Take a=3 as an example:

1. A heart-shaped line is a trajectory formed when a fixed point on a circle rolls around another circle that is tangent to it and has the same radius. It is named because it looks like a heart.

2. The center line is also a kind of loop line. The figure between Mandleberg sets is a heart-shaped line. The English name "Cardioid" of the cardiac line was published by de Castillon in the Journal of Philosophy of the Royal Society in 174 1. It means "like a heart".

Extended data

In mathematics, continuity is an attribute of a function. Intuitively, a continuous function is a function in which the change of the input value is small enough and the change of the output is small enough. If a small change in the input value will cause a sudden jump, or even the output value is uncertain, the function is called a discontinuous function (or discontinuous function).

Let f be a function projected from a subset of a set of real numbers. F is continuous at point C if and only if the following two conditions are met:

F is defined at point C, and C is a convergence point in in. No matter how the independent variable X approaches C in In, the limit of f(x) exists and is equal to f(c). We say that a function is continuous everywhere or everywhere, or if it is continuous at any point in its definition domain, it is simply continuous. More generally, we say that a function is continuous on a subset of its domain, when it is continuous at every point on this subset.

Without the concept of limit, the continuity of real function can also be defined by the following so-called method.

Let's consider the function. Suppose c is an element in the domain of f. The function f is continuous at point C if and only if the following conditions are true:

For any positive real number, there is a positive real number δ >; 0, so for any domain, as long as x satisfies c-δ.