Three-dimensional shapes are mainly classified based on their shape characteristics and the properties of their surfaces. Common ones include cylinders, cones, and spheres.

Matrix multiplication is the operation of creating a new matrix from two matrices according to certain rules. The key requirement is that the number of columns in the left matrix must equal the number of rows in the right matrix; otherwise, you can't calculate it. When calculating, the resulting matrix has the same number of rows as the left matrix and the same number of columns as the right matrix, and each element is obtained by multiplying and then adding the corresponding numbers from the row of the left matrix and the column of the right matrix.

Matrix subtraction requires the two matrices to have exactly the same number of rows and columns. When calculating, you subtract the numbers in corresponding positions one by one to get a new matrix with the same dimensions.

Distance refers to the straight-line length between two points and is a scalar; displacement refers to the actual length of an object's movement path, and it is also a scalar. The main difference is: distance is the shortest path between two points (straight-line distance) and only depends on the starting and ending positions; displacement is the length of the actual path traveled and depends on the movement trajectory.

A time-distance diagram, fully called a "time-distance diagram," is used in urban traffic signal line control and area control systems to coordinate the green light phase gaps of adjacent intersections. Line control is managed by the signal center controller, which oversees the local controllers to keep the system running smoothly.

In math, a 'result' isn't an independent axiomatic concept; it refers to the final number, expression, or state you get after a calculation, derivation, or logical process.

A History of Mathematics' was written by the American math historian Carl Benjamin Boyer and was first published in 1968. In the preface, the author clearly pointed out that the book aims to fill the gap in the field of math history textbooks at the time, especially addressing the lack of systematic textbooks in American higher education.

In math, associativity is when a binary operation on three or more elements gives the same result no matter how you group them (i.e., where the parentheses are placed).

Girolamo Cardano was an all-around scholar of the Italian Renaissance, making important contributions in math, medicine, astrology, and more.

A transversal is a line (or line segment) in mathematics and science that crosses two lines (or line segments) or more at the same time.