Beauty of math - Surfaces

This is going to be a first post about this subject - beauty of math. This one is about algebraic surfaces.

While many people either don't understand or even hate math, I tend to see it's beauty. To be honest I don't understand those who don't see it. While part of this beauty is indeed hidden, and not everyone will see it, a lot of it is pretty obvious. All you need to do is just change your mindset and be ready to receive something new.

In this post I will talk about one of the most obvious examples of math beauty - surfaces. While it may sounds bizarre at first, to understand what I am talking about take a look at this first:

x³ z + x² + yz³ + z⁴ = 3xyz

yz(x²+y-z) = 0

The equations below the images are the functions that create them. You can find more images like these here.

Now after you saw this what do you think? Does it change your attitude to math? I doubt that. If you are reading my blog you probably don't hate math, but what do you think about it?

For me the beauty in these images is their simplicity. It is surprising how such simple equations can describe such elegant surfaces. Moreover this is a general fact about math - physical laws can be written by simple and elegant equations. There is even a humorous story about this fact. Paul Dirac, widely regarded as one of the greatest physicists of all time, was asked once to lecture about philosophy of physics. He simply stood up and wrote on the board - "physical eqautions should have mathematical beauty". In these pictures we see exactly this - simplicity of equations and the complexity of the result.

The next post in this series is: Beauty of Math - Fractals.