Cartesian coordinates are a math tool used to determine the position of points with numbers, usually referring to the rectangular coordinate system. It was created by the French mathematician Descartes, and the main idea is to link geometric shapes with algebraic equations, making calculations easier.

A degree is a unit used in geometry to measure the size of an angle, symbolized as °. A full circle is divided into 360 equal parts, and each part is defined as 1 degree.

In geometry: if you move a 3D shape relative to a certain plane and it can coincide with itself, that plane is called a plane of symmetry.

Symmetry order (also called symmetry number) refers to the minimum number of times an object or system coincides with itself under operations like rotation, translation, or interval changes. It's usually denoted as n, corresponding to n-fold symmetry.

It refers to a situation where a shape or object has a one-to-one correspondence in size, shape, and arrangement relative to a point, line, or plane. Simply put, it's the regular repetition of similar parts of an object. This concept isn't just used in math and geometry; it's also widely found in physics, philosophy, and art and design. For example, the wings of a butterfly or the structure of a human face are typical examples of symmetrical forms.

An isosceles triangle is a triangle that has at least two equal sides. The two equal sides are called the legs, and the other side is called the base. The angle between the legs is called the vertex angle, and the angles between a leg and the base are called the base angles. When solving related problems, if the problem doesn't specify which side is the leg or the base, you usually need to consider different cases.

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.

An isosceles trapezoid is a special type of trapezoid with equal legs. It's a symmetrical shape, with one pair of opposite sides parallel but not equal, and the other pair not parallel but equal in length. It's a common shape you come across when learning geometry.

René Descartes (also often translated as Descartes) was a French philosopher, mathematician, and physicist born on March 31, 1596, and passed away on February 11, 1650. He's commonly called the 'father of modern science.' His most famous quote is 'I think, therefore I am,' and he also invented the Cartesian coordinate system that we often use in math class.

The 'Cartesian network' in math usually refers to an interconnection network built through the Cartesian product of graphs, not the Cartesian coordinate system itself; the latter is often mistakenly called a 'Cartesian network,' but it's actually a 'Cartesian coordinate grid'.