Implicit equations are relations between two variables. If you insert a value for one variable, you can calculate the value of the other. So the difference to functions is that you don't get the value of the second variable immediately. You first have to calculate it. However implicit equations are still linked very strong to the functions. Actually there is a theorem that says that for every implicit equations, there's an function which describes exactly the same thing. Unfortunately, the theorem just says that this function exists. It doesn't tell us what it looks like or how we could find it. Most of the time it is even so difficult that there's no way to find the corresponding function.
Functions and their graphs
Functions are a very common thing in mathematics. They are a very accurate way to describe the behaviour of various things. Now it is also possible to make graphical representations of functions. Functions with one variable are rather easy to draw. You insert a value in the function and look what results comes out. This gives you the coordinates of a point in a plane.
Functions and equations
Functions and equations
The following functions and equations are in mathematics known under the term cardioid. They got this name because they all have a particular shape, which makes it possible to recognise them very easily. There are mathematicians who studied these mathematical structures. I will present a few of their results to show that mathematics can be much more than a dry and boring subject. Mathematics can even be the most romantic thing on earth.
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