 9 seconds, [6](d)The average speed of the moving body. [4]10.A semicircle of centre O and radius 10 cm has diameter AB. The chord AQ is10 cm and the ratio of arc AP to arc AQ is 2 : 3.(a)Show that ∠AOP is 2?9 π radians.∵AO=QO=AQ=10 cm ∴∠AOQ=60° and∵the ratio of arc AP to arc AQ is2 : 3. ∴∠AOP=40°(40°/360°)×2л=2л/9[6](b)Calculate the area of segment AQP. the area of segment AQP is (50л/3)-25√3 [4]11.If x2– 2x– 3 is a factor of the expression x4+ px3+ qx– 81, find the value of p and of q. With these of p and q, factorize the expression completely. [10] 数学回答以下所有问题1.已知2x+y和ln（2x-y）= ? In 5 求x和y的值，保留根号。
mathematics 已知sin求cos公式
mathematics 已知sin求cos公式
“Mathematics 已知sin求cos公式”是指在使用数学工具时，已知一个角的正弦值，需要找出这个角的余弦值。
在三角函数中，正弦和余弦是相关的，可以通过已知的一个来找出另一个。
已知sin求cos的公式主要有以下几个：
1.恒等式转换：在任何角度下，恒等式 sin²θ + cos²θ = 1 可以用来转换已知
的sin值到cos值。
通过这个恒等式，可以建立一个方程并求解出cos的值。
2.Pythagorean identity：对于直角三角形，勾股定理可以表示为c²= a²
+ b²，其中c是斜边，a和b是两直角边。
由于正弦和余弦与三角形的边长有关系，可以利用Pythagorean identity来找出cos的值。
3.三角函数关系式：在单位圆上，正弦和余弦之间有直接的关系。
cos(θ) =
sin(90° - θ) 是一个常用的关系式，可以用来从sin值计算cos值。
4.利用反正弦或反余弦函数：在某些情况下，可以使用反正弦函数或反余弦
函数来求解cos值。
这些函数可以将一个角度值转换为其对应的sin或cos 值。
总结来说，“Mathematics 已知sin求cos公式”是指在数学领域中，使用特定的公式和方法从已知的sin值计算出cos值的过程。
这些公式包括恒等式转换、Pythagorean identity、三角函数关系式以及反正弦或反余弦函数的运用等。
介绍数学知识的英语文章
介绍数学知识的英语文章Mathematics is a fundamental and universal languagethat provides a framework for understanding and analyzing the world around us. It encompasses a wide range of concepts, including numbers, shapes, patterns, and relationships, and plays a crucial role in fields such as science, engineering, economics, and technology. In this article, we will explore some key aspects of mathematics, its significance, and its applications.First and foremost, mathematics is the study of numbers and their operations, such as addition, subtraction, multiplication, and division. It also includes the study of abstract structures, such as sets, groups, and fields, which serve as the foundation for more advanced mathematical concepts. Through the use of symbols and notation, mathematicians are able to express complex ideas and relationships in a concise and precise manner.One of the most fascinating aspects of mathematics isits ability to describe and analyze patterns and relationships in the natural world. For example, mathematical principles govern the motion of celestial bodies, the growth of populations, and the behavior of waves and particles. By using mathematical models, scientists and researchers can make predictions and test hypotheses, leading to a deeper understanding of the underlying mechanisms of the universe.Furthermore, mathematics provides powerful tools for problem-solving and decision-making. Whether it's calculating the trajectory of a spacecraft, optimizing the efficiency of a manufacturing process, or designing cryptographic algorithms for secure communication, mathematics offers a systematic approach to tackling real-world challenges. Its applications in fields such as computer science, finance, and logistics have revolutionized the way we live and work.In addition to its practical applications, mathematics also fosters critical thinking and reasoning skills. Through the process of formulating and proving theorems,students of mathematics learn to analyze problems, construct logical arguments, and think abstractly. This not only enhances their problem-solving abilities but also equips them with a valuable mindset for approaching complex issues in other disciplines.In conclusion, mathematics is a rich and diverse field with profound implications for our understanding of the world and our ability to shape it. Its role in science, technology, and everyday life cannot be overstated, and its beauty lies in its ability to reveal the hidden order and structure underlying the universe. By studying mathematics, we gain not only knowledge but also a powerful set of tools for exploring the unknown and making meaningful contributions to society.。
mathematics注释
mathematics注释
你提到的"mathematics 注释" 可以涵盖很多不同的方面，具体要看你是指数学中的哪个部分以及在什么上下文中需要注释。
以下是一些可能的解释：
LaTeX 注释：
如果你是在使用 LaTeX 进行数学写作，你可能会在数学公式中使用注释。
在LaTeX 中，你可以使用% 符号添加注释，或者使用\text{} 命令插入文字。
例如：
\[
y = x^2 + 1 \% \text{这是一个注释}
\]
MATLAB 注释：
在 MATLAB 中，你可以在代码中使用 % 符号添加单行注释，或者使用 %{ 和 %} 将多行文本作为注释。
例如：
% 这是一个 MATLAB 单行注释
%{
这是一个
多行注释
%}
Python 注释：
在 Python 中，你可以使用 # 符号添加单行注释，或者使用 ''' 或 """ 将多行文本作为注释。
例如：
# 这是一个 Python 单行注释
'''
这是一个
多行注释
'''
注释数学理论：
如果你是在写数学理论的文章或笔记，你可以使用适当的数学符号和格式来表达注释。
例如，在解释一个定理或证明的步骤时，你可能会使用文字来解释每个符号的含义。
请提供更多的上下文信息，这样我可以为你提供更具体的帮助。
数学的重要性英语作文
数学的重要性英语作文Mathematics is a subject that plays an integral role in our daily lives, from simple arithmetic to complex problem-solving. It is not just a field of study but a language that helps us understand the world around us.Firstly, mathematics is the foundation of science and engineering. Without the ability to calculate and reason mathematically, we would not have the technological advancements that we enjoy today. From the development of computers and smartphones to the construction of buildings and bridges, mathematics is the key to making these innovations possible.Secondly, math teaches us critical thinking and logical reasoning. It is a discipline that requires precision and accuracy, which are skills that are applicable in all areas of life. By learning math, we learn to approach problems systematically and to think through solutions step by step.Thirdly, mathematics is essential for financial literacy. Understanding basic math concepts allows us to manage our personal finances, from budgeting to investing. It helps us make informed decisions about our spending and saving, which is crucial for our financial well-being.Moreover, math is a universal language that transcends cultural and linguistic barriers. It is a tool that can beused to communicate complex ideas and concepts in a clear and concise manner. This universality makes it an invaluable asset in the global community.Lastly, the study of mathematics helps to develop problem-solving skills. It encourages creativity and innovation, as mathematicians often have to think outside the box to solve complex problems. This ability to think creatively is a valuable skill in any field, not just in mathematics.In conclusion, the importance of mathematics cannot be overstated. It is a subject that impacts every aspect of our lives, from the technology we use to the way we manage our finances. By embracing the study of mathematics, we equip ourselves with the tools necessary to navigate and succeed in the modern world.。
数学与生活的英文
数学与生活的英文Mathematics is an essential part of our daily lives, impacting everything from budgeting and cooking to architecture and technology. 数学是我们日常生活中至关重要的一部分，影响着预算编制、烹饪、建筑和技术等方方面面。
When we go to the grocery store and compare prices to find the best deals, we are using mathematical principles such as percentages and ratios. 当我们去杂货店比较价格以找到最好的优惠时，我们正在使用百分比和比率等数学原理。
In the kitchen, we use measurements and conversions to follow recipes and bake delicious treats. 在厨房里，我们使用测量和转换来按照食谱烘烤美味的点心。
When we are driving, we calculate distances and travel times to plan our routes and reach our destinations efficiently. 当我们开车时，我们要计算距离和行程时间，以便规划我们的路线，高效地到达目的地。
Mathematics also plays a crucial role in fields such as science, engineering, and finance, where complex calculations and problem-solving are essential for success. 数学在科学、工程和金融等领域也起着至关重要的作用，复杂的计算和问题解决对于成功至关重要。
maths 数学类词汇
定义definition变量variable面积area直径diameter半径radius公式formula单价u nit price范围range/scope/extent集合set法则principle本金principal利率interest ra te利息interest单利simple interest复利compound interest正数positive number负数negative number解析式analytic expression分类讨论classified discussion性质nature （不是很确定）奇函数odd function偶函数even function对称symmetric坐标原点o rigin单调性monotonicity（不是很确定）任意random周期性periodic 有界性bounde dness 数学mathematics, maths(BrE), math(AmE) 公理axiom 定理theorem 计算cal culation 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multi plicand, faciend 乘数multiplicator 积product 除divided by(prep.), divide(v.), divisio n(n.) 被除数dividend 除数divisor 商quotient 等于equals, is equal to, is equivalent 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 mea n 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imagina ry 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po sitive 负negative 零null, zero, nought, nil 十进制decimal system 二进制binary sys tem 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cu be 四次方the power of four, the fourth power n次方the power of n, the nth pow er 开方evolution, extraction 二次方根，平方根square root 三次方根，立方根cube r oot 四次方根the root of four, the fourth root n次方根the root of n, the nth root sqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.236 常量constant 变量variable 坐标系co ordinates 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geometr y 点point 线line 面plane 体solid 线段segment 射线radial 平行parallel 相交int ersect 角angle 角度degree 弧度radian 锐角acute angle 直角right angle 钝角obt use angle 平角straight angle 周角perigon 底base 边side 高height 三角形triangl e 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 triangl e 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are a 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 of definition 值域r ange 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.) i nfinity(n.) 无穷小infinitesimal 积分integral 定积分definite integral 不定积分indefinit e integral 复数complex number 矩阵matrix 行列式determinant 圆circle 圆心centr e(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pa rallelepiped 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icosa hedron 多面体polyhedron 旋转rotation 轴axis 球sphere 半球hemisphere 底面un dersurface 表面积surface area 体积volume 空间space 双曲线hyperbola 抛物线pa rabola 四面体tetrahedron 五面体pentahedron 六面体hexahedron菱形rhomb, rhom bus, 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dodecag on 多边形polygon 正多边形equilateral polygon 相位phase 周期period 振幅amplit ude 内心incentre(BrE), incenter(AmE) 外心excentre(BrE), excenter(AmE) 旁心escen tre(BrE), escenter(AmE) 垂心orthocentre(BrE), orthocenter(AmE) 重心barycentre(Br E), 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-square devia tion, 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distributi on 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curv e diagram 扇形统计图pie diagram 数列是sequence极限是limit导数是derivative微分是differential积分是integral常数constant级数series幂级数power series二重积分d ouble integral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, is equivalent 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 power n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 root n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 of definition 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-square deviation, 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 diagram1。
mathematics计算方差
mathematics计算方差方差的概念在统计学中，方差是衡量数据分布离散程度的一个指标。
它表示数据点与均值之间的平均差异平方。
方差越大，数据点越分散；方差越小，数据点越集中。
计算方差的步骤1. 计算样本均值(μ)：- 首先，将所有数据点相加- 然后，将和除以数据点的数量2. 计算每个数据点与均值的差值：- 对于每个数据点，从该点中减去均值- 这些差值称为离差3. 求离差的平方：- 对于每个离差，将其平方4. 计算离差平方的和：- 将所有离差平方相加- 离差平方的和称为平方差和 (SS) 5. 除以自由度 (df)：- 自由度是数据点数量减 1- 平方差和除以自由度得到方差方差的数学公式方差的数学公式为：```σ² = SS / df```其中：- σ²是方差- SS 是平方差和- df 是自由度方差的应用方差在统计学和概率论中有着广泛的应用，包括： - 衡量数据分布的离散程度- 进行假设检验- 估计总体参数- 建立置信区间- 进行回归分析例子假设我们有一个以下数据点的数据集：{10, 12, 14, 16, 18}1. 计算样本均值：(10 + 12 + 14 + 16 + 18) / 5 = 142. 计算离差：{10 - 14, 12 - 14, 14 - 14, 16 - 14, 18 - 14} = {-4, -2, 0, 2, 4}3. 求离差的平方：{16, 4, 0, 4, 16}4. 计算平方差和：16 + 4 + 0 + 4 + 16 = 405. 计算自由度：5 - 1 = 46. 计算方差：40 / 4 = 10因此，该数据集的方差为 10。
这表明数据点相对于均值具有较大的离散性。
数学英文名词
数学英文名词Mathematics, a language of patterns and logic, is the foundation of our understanding of the universe. The terminology associated with this subject is not just a collection of words; it's a universe of ideas, concepts, and theories that have shaped our world. From the simplest arithmetic operations to the most complex theorems, mathematical terminology is rich, diverse, and oftentimes, incredibly beautiful.Let's delve into some of the fundamental mathematical terms that have a profound impact on our lives. The word "algebra" originates from the Arabic word "al-jebr," which means "reunion of broken parts." Algebra represents a branch of mathematics that deals with variables, equations, and inequalities. It's the language of problem-solving, allowing us to model real-world situations and find solutions.Another crucial term is "geometry," which comes from the Greek word "γεωμετρία," meaning "earth measurement." Geometry deals with the properties of shape, size, and space. It has applications in architecture,engineering, and even art, demonstrating the wide-reaching impact of mathematical terminology.Moreover, "calculus" is a Latin word meaning "small pebble," referring to the small changes that accumulate to form larger outcomes. Calculus is a branch of mathematics that studies rates of change, such as derivatives and integrals, and has applications in physics, engineering,and economics.These are just a few examples of the rich tapestry of mathematical terminology. The beauty of this language liesin its precision and universality. Mathematical terms arenot ambiguous; they have exact meanings that are applicable across different fields and cultures. This precision allows us to communicate complex ideas with clarity and confidence. Beyond precision, mathematical terminology is also beautiful in its simplicity. Often, a single word or symbol can represent a profound concept or theory. For instance,the symbol "π" represents an infinite series of numbersthat govern the properties of circles, a fundamental shapein nature. The elegance of this symbolism is a testament to the beauty of mathematical terminology.In conclusion, mathematical terminology is not just a collection of words; it's a universe of ideas and concepts that have shaped our understanding of the world. The precision, universality, and simplicity of this language make it beautiful and fascinating. As we delve deeper into the mysteries of mathematics, we discover more and more beautiful terminology that continues to inspire and amaze us.**数学在我们的世界：数学术语的美丽**数学，作为模式和逻辑的语言，是我们理解宇宙的基础。
数学 mathematics
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, is equivalent 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 power n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 root n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 of definition 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-square deviation, 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 diagram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.), additio n(n.)被加数 augend, summand 加数 addend和 sum 减 minus(prep.), subtract(v.), s ubtraction(n.)被减数 minuend 减数 subtrahend差 remainder 乘 times(prep.), multiply(v.), m ultiplication(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, is equ ivalent 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 fo urth 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 root n次方根 the root of n, the n th root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 of definiti on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 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, loca(pl.)相似 similar 全等 congruent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空间 space 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 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-square deviation, s tandard 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 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 diagram。
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数学Project（2）
本次数学project要求我们利用Mathematica软件处理莫比乌斯带、曲面曲线积分以及傅
里叶级数。通过运用Mathematica软件，不仅使我们更掌握运用该软件，更重要的是使我们
对这三类函数有了更深刻的了解，对今后的学习与生活带来帮助。
第一题：莫比乌斯带
利用Mathematica 软件求出该莫比乌斯带参数方程的图形：
由图上可以看出莫比乌斯带有一个魔术般的性质，它是经扭转180度后再两头粘接。
与普通纸带具有两个面——双侧曲面不同，这样的纸带只有一个面——单侧曲面。莫比乌斯
带横躺着时就如同一个无穷大的符号“∞”，而莫比乌斯带也正如这样无穷扭曲向前。
第二题：斯托克斯公式
（1） 求F（x，y，z）在平面x+y+z=1与柱面x^2+y^2=9的交线下的曲线积分，应用
Mathematica软件求得
依据我们上课所学的斯托克斯公式，同样可求得曲线积分答案一致。
（2） 用Mathematica 做出（1）中的平面与柱面的交线
利用斯托克斯公式求解该曲线积分需要用到曲线所围成的曲面，将第二类曲线积分化为第二
类曲面积分。可见该曲线所围成的是倾斜的椭圆面，在根据第二曲面积分求解
（3） 求出交线的参数方程。通过变量替换求得：x=3*Cos[] y=3*Sin[]
z=1-3*Cos[]-3*Sin[]
用Mathematica做出该参数的图形：
2022022024
第三题：傅里叶级数
321123
0.2
0.4
0.6
0.8
1.0
由图可见傅里叶级数的部分和逐步逼近f（x）
总结
通过这次Mathematica软件完成project，我学到了许多东西。学到Mathematica软件的
操作只是一方面的。另一方面，从第一题中学到了一类能表示莫比乌斯带的函数，同时通过
立体构图看到了这个图形的神奇之处。从第二题中，利用斯托克斯公式求曲线积分。求解的
过程中要求运用到解析几何，通过Mathematica 分析了这类曲线积分的求解过程，将曲线积
分通过斯托克斯公式化为第二类曲面积分，方便了我们求解。第三题中，通过做傅里叶级数
的部分和我们的f（x）不断逼近，由此我们可知可以利用傅里叶级数做某些数的近似，类
似于泰勒级数。本次project尽管内容少，但我们仍可以从中学到很多东西。