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Mathematical Term	Useful expressions
Introductory Idea acute angle 锐角 right angle 直角 obtuse angle 钝角 perpendicular 垂直 rectangle 矩形 triangle 三角形 parallelogram平行四边形 ray 射线 radius, radii 半径 circle 圆 center of a circle 圆心 circumference圆周 isosceles triangle等腰三角形 isosceles trapezoid 等腰梯形 isomorphism 同构 isometric 等量 monotonic mapping 单射 rational number 有理数 irrational number 无理数 ratio 比 natural number 自然数 integer 整数 real number 实数 imaginary number 虚数 complex number 复数 associative property结合率 commutative property交换率 distributive property分配率 ordinal number序数 cardinal number基数 complementary angle余角 supplementary angle 补角 concentric circles同心圆 concyclic共圆 concave凹 convex凸 bisector平分线 binomial二项式 factor因式 factorial阶乘 fraction分数 prime number素数 poly, bi, semi,多，二，半 triangle三角形 quadrilateral四边形 pentagon五边形 hexagon六边形 septangle七边形 octangle八边形 nonagon九边形 decagon十边形 dodecagon十二边形 braces{ } bracket括弧 Algebra Idea 1-4 is equal to, equals等于 add, minus, times, divide加，减乘，除 sum, difference, product, quotient和，差，积，商 multiple addition of 多重和 equation方程式，等式 definition定义 decrease, increase减少，增加 positive number, negative number正数，负数 successive后续的 exponent, base指数，底数 monomial, binomial, trinomial, polynomial单项式，二项式，三项式，多项式 shaded 有阴影的 represent, identify 表示 construct构造 side边 middle term中间项 is equivalent to 等价于 factoring a trinomial对三项式进行因式分解 top right, bottom left右上，左下 possibility可能性，概率 algebraic expression代数表达式 Algebra Ideas(5-6) algebraic computation代数计算 procedure过程 partition分割 diagram图表 width宽度 reverse相反 contrive发明设计 completing the square完成正方形 Algebra Ideas(7-8) coefficient系数 manipulation操作 scheme计划 incline倾斜 resemble象 strategy策略 Algebra idea of 9 algorithm算法 an automatic procedure 一个自动的过程 Algebra idea of 10 Geometer's Sketchpad program几何画板 Algebra idea of 11-12 sequence数列 consecutive连续的 predecessor前面的 pattern模式 horizontal水平的 general term 通项 geometric interpretation几何解释 Algebra Idea 13-14 parabola抛物线 abscissa横坐标 ordinate纵坐标 segment段 intersect相交 accuracy精确性 slope斜率 literal字面上的 cancellation取消 reduction约分 numerator分子 denominator分母 two-digit number两位数 Algebra Idea 15－16 nonpositive非正数 arithmetic算术 demonstration示范 weird不可思议的 reciprocal倒数 contradiction矛盾 clockwise 顺时针的 anticlockwise逆时针的 Algebra Idea 17－18 abstract concept抽象概念 domain定义域 range值域 element元素 mapping映射 an onto function 满射 a one-to-one function 单射 a one-to-one onto function/a one-to-one correspondence 满单射/一一对应 digit数字 quartic equation四次方程 Algebra idea 19－20 rationale基本原理 derivation导出 uncanny离奇的 hindrance障碍 digress离题 apportion分配 ALGEBRA IDEA 21-22 triangular 三个的 equilateral等边的 notation符号 inductively 归纳地 quadratic equation二次方程 formula公式 rate比率 ratio比 proportion比例 geometric mean几何平均数 harmonic mean调和平均数 weighted mean加权平均数 focus聚点 directrix准线 hyperbola双曲线 Algebra Idea 25-26 envelope包络 constitute组成 tangent切线 curve曲线 reveal揭示 foci焦距 bulletin board公告牌 conic圆锥的 locus轨迹 intersection交集 justification理由 analogy类似 converse theorem逆定理 Algebra Idea 27-28 concentric同中心的 a pair of compasses圆规 accompanying figure附图 initial初始的 consistent相容的 Algebra Idea 29-30 summing a series of powers幂级数求和 derive导出 expansion展开式 substitute into代入 Algebra Idea 29－30 Indicated显示 Algebra idea 32－33 Diophantus 丢番图 compound interest复利 interest rate利率 arithmetic mean算术平均数 tripling 三倍 quadrupling四倍 k-tupling k倍 Algebra idea 34 parametric equation参数方程 Pythagorean triples毕达哥拉斯三元数组 prominence突出 primitive triples 最原始的三元数组 hypotenuse斜边 Algebra idea 35 induction归纳 summation和 hypothesis假设 simultaneously同时 Geometry idea 1 vertex顶点 tantamount等价 midpoint中点 Geometry idea 2-3 triangulate分成三角形 overlap重合 diagonal对角线 endpoint端点 Geometry idea 4-5 supplementary angle互补角 triangle inequality三角不等式 Geometry idea 6 discriminate 不一般的 crosshatch以交叉线作阴影 unencumbered不受妨碍的 inscribed内接的 circumscribe外接圆 intuitively直观地 Geometry idea 7 heed注意 scalene triangle 不等边三角形 fallacy谬论 diameter直径 hinge关键 paradox自相矛盾的话 violation违背 isosceles triangle等腰三角形 equilateral triangle 等边三角形 Geometry idea 8－9 congruent全等 parallelepiped平行六面体 rhombus菱形 Geometry idea 12-13 Pythagorean theorem勾股定理 affixed 粘 chord 弦 secant割线 Geometry idea 14 -15 intercept截取 arc弧 motivate激发 fruitful多产的 perpendicularity垂直 frustration挫折 Geometry idea 17 straightedge直尺 Geometry idea 18-19 circumscribed外接的 altitude高 median中线 centroid质心 symmetric相称的 scale刻度，比例尺 trisect三等分 Geometry Idea 21 prevalent 流行的，盛行的，普遍的 knot 节，打节 pentagram 五角星型 analogue 类似物 interlink 把。。。连接起来 GEOMETRY IDEA 22-23 cylindrical圆柱的 conjecture猜想，推测 approximation近似值 cubit腕尺 decimal小数 perimeter周长 protractor量角器 Geometry Idea 24－25 linear measures长度单位 area measures面积单位 similitude相似 semicircle半圆 caution小心 GEOMETRY IDEA26－27 invariant不变量 distort 弯曲 auxiliary line 辅助线 uniqueness唯一性 Geometry Idea 28－29 toothpick牙签 summand被加数 prediction预言 respectively依次地 intuitive 直觉的 Trigonometry Idea 2 the law of sines 正弦定理 drill操练 concise简明的 maximized最大化的 Trigonometry Idea 3－4 relegate 将…归于 excursion 偏离 Trigonometry Idea 5-6 Ptolemy's Theorem托勒密定理 trigonometric identities三角恒等式 cyclic quadrilateral圆内接四边形 label标签 the law of cosines余弦定理 Trigonometry Idea 9-10 inscribed angle圆周角	add 1 to both sides of the equation by adding 1 to both sides of the equation by multiplying both sides of the equation by 2 most likely, least likely the nth power of a, a to n a rectangle with length 1 and width 2 x², x square, x³, x cube relating the resulting trinomial to these factors by distributing the first binomial over the terms of the second binomial to split the middle term into two terms be adept at factoring divide the ellipse in half , partition the ellipse into four regions By subtracting these two equations The vertical line segment cuts a piece off region Q Make conjectures about acute-angled triangle adjacent angle 邻角 adjacent side alternate angle corresponding angles 对应角 corresponding sides angles at a point angle at the centre angle at the circumference angle bisector Angle of intersection angle of rotation angle sum of a triangle axis of rotation arc length axis of symmetry axis of parabola base angle central line centre of gravity chord of contact circle, circular, circular measure Circumcentre, circumcircle, circumscribed circle, circumference, circumradius collinear, collinear planes common tangent compasses construction concentric circles concurrent Concyclic points congruence congruent triangles cuboid Mathematical induction a/b a over b 1/2 a half, one over two 1/3 a third, one over three 1/4 a quarter, one fourth 1/5 one fifth 1/10 one tenth 1/25 one twenty-fifth 1/100 one hundredth 125/1000 one hundred and twenty five thousandths 2+1/2 two and a half 1/b the reciprocal of b 0.2 O point two, zero point two, point two, nought point two 0.75 nought point seventy-five, point seven five 1.15 one point one five 12.707 twelve point seven O seven 4.999… four point nine recurring 3.032626… three point O three two six, two six recurring ( ) round brackets [ ] square brackets { } braces x->∞ x approaches infinity a:b the ratio of a to b 5² 5 square, 5 to the second power, 5 raised to the second power, 5 to the second 2^－10 2 to the minus tenth the square root of a the fifth root of a square a to the m by n-th is the n-th root of a to the m-th power y=f(x) y is a function of x Non-empty set aεA a belongs to set A, a is a number of set A set A is included in set B set A contains set B intersection of sets A and B union of sets A and B there is / there exists an x such that for all / every x A function f from S to T, where S and T are non-empty sets, is a rule that associates with each element of S a unique element of T. Thus it is the same thing as a mapping. The notation f: S->T, read as “f from S to T”. If xεS, then f(x) is the image of x under f. When x=a, f(a) is the corresponding value of the function. Mathematical induction Let there be associated, with each positive integer n, a proposition P(n), which is either true or false. If P(1) is true For all k, P(k) implies P(k+1) Then P(n) is true for all positive integers n. A modified form of the principle is …… P(n0) is true For all k>=n0, P(k) implies P(k+1) ……. rise / drop Assign a number The ratio of A to B uphill / downhill a diameter of length 1 the side opposite ..(an angle) square both sides of ..