The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
毕达哥拉斯定理表明,在直角三角形中,斜边长度的平方等于其他两边长度平方之和。
According to the Law of Sines, in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
根据正弦定律,在任何三角形中,边长与其对边角度正弦值的比值是恒定不变的。
Euler's Theorem asserts that for a connected graph, the number of vertices plus the number of edges minus the number of regions is always 2.
欧拉定理指出在一个连通图中,顶点数加上边数减去区域数始终等于2。
The Fundamental Theorem of Calculus connects the concept of an antiderivative with the area under a curve.
微积分基本定理将原函数的概念与曲线下方的面积联系起来。
The Central Limit Theorem explains that the distribution of sample means will approach a normal distribution as the sample size increases, regardless of the population distribution.
中心极限定理解释了无论总体分布如何,随着样本量增加,样本均值的分布将趋向于正态分布。
The Second Law of Thermodynamics states that the total entropy of an isolated system can only increase over time.
热力学第二定律指出一个孤立系统的总熵随时间只能增加。
The Axiom of Choice is a controversial theorem in set theory which allows one to select exactly one element from each of an infinite collection of non-empty sets.
选择公理是集合论中一个有争议的定理,它允许从无限多个非空集合中各选取一个元素。
The Binomial Theorem describes the algebraic expansion of powers of a binomial.
二项式定理描述了二项式的幂的代数展开式。
Bayes' Theorem provides a way to calculate conditional probabilities by incorporating prior knowledge and evidence.
贝叶斯定理提供了一种通过结合先验知识和证据来计算条件概率的方法。
Noether's Theorem establishes a connection between symmetries in physical laws and conservation principles.
诺特定理建立了物理定律中的对称性与守恒原理之间的联系。
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