Bayes' Theorem is a core formula in probability theory that describes the relationship between conditional probabilities. Its essence is using new evidence to dynamically update your initial (prior) belief about a hypothesis, which gives you the updated (posterior) probability. This theorem isn't just the foundation of Bayesian inference in statistics—it’s also widely used in areas like machine learning, medical diagnosis, and spam filtering.

In math, multiples describe the divisibility relationship between integers. If a divided by b equals c, and a, b, and c are all non-zero integers, then a is a multiple of b and c, while b and c are factors of a. It's like a rectangle with an area of 42—if the length and width are natural numbers, 42 is a multiple of both the length and the width.

The Prime Meridian is the 0° longitude line on Earth, located at the old site of the Royal Observatory in Greenwich, London. It was established as the global reference point for longitude and time calculation at the international conference in 1884.

Its core meaning is comparison or contest, and it can also refer to analogy, closeness, or a mathematical ratio.

A ratio is an expression that shows two ratios are equal, and in everyday life, it also refers to the proportion of a part to the whole.

Scale is the ratio of distance on a map to the actual distance. It shows how much the lengths on a map or drawing are reduced (or enlarged), and you need to use the same units when calculating.

Ratios are general multiplicative relationships, while percentages are a special type of ratio with the denominator fixed at 100. The main differences lie in how they're written, the base number, and their use. Both can show quantity relationships, but percentages make it easier to intuitively compare different data.

A proportionality constant is a fixed number in math and physics formulas that links two variables. It's usually represented by the letter k and determines how the variables change in relation to each other or multiply together.

The Pythagorean theorem is the same as the right triangle theorem, which means the sum of the squares of the two legs of a right triangle equals the square of the hypotenuse. The formula is a² + b² = c². This theorem is one of the most basic rules in geometry and is used to calculate the relationship between the sides of a right triangle, playing an important role in both Western and Chinese math history.

The rate of change is basically a measure of how fast something is changing. In math, we often use derivatives to calculate the instantaneous rate of change accurately. In physics, for example, speed is the rate of change of position.