JavaScript 数学对象备忘单

javascript 数学对象备忘单

javascript 中的 math 对象提供了一组用于执行数学任务的属性和方法。这是 math 对象的综合备忘单。

属性

math 对象有一组常量：

property	description	value (approx.)
math.e	euler's number	2.718
math.ln2	natural logarithm of 2	0.693
math.ln10	natural logarithm of 10	2.302
math.log2e	base 2 logarithm of math.e	1.442
math.log10e	base 10 logarithm of math.e	0.434
math.pi	ratio of a circle's circumference to its diameter	3.14159
math.sqrt1_2	square root of 1/2	0.707
math.sqrt2	square root of 2	1.414

方法

1.舍入方法

method	description	example
math.round(x)	rounds to the nearest integer	math.round(4.5) → 5
math.floor(x)	rounds down to the nearest integer	math.floor(4.7) → 4
math.ceil(x)	rounds up to the nearest integer	math.ceil(4.1) → 5
math.trunc(x)	removes the decimal part (truncates)	math.trunc(4.9) → 4

2.随机数生成

method	description	example
math.random()	generates a random number between 0 and 1 (exclusive)	math.random() → 0.53
custom random int generator	random integer between min and max	math.floor(math.random() * (max - min 1)) min

3.算术方法

method	description	example
math.abs(x)	absolute value	math.abs(-7) → 7
math.pow(x, y)	raises x to the power of y	math.pow(2, 3) → 8
math.sqrt(x)	square root of x	math.sqrt(16) → 4
math.cbrt(x)	cube root of x	math.cbrt(27) → 3
math.hypot(...values)	square root of the sum of squares of arguments	math.hypot(3, 4) → 5

4.指数和对数方法

method	description	example
math.exp(x)	e^x	math.exp(1) → 2.718
math.log(x)	natural logarithm (ln(x))	math.log(10) → 2.302
math.log2(x)	base 2 logarithm of x	math.log2(8) → 3
math.log10(x)	base 10 logarithm of x	math.log10(100) → 2

5.三角函数

method	description	example
math.sin(x)	sine of x (x in radians)	math.sin(math.pi / 2) → 1
math.cos(x)	cosine of x (x in radians)	math.cos(0) → 1
math.tan(x)	tangent of x (x in radians)	math.tan(math.pi / 4) → 1
math.asin(x)	arcsine of x (returns radians)	math.asin(1) → 1.57
math.acos(x)	arccosine of x	math.acos(1) → 0
math.atan(x)	arctangent of x	math.atan(1) → 0.785
math.atan2(y, x)	arctangent of y / x	math.atan2(1, 1) → 0.785

6.最小值、最大值和钳位

method	description	example
math.max(...values)	returns the largest value	math.max(5, 10, 15) → 15
math.min(...values)	returns the smallest value	math.min(5, 10, 15) → 5
custom clamping	restrict a value to a range	math.min(math.max(x, min), max)

7.其他方法

method	description	example
math.sign(x)	returns 1, -1, or 0 based on sign of x	math.sign(-10) → -1
math.fround(x)	nearest 32-bit floating-point number	math.fround(5.5) → 5.5
math.clz32(x)	counts leading zero bits in 32-bit binary	math.clz32(1) → 31

示例

1 到 100 之间的随机整数

const randomint = math.floor(math.random() * 100) + 1;
console.log(randomint);

计算圆面积

const radius = 5;
const area = math.pi * math.pow(radius, 2);
console.log(area); // 78.54

将度数转换为弧度

const degrees = 90;
const radians = degrees * (math.pi / 180);
console.log(radians); // 1.57

找到数组中最大的数字

const nums = [5, 3, 9, 1];
console.log(math.max(...nums)); // 9

数学对象的扩展用例

math 对象有许多实际应用。以下列出了常见场景和示例，以说明如何有效使用它。

1.随机化

生成一个范围内的随机整数

function getrandomint(min, max) {
    return math.floor(math.random() * (max - min + 1)) + min;
}
console.log(getrandomint(1, 10)); // random number between 1 and 10

打乱数组

function shufflearray(arr) {
    return arr.sort(() => math.random() - 0.5);
}
console.log(shufflearray([1, 2, 3, 4, 5])); // shuffled array

模拟掷骰子

function rolldice() {
    return math.floor(math.random() * 6) + 1; // random number between 1 and 6
}
console.log(rolldice());

2.几何和形状

计算圆的面积

const radius = 5;
const area = math.pi * math.pow(radius, 2);
console.log(area); // 78.54

计算三角形的斜边

const a = 3, b = 4;
const hypotenuse = math.hypot(a, b);
console.log(hypotenuse); // 5

将度数转换为弧度

function degreestoradians(degrees) {
    return degrees * (math.pi / 180);
}
console.log(degreestoradians(90)); // 1.57

3.金融与商业

复利公式

function compoundinterest(principal, rate, time, n) {
    return principal * math.pow((1 + rate / n), n * time);
}
console.log(compoundinterest(1000, 0.05, 10, 12)); // $1647.01

四舍五入货币值

const amount = 19.56789;
const rounded = math.round(amount * 100) / 100; // round to 2 decimal places
console.log(rounded); // 19.57

计算折扣

function calculatediscount(price, discount) {
    return math.floor(price * (1 - discount / 100));
}
console.log(calculatediscount(200, 15)); // $170

4.游戏和动画

模拟抛硬币

function cointoss() {
    return math.random() < 0.5 ? 'heads' : 'tails';
}
console.log(cointoss());

平滑动画的缓动函数

function easeoutquad(t) {
    return t * (2 - t); // simple easing function
}
console.log(easeoutquad(0.5)); // 0.75

二维网格中的随机生成坐标

function randomcoordinates(gridsize) {
    const x = math.floor(math.random() * gridsize);
    const y = math.floor(math.random() * gridsize);
    return { x, y };
}
console.log(randomcoordinates(10)); // e.g., {x: 7, y: 2}

5.数据分析

求数组中的最大值和最小值

const scores = [85, 90, 78, 92, 88];
console.log(math.max(...scores)); // 92
console.log(math.min(...scores)); // 78

标准化数据

function normalize(value, min, max) {
    return (value - min) / (max - min);
}
console.log(normalize(75, 0, 100)); // 0.75

6.物理与工程

计算自由落体后的速度

const gravity = 9.8; // m/s^2
const time = 3; // seconds
const velocity = gravity * time;
console.log(velocity); // 29.4 m/s

钟摆周期

function pendulumperiod(length) {
    return 2 * math.pi * math.sqrt(length / 9.8);
}
console.log(pendulumperiod(1)); // 2.006 seconds

7.数字操纵

将数字限制在某个范围内

function clamp(value, min, max) {
    return math.min(math.max(value, min), max);
}
console.log(clamp(15, 10, 20)); // 15
console.log(clamp(5, 10, 20));  // 10

将负数转换为正数

console.log(math.abs(-42)); // 42

查找数字的整数部分

console.log(math.trunc(4.9)); // 4
console.log(math.trunc(-4.9)); // -4

8.解决问题

检查一个数字是否是 2 的幂

function ispoweroftwo(n) {
    return math.log2(n) % 1 === 0;
}
console.log(ispoweroftwo(8)); // true
console.log(ispoweroftwo(10)); // false

生成斐波那契数

function fibonacci(n) {
    const phi = (1 + math.sqrt(5)) / 2;
    return math.round((math.pow(phi, n) - math.pow(-phi, -n)) / math.sqrt(5));
}
console.log(fibonacci(10)); // 55

9.杂项

生成随机颜色 (rgb)

function getrandomcolor() {
    const r = math.floor(math.random() * 256);
    const g = math.floor(math.random() * 256);
    const b = math.floor(math.random() * 256);
    return `rgb(${r}, ${g}, ${b})`;
}
console.log(getrandomcolor()); // e.g., rgb(123, 45, 67)

根据出生日期计算年龄

function calculateAge(birthYear) {
    const currentYear = new Date().getFullYear();
    return currentYear - birthYear;
}
console.log(calculateAge(1990)); // e.g., 34