2019电大应用概率统计试题考试必考重点

应用数学 一、填空题 （每小题3分，共21分） 1．已知则 2．设且则 3．已知随机变量在[0，5]内服从均匀分布，则 4．设袋中有5个黑球、3个白球，现从中随机地摸出4个，则其中恰有3个白球的概率为 . 5．设是来自正态总体的一个样本，则 6．有交互作用的正交试验中，设与皆为三水平因子，且有交互作用，则的自由度为 . 7．在MINITAB菜单下操作，选择可用来讨论 的问题，输出结果尾概率为，给定，可做出 的判断. 二、单项选择题（每小题3分，共15分） 1．设为两随机事件，则结论正确的是（ ） （A）独立 （B）互斥 （C） （D） 2. 设与分别为随机变量与的分布 函数 excel方差函数excelsd函数已知函数     2 f x m x mx m      2 1 4 2拉格朗日函数pdf函数公式下载 .为使是某一随机变量的分布函数，在下列给定的各组数值中应取（ ） （A）（B）（C）（D） 3．设和分别来自两个正态总体与的样本，且相互独立，与分别是两个样本的方差，则服从的统计量为（ ） （A） （B） （C） （D） 4. 设关于的线性回归方程为则、的值分别为（ ） （） （A）8.8，-2.4 （B）-2.4，8.8 （C）-1.2，4.4（D）4.4，1.2 5．若分布，则服从（ ）分布. （A）（B）（C）（D） 四、计算题（共56分） 1．据以往资料表明，某一3口之家，患某种传染病的概率有以下规律： P{孩子得病}=0.6 ，P{母亲得病 | 孩子得病}=0.5 ， P{父亲得病 | 母亲及孩子得病}=0.4 ，求母亲及孩子得病但父亲未得病 的概率.（8分） 2.一学生接连参加同一课程的两次考试.第一次及格的概率为0.6，若第一次及格则第二次及格的概率也为0.6；若第一次不及格则第二次及格的概率为0.3. （1）若至少有一次及格则能取得某种资格，求他取得该资格的概率？ （2）若已知他第二次已经及格，求他第一次及格的概率？（12分） 3．假定连续型随机变量的概率密度为，求 （1）常数，数学期望，方差； （2）的概率密度函数.（12分） 4. 某工厂采用新法处理废水，对处理后的水测量所含某种有毒物质的浓度，得到10个数据（单位：mg/L）: 22 , 14 , 17 , 13 , 21 , 16 , 15 , 16 , 19 , 18 而以往用老办法处理废水后，该种有毒物质的平均浓度为19.问新法是否比老法效果好？假设检验水平，有毒物质浓度.（12分） （） 5. 在某橡胶配方中，考虑三种不同的促进剂（A），四种不同份量的氧化锌（B），每种配 方各做一次试验，测得300%定强如下： 定强　氧化锌 促进剂 B1 B2 B3 B4 A1 31 34 35 39 A2 33 36 37 38 A3 35 37 39 42 试检验促进剂、氧化锌对定强有无显著的影响？（12分） ( 　) 四. 综合 实验报告 化学实验报告单总流体力学实验报告观察种子结构实验报告观察种子结构实验报告单观察种子的结构实验报告单 （8分） 052应用数学 一、 填空题（每小题2分，共2(6=12分） 1、设一维连续型随机变量X服从指数分布且具有方差4，那么X的概率密度 函数为： 。 2、设一维连续型随机变量X的分布函数为 ， 则随机变量 的概率密度函数为： 。 3、设总体X服从正态分布 ，它的一个容量为100的样本的均值 服从正态分布 。 4、设 是参数 的估计量，若 成立，则称 是 的无偏估计量。 5、在无交互作用的双因素试验的方差分析中，若因素A有三个水平，因素B 有四个水平，则误差平方和SSE的自由度 。 6、设关于随机变量Y与X的线性回归方程为 ，则 。 （ ） 二、单项选择题（每小题2分，共2(6=12分） 1、 设相互独立的两个随机变量X、Y具有同一分布，且X的分布律为： 则随机变量 的分布律为（ ） 2、若随机变量X的数学期望E（X）存在，则 （ ） 3、设X为随机变量，下列哪个是X的3阶中心矩？（ ） 4、设两总体 ，且 未知，从X中抽取一 容量为 的样本，从Y中抽取一容量为 的样本，对检验水平 ，检验假设： 由样本计算出来的统计量 的观察 值应与下列哪个临界值作比较？（ ） 5、在对回归方程的统计检验中，F检验法所用的统计量是：（ ） （其中SSR是回归平方和，SSE是剩余平方和， 是观察值的个数） 6、设总体 ，从X中抽取一容量为 的样本，样本均值为 ， 则统计量 服从什么分布？（ ） 三、判别题（每小题2分，共2(6=12分） （请在你认为对的小题对应的括号内打“√”，否则打“(”） 1、设A、B是两个随机事件，则 （ ） 2、设 是服从正态分布 的随机变量的分布函数，则 （ ） 3、相关系数为零的两个随机变量是相互独立的。 （ ） 4、如果X、Y是两个相互独立的随机变量，则 （ ） 5、若两随机变量具有双曲线类型的回归关系，则可作适当的变量代换转化为 线性回归关系。（ ） 6、用MINITAB软件做有交互作用的双因素试验的方差分析时可在菜单中选择： （ ） 四、计算题（每小题8分，共8(7=56分） 1、 一射手对同一目标独立进行四次射击，若至少命中一次的概率为 ， （1） 求该射手的命中率 ； （2） 求四次射击中恰好命中二次的概率。 2、 如下图，某人从A点出发，随意沿四条路线之一前进，当他到达B1，B2， B3，B4 中的任一点时，在前进方向的各路线中再随意选择一条继续行进。 （1） 求此人能抵达C点的概率； （2） 若此人抵达了C点，求他经过点B1的概率。 3、某公共汽车站从早上6时起每隔15分钟开出一趟班车，假定某人在6点以后 到达车站的时刻是随机的，所以有理由认为他等候乘车的时间X服从 均匀分布，其密度函数为： ，求 （1） 此人等车时间少于5分钟的概率 ；此人的平均等车时间E（X）。 4、 设二维随机变量（X，Y）的联合密度函数为 （1）判断X与Y是否相互独立；（2）求概率 5、设某种清漆9个样本的干燥时间（单位：h）分别为6.0，5.7，5.8，6.5，7.0， 6.3，5.6，6.1，5.0，设干燥时间总体服从正态分布 ，求平均干燥 时间 的置信度为0.95的置信区间。 （ ） 6、 某种导线，要求其电阻的 标准 excel标准偏差excel标准偏差函数exl标准差函数国标检验抽样标准表免费下载红头文件格式标准下载 差不得超过 ,今在生产的一批导线中取 样品9根，测得 ，设总体为正态分布，问在水平 下 能否认为这批导线的标准差显著地偏大？ （ ） 7、 有三台机床生产某种产品，观察各台机床五天的产量，由样本观察值算出 组间平方和 ，误差平方和 ，总离差平方和 ，试问三台机床生产的产品产量间的差异在检验水平 下是否有统计意义？ （ ） 五、综合实验（本题8分，开卷，解答另附于《数学实验报告》中） 062应用数学 一、 填空题（每小题2分，共2(6=12分） 1、设服从0—1分布的一维离散型随机变量X的分布律是： ， 若X的方差是 ，则P=________。 2、设一维连续型随机变量X服从正态分布 ，则随机变量 的概率密度函数为__________________________。 3、设二维离散型随机变量X、Y的联合分布律为： 则a, b满足条件：___________________。 4、设总体X服从正态分布 ， 是它的一个样本，则样本均值 的方差是_____​​___。 5、假设正态总体的方差未知，对总体均值 ( 作区间估计。现抽取了一个容量 为n的样本，以 表示样本均值，S表示样本均方差，则( 的置信度为1-( 的置信区间为：_______________________________。 6、求随机变量Y与X的线性回归方程 ，在计算公式 中， ， 。 二、单项选择题（每小题2分，共2(6=12分） 1、设A，B是两个随机事件，则必有（ ） 2、设A，B是两个随机事件， 则（ ） 3、设X，Y为相互独立的两个随机变量，则下列不正确的结论是（ ） 4、设两总体 未知，从X中抽取一容量为 的样本，从Y中抽取一容量为 的样本，作假设检验： 所用统计量 服从（ ） 5、在对一元线性回归方程的统计检验中，回归平方和SSR的自由度是：（ ） 6、设总体 ，从X中抽取一容量为 的样本，样本均值为 ， 则统计量 服从什么分布？（ ） 三、判别题（每小题2分，共2(6=12分） （请在你认为对的小题对应的括号内打“√”，否则打“(”） 1、（ ）设随机变量X的概率密度为 ，随机变量Y的概率密度为 ，则二维随机变量（X、Y）的联合概率密度为 。 2、（ ）设 是服从标准正态分布 的随机变量的分布函数， X是服从正态分布 的随机变量，则有 3、（ ）设二维随机变量（X、Y）的联合概率密度为 ，随机变量 的数学期望存在，则 4、（ ）设总体X的分布中的未知参数 的置信度为 的置信区间为 则有 。 5、（ ）假设总体X服从区间 上的均匀分布，从期望考虑， 的矩估 计是 （ 是样本均值）。 6、（ ）用MINITAB软件求回归方程，在菜单中选择如下命令即可得： 四、计算题（每小题8分，共8(7=56分） 1、某连锁总店属下有10家分店，每天每家分店订货的概率为p，且每家分 店的订货行为是相互独立的，求 （1） 每天订货分店的家数X的分布律；（2） 某天至少有一家分店订货的概率。 2、现有十个球队要进行乒乓球赛，第一轮是小组循环赛，要把十支球队平分成 两组，上届冠亚军作为种子队分别分在不同的两组，其余八队抽签决定分组， 甲队抽第一支签，乙队抽第二支签。 （1）求：甲队抽到与上届冠军队在同一组的概率； （2）求：乙队抽到与上届冠军队在同一组的概率； （3）已知乙队抽到与上届冠军队在同一组，求：甲队也是抽到与上届冠军队在 同一组的概率。 3、已知随机变量X服从参数为 的指数分布，且 ，求 （1）参数 ； （2） 4、设一维随机变量X的分布函数为： ，求： （1） X的概率密度；（2） 随机变量Y=2(X+1)的数学期望。 5、 设二维随机变量（X，Y）的联合概率密度为 ，求 （1）该二维随机变量的联合分布函数值 ； （2）二维随机变量（X，Y）的函数Z=X+Y的分布函数值FZ(1)。 6、 用某种仪器间接测量某物体的硬度，重复测量5次，所得数据是175、173、178、174、176，而用别的精确方法测量出的硬度为179(可看作硬度真值)。设测量硬度服从正态分布，问在水平( =0.05下，用此种仪器测量硬度所得数值是否显著偏低？( ) 7、 某厂生产某种产品使用了3种不同的催化剂（因素A）和4种不同的原料（因素B），各种搭配都做一次试验测得成品压强数据。由样本观察值算出各平方和分别为：SSA=25.17，SSB=69.34，SSE=4.16，SST=98.67，试列出方差分析表，据此检验不同催化剂和不同原料在检验水平( =0.05下对产品压强的影响有没有统计意义？ （ ） 五、综合实验（本题8分，开卷，解答另附于《数学实验报告》中） 072 大学数学Ⅱ 一、 填空题（每小题2分，本题共12分） 1．若事件 相互独立，且 ， ，则 = ； 2．设随机变量 的分布列为： 0 1 2 3 4 5 6 0.1 0.15 0.2 0.3 0.12 0.1 0.03 则 ； 3．设随机变量 服从参数为 的Poisson分布，且已知 ，则 ； 4．设 是来自正态总体 的样本，则 ； ； 5．设 是来自总体 的一个样本， ，则 ； 6．假设某种电池的工作时间服从正态分布，观察五个电池的工作时间（小时），并求得其样本均值和标准差分别为： ，若检验这批样本是否取自均值为50（小时）的总体，则零假设为 ， 其检验统计量为 。 二、单项选择题（每小题3分，本题共18分） 1．从数字1，2，3，4，5中，随机抽取3个数字（允许重复）组成一个三位数， 其各位数字之和等于9的概率为（ ）． A． ； B． ； C． ； D． ． 2．如果随机变量 的密度函数为 ， 则 （ ）． A．0.875； B． ； C． ； D． ． 3．设物件的称重 则至少应称多少次？（ ）． A．16； B．15； C．4； D．20． 4．设随机变量X的概率密度函数为 ，则常数C=（ ）． A． ； 　 B．5；　　　　　 C．2； 　　　 D． ． 5．在一个已通过F检验的一元线性回归方程中，若给定 的预测区间精确表示为（ ）． A． ； B． ； C． ； D． ． 6．样本容量为 时，样本方差 是总体方差 的无偏估计量，这是因为（ ）． A． ；　 B． ；　 C． ；　 D． ． 三、解下列各题（6小题，共48分） 1．设总体 ， 为简单随机样本，且 ．证明： ． （6分） 2．已知连续型随机变量 的分布函数为 ① 试确定常数 ； ② 求 ； ③ 求 的密度函数．（10分） 3．若从10件正品、2件次品的一批产品中，无放回地抽取2次，每次取一个，试求第二次取出次品的概率．　　　（6分） 4．设 的密度函数为 ． ① 求 的数学期望 和方差 ； ② 求 与 的协方差和相关系数，并讨论 与 是否相关． （8分） 5．设二维随机变量 在区域 上服从均匀分布，其中 是由曲线 和直线 所围成．试求 的联合分布密度及关于 的边缘分布密度 与 ，并判断 是否相互独立．（10分） 6．设随机变量 服从区间 上的均匀分布，试证明： （ 为常数）也服从均匀分布．　（8分） 四、应用题：以下是某农作物对三种土壤 ，两种肥料 ，每一个处理作四次重复试验后所得产量的方差分析表的部分数据，分别写出各零假设，并完成方差分析表，写出分析结果 ． （12分） 方差来源 平方和 自由度 均方和 值 临界值 土壤因素 肥料因素 2 误差 18 总和 23 已知参考临界值： 五. 综合实验报告（10分） 请您删除一下内容，O(∩_∩)O谢谢！！！2016年中央电大期末复习考试小抄大全，电大期末考试必备小抄，电大考试必过小抄Acetylcholine is a neurotransmitter released from nerve endings (terminals) in both the peripheral and the central nervous systems. It is synthesized within the nerve terminal from choline, taken up from the tissue fluid into the nerve ending by a specialized transport mechanism. The enzyme necessary for this synthesis is formed in the nerve cell body and passes down the axon to its end, carried in the axoplasmic flow, the slow movement of intracellular substance (cytoplasm). Acetylcholine is stored in the nerve terminal, sequestered in small vesicles awaiting release. When a nerve action potential reaches and invades the nerve terminal, a shower of acetylcholine vesicles is released into the junction (synapse) between the nerve terminal and the ‘effector’ cell which the nerve activates. This may be another nerve cell or a muscle or gland cell. Thus electrical signals are converted to chemical signals, allowing messages to be passed between nerve cells or between nerve cells and non-nerve cells. This process is termed ‘chemical neurotransmission’ and was first demonstrated, for nerves to the heart, by the German pharmacologist Loewi in 1921. Chemical transmission involving acetylcholine is known as ‘cholinergic’. Acetylcholine acts as a transmitter between motor nerves and the fibres of skeletal muscle at all neuromuscular junctions. At this type of synapse, the nerve terminal is closely apposed to the cell membrane of a muscle fibre at the so-called motor end plate. On release, acetylcholine acts almost instantly, to cause a sequence of chemical and physical events (starting with depolarization of the motor endplate) which cause contraction of the muscle fibre. This is exactly what is required for voluntary muscles in which a rapid response to a command is required. The action of acetylcholine is terminated rapidly, in around 10 milliseconds; an enzyme (cholinesterase) breaks the transmitter down into choline and an acetate ion. The choline is then available for re-uptake into the nerve terminal. These same principles apply to cholinergic transmission at sites other than neuromuscular junctions, although the structure of the synapses differs. In the autonomic nervous system these include nerve-to-nerve synapses at the relay stations (ganglia) in both the sympathetic and the parasympathetic divisions, and the endings of parasympathetic nerve fibres on non-voluntary (smooth) muscle, the heart, and glandular cells; in response to activation of this nerve supply, smooth muscle contracts (notably in the gut), the frequency of heart beat is slowed, and glands secrete. Acetylcholine is also an important transmitter at many sites in the brain at nerve-to-nerve synapses. To understand how acetylcholine brings about a variety of effects in different cells it is necessary to understand membrane receptors. In post-synaptic membranes (those of the cells on which the nerve fibres terminate) there are many different sorts of receptors and some are receptors for acetylcholine. These are protein molecules that react specifically with acetylcholine in a reversible fashion. It is the complex of receptor combined with acetylcholine which brings about a biophysical reaction, resulting in the response from the receptive cell. Two major types of acetylcholine receptors exist in the membranes of cells. The type in skeletal muscle is known as ‘nicotinic’; in glands, smooth muscle, and the heart they are ‘muscarinic’; and there are some of each type in the brain. These terms are used because nicotine mimics the action of acetylcholine at nicotinic receptors, whereas muscarine, an alkaloid from the mushroom Amanita muscaria, mimics the action of acetylcholine at the muscarinic receptors. Acetylcholine is the neurotransmitter produced by neurons referred to as cholinergic neurons. In the peripheral nervous system acetylcholine plays a role in skeletal muscle movement, as well as in the regulation of smooth muscle and cardiac muscle. In the central nervous system acetylcholine is believed to be involved in learning, memory, and mood. Acetylcholine is synthesized from choline and acetyl coenzyme A through the action of the enzyme choline acetyltransferase and becomes packaged into membrane-bound vesicles . After the arrival of a nerve signal at the termination of an axon, the vesicles fuse with the cell membrane, causing the release of acetylcholine into the synaptic cleft . For the nerve signal to continue, acetylcholine must diffuse to another nearby neuron or muscle cell, where it will bind and activate a receptor protein. There are two main types of cholinergic receptors, nicotinic and muscarinic. Nicotinic receptors are located at synapses between two neurons and at synapses between neurons and skeletal muscle cells. Upon activation a nicotinic receptor acts as a channel for the movement of ions into and out of the neuron, directly resulting in depolarization of the neuron. Muscarinic receptors, located at the synapses of nerves with smooth or cardiac muscle, trigger a chain of chemical events referred to as signal transduction. For a cholinergic neuron to receive another impulse, acetylcholine must be released from the receptor to which it has bound. This will only happen if the concentration of acetylcholine in the synaptic cleft is very low. Low synaptic concentrations of acetylcholine can be maintained via a hydrolysis reaction catalyzed by the enzyme acetylcholinesterase. This enzyme hydrolyzes acetylcholine into acetic acid and choline. If acetylcholinesterase activity is inhibited, the synaptic concentration of acetylcholine will remain higher than normal. If this inhibition is irreversible, as in the case of exposure to many nerve gases and some pesticides, sweating, bronchial constriction, convulsions, paralysis, and possibly death can occur. Although irreversible inhibition is dangerous, beneficial effects may be derived from transient (reversible) inhibition. Drugs that inhibit acetylcholinesterase in a reversible manner have been shown to improve memory in some people with Alzheimer's disease. abstract expressionism, movement of abstract painting that emerged in New York City during the mid-1940s and attained singular prominence in American art in the following decade; also called action painting and the New York school. It was the first important school in American painting to declare its independence from European styles and to influence the development of art abroad. Arshile Gorky first gave impetus to the movement. His paintings, derived at first from the art of Picasso, Miró, and surrealism, became more personally expressive. Jackson Pollock's turbulent yet elegant abstract paintings, which were created by spattering paint on huge canvases placed on the floor, brought abstract expressionism before a hostile public. Willem de Kooning's first one-man show in 1948 established him as a highly influential artist. His intensely complicated abstract paintings of the 1940s were followed by images of Woman, grotesque versions of buxom womanhood, which were virtually unparalleled in the sustained savagery of their execution. Painters such as Philip Guston and Franz Kline turned to the abstract late in the 1940s and soon developed strikingly original styles—the former, lyrical and evocative, the latter, forceful and boldly dramatic. Other important artists involved with the movement included Hans Hofmann, Robert Motherwell, and Mark Rothko; among other major abstract expressionists were such painters as Clyfford Still, Theodoros Stamos, Adolph Gottlieb, Helen Frankenthaler, Lee Krasner, and Esteban Vicente. Abstract expressionism presented a broad range of stylistic diversity within its largely, though not exclusively, nonrepresentational framework. For example, the expressive violence and activity in paintings by de Kooning or Pollock marked the opposite end of the pole from the simple, quiescent images of Mark Rothko. Basic to most abstract expressionist painting were the attention paid to surface qualities, i.e., qualities of brushstroke and texture; the use of huge canvases; the adoption of an approach to space in which all parts of the canvas played an equally vital role in the total work; the harnessing of accidents that occurred during the process of painting; the glorification of the act of painting itself as a means of visual communication; and the attempt to transfer pure emotion directly onto the canvas. The movement had an inestimable influence on the many varieties of work that followed it, especially in the way its proponents used color and materials. Its essential energy transmitted an enduring excitement to the American art scene. Science and technology is quite a broad category, and it covers everything from studying the stars and the planets to studying molecules and viruses. Beginning with the Greeks and Hipparchus, continuing through Ptolemy, Copernicus and Galileo, and today with our work on the International Space Station, man continues to learn more and more about the heavens.  From here, we look inward to biochemistry and biology. To truly understand biochemistry, scientists study and see the unseen by studying the chemistry of biological processes. This science, along with biophysics, aims to bring a better understanding of how bodies work – from how we turn food into energy to how nerve impulses transmit. analytic geometry, branch of geometry in which points are represented with respect to a coordinate system, such as Cartesian coordinates, and in which the approach to geometric problems is primarily algebraic. Its most common application is in the representation of equations involving two or three variables as curves in two or three dimensions or surfaces in three dimensions. For example, the linear equation ax+by+c=0 represents a straight line in thexy-plane, and the linear equation ax+by+cz+d=0 represents a plane in space, where a, b, c, and dare constant numbers (coefficients). In this way a geometric problem can be translated into an algebraic problem and the methods of algebra brought to bear on its solution. Conversely, the solution of a problem in algebra, such as finding the roots of an equation or system of equations, can be estimated or sometimes given exactly by geometric means, e.g., plotting curves and surfaces and determining points of intersection.  In plane analytic geometry a line is frequently described in terms of its slope, which expresses its inclination to the coordinate axes; technically, the slope m of a straight line is the (trigonometric) tangent of the angle it makes with the x-axis. If the line is parallel to the x-axis, its slope is zero. Two or more lines with equal slopes are parallel to one another. In general, the slope of the line through the points (x1, y1) and (x2, y2) is given by m= (y2-y1) / (x2-x1). The conic sections are treated in analytic geometry as the curves corresponding to the general quadratic equation ax2+bxy+cy2+dx+ey+f=0, where a, b, … , f are constants and a, b, and c are not all zero. In solid analytic geometry the orientation of a straight line is given not by one slope but by its direction cosines, λ, μ, and ν, the cosines of the angles the line makes with the x-, y-, and z-axes, respectively; these satisfy the relationship λ2+μ2+ν2= 1. In the same way that the conic sections are studied in two dimensions, the 17 quadric surfaces, e.g., the ellipsoid, paraboloid, and elliptic paraboloid, are studied in solid analytic geometry in terms of the general equationax2+by2+cz2+dxy+exz+fyz+px+qy+rz+s=0. The methods of analytic geometry have been generalized to four or more dimensions and have been combined with other branches of geometry. Analytic geometry was introduced by RenéDescartes in 1637 and was of fundamental importance in the development of the calculus by Sir Isaac Newton and G. W. Leibniz in the late 17th cent. More recently it has served as the basis for the modern development and exploitation of algebraic geometry. circle, closed plane curve consisting of all points at a given distance from some fixed point, called the center. A circle is a conic section cut by a plane perpendicular to the axis of the cone. The term circle is also used to refer to the region enclosed by the curve, more properly called a circular region. The radius of a circle is any line segment connecting the center and a point on the curve; the term is also used for the length r of this segment, i.e., the common distance of all points on the curve from the center. Similarly, the circumference of a circle is either the curve itself or its length of arc. A line segment whose two ends lie on the circumference is a chord; a chord through the center is the diameter. A secant is a line of indefinite length intersecting the circle at two points, the segment of it within the circle being a chord. A tangent to a circle is a straight line touching the circle at only one point, the point of contact, or tangency, and is always perpendicular to the radius drawn to this point. A circle is inscribed in a polygon if each side of the polygon is tangent to the circle; a circle is circumscribed about a polygon if all the vertices of the polygon lie on the circumference. The length of the circumference C of a circle is equal to π (see pi) times twice the radius distance r, or C=2πr. The area A bounded by a circle is given by A=πr2. Greek geometry left many unsolved problems about circles, including the problem of squaring the circle, i.e., constructing a square with an area equal to that of a given circle, using only a straight edge and compass; it was finally proved impossible in the late 19th cent. (see geometric problems of antiquity). In modern mathematics the circle is the basis for such theories as inversive geometry and certain non-Euclidean geometries. The circle figures significantly in many cultures. In religion and art it frequently symbolizes heaven, eternity, or the universe. 整理范文，仅供参考 欢迎您下载我们的文档 资料可以编辑修改使用 致力于合同简历、 论文 政研论文下载论文大学下载论文大学下载关于长拳的论文浙大论文封面下载 写作、PPT设计、 计划 项目进度计划表范例计划下载计划下载计划下载课程教学计划下载 书、策划案、学习课件、各类模板等方方面面，打造全网一站式需求 觉得好可以点个赞哦 如果没有找到合适的文档资料，可以留言告知我们哦 B4 A B1 B2 B3 C PAGE 14 _1212126552.unknown _1242570976.unknown _1275810677.unknown _1275822565.unknown _1275822877.unknown _1275823784.unknown _1275824626.unknown _1275824749.unknown _1301465225.unknown _1275824636.unknown _1275824404.unknown _1275823569.unknown _1275823612.unknown _1275823202.unknown _1275823215.unknown _1275823033.unknown _1275823061.unknown _1275822736.unknown _1275822773.unknown _1275822819.unknown _1275822751.unknown _1275822637.unknown _1275822714.unknown _1275822581.unknown _1275811469.unknown _1275812073.unknown _1275812121.unknown _1275822439.unknown _1275822469.unknown _1275812155.unknown _1275812161.unknown _1275812479.unknown _1275812124.unknown _1275812105.unknown _1275812113.unknown _1275812098.unknown _1275811579.unknown _1275811588.unknown _1275811550.unknown _1275811560.unknown _1275810886.unknown _1275811350.unknown _1275811453.unknown _1275810912.unknown _1275810838.unknown _1275810861.unknown _1275810738.unknown _1275805569.unknown _1275810519.unknown _1275810548.unknown _1275810594.unknown _1275810535.unknown _1275805851.unknown _1275806302.unknown _1275806695.unknown _1275806721.unknown _1275806660.unknown _1275805965.unknown _1275805576.unknown _1274863647.unknown _1274876276.unknown _1275052469.unknown _1275110159.unknown _1275053621.unknown _1275052297.unknown _1274964319.unknown _1274863704.unknown _1274863748.unknown _1274864927.unknown _1274863739.unknown _1274863679.unknown _1242634493.unknown _1242716109.unknown _1243335856.unknown _1242636011.unknown _1242629401.unknown _1242631980.unknown _1242632022.unknown _1242632083.unknown _1242631213.unknown _1242631937.unknown _1242631069.unknown _1242629272.unknown _1212170463.unknown _1234567907.unknown _1242376066.unknown _1242459728.unknown _1242570903.unknown _1242458635.unknown _1234567960.unknown _1242368065.unknown _1242374735.unknown _1242375345.unknown _1242368089.unknown _1234567981.unknown _1234567983.unknown _1242367476.unknown _1234567982.unknown _1234567980.unknown _1234567917.unknown _1234567918.unknown _1234567915.unknown _1212209933.unknown _1234567905.unknown _1234567906.unknown _1234567892.unknown _1212172265.unknown _1212173554.unknown _1212173648.unknown _1212209215.unknown _1212172509.unknown _1212170580.unknown _1212171385.unknown _1212170482.unknown _1212133592.unknown _1212143709.unknown _1212147169.unknown _1212151478.unknown _1212152235.unknown _1212151149.unknown _1212147273.unknown _1212146765.unknown _1212146818.unknown _1212146959.unknown _1212144852.unknown _1212142814.unknown _1212143197.unknown _1212143622.unknown _1212143073.unknown _1212142224.unknown _1212130789.unknown _1212131436.unknown _1212132235.unknown _1212130822.unknown _1212128372.unknown _1212130355.unknown _1212126812.unknown _1212128269.unknown _1212127442.unknown _1212126625.unknown _1071353212.unknown _1212045498.unknown _1212062118.unknown _1212123400.unknown _1212126232.unknown _1212126454.unknown _1212123424.unknown _1212123653.unknown _1212062335.unknown _1212123373.unknown _1212062214.unknown _1212061294.unknown _1212062112.unknown _1148998518.unknown _1194332980.unknown _1211963636.unknown _1212041905.unknown _1194349136.unknown _1194349141.unknown _1194349135.unknown _1149316122.unknown _1194154483.unknown _1149015857.unknown _1149015886.unknown _1149015918.unknown _1149015807.unknown _1148712855.unknown _1148712882.unknown _1148911460.unknown _1148712899.unknown _1148712874.unknown _1071353549.unknown _1071353747.unknown _1071353296.unknown _1071353422.unknown _1071350494.unknown _1071352934.unknown _1071353129.unknown _1071353178.unknown _1071353199.unknown _1071352954.unknown _1071353050.unknown _1071352499.unknown _1071352890.unknown _1071352931.unknown _1071352783.unknown _1071352817.unknown _1071352480.unknown _1071350165.unknown _1071350167.unknown _1071350168.unknown _1071350166.unknown _1071350163.unknown _1071350164.unknown _1071350162.unknown