A hypersurface is an n-1 dimensional submanifold in n-dimensional space. Simply put, it's a geometric structure whose dimension is one less than the surrounding space. It's the generalization of lines in a plane and planes in space to higher-dimensional spaces.

The Earth does two kinds of movements every day: one is rotating around its axis, and the other is revolving around the Sun, both moving from west to east. Rotation gives us the alternation of day and night, while revolution brings about the changing seasons.

Multiplication is a shortcut for adding the same number repeatedly. The result is called the product, and the symbol is '×'.

A map is a representation of the Earth's surface on a flat plane, scaled down using symbols according to mathematical rules. It's not just a simple photo, but a geographic model that's been filtered and summarized.

The multiplication table usually refers to the 9x9 multiplication table, which goes from 'one times one equals one' to 'nine times nine equals eighty-one.' It's a basic tool for doing math calculations. It uses the rules of the decimal system to simplify complex multiplication into easy-to-remember rhymes.

A geometric sequence is a sequence where, starting from the second term, each term divided by the previous term equals the same constant, which is called the common ratio, usually denoted by the letter q.

Compass-and-straightedge construction refers to the method of drawing geometric figures using only an unmarked straightedge and a compass, performing a limited number of steps. For example, drawing a line segment equal to a given one is one of its basic applications. This way of constructing shapes originated in ancient Greece and is a classic topic in plane geometry, emphasizing logical rigor and the limitations of the tools.

An equilateral triangle is a triangle where all three sides are of equal length, also called a regular triangle. It's a special kind of isosceles triangle, and all three angles are 60 degrees.

The equator is the circle on the Earth's surface with a latitude of 0°, dividing the Earth into the Southern and Northern Hemispheres, and it's also the longest line of latitude on Earth.

An arithmetic sequence is a sequence where, starting from the second term, the difference between each term and the previous one is the same constant. This fixed difference is called the common difference, usually represented by the letter d. For example, the common odd number sequence 1, 3, 5, 7... has a difference of 2 between each pair of consecutive numbers, which makes it an arithmetic sequence with a common difference of 2.